TW505793B

TW505793B - Autonomous phase-gain rotation/linear piezoelectric optimal sensing device

Info

Publication number: TW505793B
Application number: TW88117301A
Authority: TW
Inventors: Shr-Guang Lee; Yu-Shiang Shiu
Original assignee: Shr-Guang Lee
Priority date: 1999-10-07
Filing date: 1999-10-07
Publication date: 2002-10-11

Abstract

A novel series of autonomous phase-gain rotation/linear piezoelectric optimal sensing (APROPOS) devices, designed on a sensor structure and constructed by using the advantage of piezoelectric distributed-sensor and the incorporation of the interface circuit, is disclosed in the present invention. Several different series of APROPOS devices are proposed in the present invention. By ingeniously using the design of piezoelectric thin film, the sensor structure characteristic, the feedback control theory, the wave transmission theory, the integration of boundary conditions and the application of interface circuit, a series of vibration sensing apparatus with the filtering and frequency selection characteristics of high pass, low-pass, band-pass and band-obstruction are designed. For the point-type sensor, the applicable bandwidth of the sensor can be effectively increased. Due to its type difference and characteristic difference, the series of vibration sensing apparatus proposed in the invention can be evolved to form different kinds of vibration sensing apparatus so as to raise the applicable range of the vibration sensing apparatus. In the invention, the design method of distributed sensor is ingeniously used in the structure of point-type sensor itself such that a novel autonomous phase-gain rotation/linear piezoelectric optimal sensing device is designed. Thus, an innovative point-type vibration sensing apparatus having the convenience characteristic of point type sensor as well as even bigger freedom and wider application range than the conventional sensor structure can be created by only one time of design for the sensor structure body.

Description

505793 五、發明說明（Ο 發明領域：本發明係有關為一系列之創新增益函數但相位可分立設# 之振動檢測裝置（Autonomous Phase - gain505793 V. Description of the invention (0 Field of the invention: The present invention relates to a series of innovative gain functions, but the phase can be set separately for the vibration detection device (Autonomous Phase-gain

Rotat i on/1i near Piezoelectric Optimal Sensing device，簡稱APROPOS device)，此一系列新發明的振動檢測裝置，在任何具有彎曲效應且感應子本體結構」用四次本構方程式（government equation)來表示者皆^p J 力隹用。並對，各種結構的邊界條件，或結構本身的結構" 如阻尼專，皆可應用在這一糸列的新式振動檢測裝置且再結合電子電路及迴授控制系統，更可完成一系歹，2 ’ 波選頻特性之全新的低通、帶通、高通及帶不通等多具據重要創見之振動檢測裝置。 > 項具發明背景：號此Rotat i on / 1i near Piezoelectric Optimal Sensing device (referred to as APROPOS device), this series of newly invented vibration detection devices, which has a bending effect and inductive sub-body structure "is represented by a fourth-order constitutive equation (government equation) ^ P J It's used. In addition, the boundary conditions of various structures, or the structure of the structure itself, such as damping, can be applied to this series of new vibration detection devices, combined with electronic circuits and feedback control systems, can complete a series of systems, 2 'The new low-pass, band-pass, high-pass, and band-non-pass vibration detection devices with new and important insights. > Item Background: No. This

傳統的點式感應子最主要是置測特定一點的振動ι 外也可以利用改變感應子結構的形狀或型態來量消】-The traditional point type inductor is mainly used to measure the vibration of a specific point. In addition, it can also be eliminated by changing the shape or shape of the inductor structure.-

定軸向的振動訊號，再由於其不受待測結構物特性某特響，因此使用範圍非常的廣泛且容易。以傳統上=影電感應子為例，其往往受到感應子的結構特性影響點式壓使其可應用頻寬有所限制，若如傳統濾波方式了 & ’因而設備進行濾波，則將會改變感應子的頻率響應特彳生用電子降似The vibration signal in the fixed axial direction, because it is not affected by the characteristics of the structure to be measured, is very wide and easy to use. Taking the traditional = video electric inductor as an example, it is often affected by the structural characteristics of the inductor. The point pressure makes its applicable bandwidth limited. If the traditional filtering method & 'so the device filters, it will Changing the frequency response of the inductor

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505793 五、發明說明（2) 其功能。值得注思的疋點式感應子只能置測取得被測體上單點的結構特性，並不能直接表現出整個結構物的動態特性曲線。但是當量測範圍極廣泛時，所需使用的點式感應子數量相對地也會增多，這些大量的振動訊號也將會造成訊號處理上的困難，而使得即時控制（r e a 1 t i m e contro 1 )變得困難與複雜。相形之下，自從均佈减應子 (distributed sensor)的理論於一九八〇年***始蓬勃發展後，即已清楚指出如何可藉由不同的表面電極形狀及電極極化方向來設計甚至控制感應子的可用頻寬 (bandwidth)。且因為電極在空間上為連續分佈，因此除了可以量測被測結構的整體振動資訊外，更可以用來量測結構上的均佈力。但因為均佈型感應子需要隨著被測體結構而重新設計，所以其應用範圍多僅限於特殊結構上，較 =易被推廣應用到各種多樣之結構上，此一缺憾即是使均 <式感應子發展至今仍無法像點式感應子那樣的被廣泛而容易應用之主因。 $ ^明所提δ又计架構乃是以中華民國專利申請案8 8丨丨3 5 9 i ^ ί ί發點’藉由結構振動模態正交特性及波傳理論，利 $態感應子與空間濾波器等均佈型感應子基本架構為出 ^點1來設計增益函數但相位可分立設計之振動檢測裝。亚引入回授控制理論來調整各種不同種類的增益函數 :相位可分立没計之振動檢測裝置的頻率響應，以提高本二，之振動檢測裝置本身的應用範圍及性能。此新發明之幽數但相位可分立設計之振動檢測裝置，其本身可為 505793 五、發明說明（3) 一點式感應子，設置在一待測結構物上，量測外來振動的特性，為一種增益函數但相位可分立設計之一選頻點式量測之檢測裝置，亦可設置在一柔性結構上，量測結構上某量測點之結構特性，是為一種增益函數但相位可分立設計之一柔性結構選頻量測之檢測裝置。壓電性質（piezoelectric)是一種具機械能與電能交互作用的材料，在西元1880年由居禮兄弟（Pierre Curie及 Jacques Curie)所發現，這種因變形而產生電極化 (electrical p〇larizati〇n)現象的材料特性定名為壓電性。一具有壓電性的材料受力後產生形變，此變形的能量會由電極化的過程轉換成電能，反之亦然。本發明驗證實施例效能時所採用的聚偏二氟乙烯（pVF2，505793 V. Description of the invention (2) Its function. It is worth noting that the puppet-type inductor can only obtain the structural characteristics of a single point on the object under test, and cannot directly show the dynamic characteristic curve of the entire structure. However, when the measurement range is extremely wide, the number of point sensors needed to be used will also increase. These large vibration signals will also cause difficulties in signal processing and make real-time control (rea 1 time contro 1). It becomes difficult and complicated. In contrast, since the theory of distributed sensors began to flourish in the 1980s, it has been clearly pointed out how to design and even control the induction through different surface electrode shapes and electrode polarization directions. The available bandwidth of the child. And because the electrodes are continuously distributed in space, in addition to measuring the overall vibration information of the structure under test, it can also be used to measure the uniform force on the structure. But because the uniformly distributed inductor needs to be redesigned with the structure of the measured body, its application range is mostly limited to special structures, which is easy to be promoted and applied to a variety of structures. This shortcoming is that ; The main reason for the development of the type inductor is still not as widespread and easy to apply as the point type inductor. The structure of δ mentioned by Ming is based on the patent application of the Republic of China 8 8 丨丨 3 5 9 i ^ ί The point of origin is based on the orthogonal characteristics of the vibrational modes of the structure and the wave propagation theory, which will benefit the $ state inductor. The basic structure of uniformly distributed inductors such as the space filter is a vibration detection device with a gain function of ^ 1 to design a discrete phase. Asia introduces feedback control theory to adjust various different types of gain functions: the frequency response of a vibration detection device with discrete phases can be improved to improve the application range and performance of the vibration detection device itself. This newly invented vibration detection device with discrete phase design can itself be 505793 V. Description of the invention (3) One-point inductor is set on a structure to be measured, and the characteristics of external vibration are measured as A detection function of a frequency-selective point-type measurement device with a gain function but a discrete phase design can also be provided on a flexible structure. The structure characteristic of a measurement point on the structure is a gain function but the phases can be separated. Design of a flexible structure frequency selective measurement detection device. Piezoelectricity is a material that interacts with mechanical energy and electrical energy. It was discovered in 1880 by the brothers Pierre Curie and Jacques Curie that this kind of deformation caused electrical polarization (electrical polarization). n) The material property of the phenomenon is named piezoelectricity. A piezoelectric material undergoes deformation when subjected to a force, and the energy of this deformation is converted into electrical energy by the process of electrodeposition, and vice versa. The polyvinylidene fluoride (pVF2,

Polyvinyl i dene Fluoride)為一常用的壓電感應子材料。 PVF2是個擁有良好彈性的高分子聚合物，可承受拉力及壓力，且擁有極高的壓電常數，故為一良好之感應子材料。又壓電材料的壓電性具有互補特性（recipr〇cal relationship)，任何型式的壓電感應子，若以電壓輸入即可製作成為與感應子具互補特性的致動器、，本發明利用此一互補特性來建構增益函數但相位可分立設計之動k測舣置中感應子結構的迴授控制系統。雖然本發明所提之實施例均以壓電聚合物pvF2為基本感應 =材料丄但本發明所提出的各種創新設計之振動檢測裝木構’貫可適用於所有的壓電材料及各種壓電感應子掣程，故僅修改所使用之壓電感應子材料或修改製程，實不Polyvinyl i dene Fluoride) is a commonly used piezoelectric inductor material. PVF2 is a high-molecular polymer with good elasticity, can withstand tensile and compressive forces, and has a very high piezoelectric constant, so it is a good inductive material. In addition, the piezoelectricity of piezoelectric materials has a complementary relationship (reciprcal relationship). Any type of piezoelectric inductor can be made into an actuator with complementary characteristics to the inductor if a voltage is input. The present invention uses this A feedback control system for constructing a gain function but a phase-discrete design of a dynamic k-measurement center inductive substructure with complementary characteristics. Although the embodiments mentioned in the present invention all use piezoelectric polymer pvF2 as the basic induction = material, the various innovative design vibration detection equipment wooden structures proposed by the present invention can be applied to all piezoelectric materials and various piezoelectric materials. Inductor triggering process, so only modify the piezoelectric inductor material used or modify the process, it is not

505793505793

五、發明說明（4) 脫本發明創新範疇，仍應視為屬於本發明的發明範圍。易言之，本發明中之幾項說明，應視為閣述本專利案之臭本創新架構與方法，不論是何種壓電材料，或以何種製^取得’均應視為本發明保護之範圍。發明概述：延1中華民國專利申請案88 1 1 35 9 1的基本創新理念，本明k出一系列的創新增益函數但相位可分立設 ^ 譽測裝置，利用這一系列新發展之設計方法，發展出^種^ 同種類之振動檢測裝置，同時並提出如何以這些動榀測凌置父互組合以組成各種不同特性的振動檢測裝置。在以下說明中，本發明係將先以懸臂樑為例進行^ 明，再討論不同的振動檢測裝置本體結構設計及邊界條的應用，配合上壓電感應元件界面電路，乃可據以設一系列不同的增益函數但相位可分立設計之振動檢測裝置’、他如自由自由樑（free-free beam)和固定—固定標 (f ixed f i xed beam)等可用四階本體結構方程式表示皆應屬於本發明的範圍。V. Description of the invention (4) Deviating from the scope of the invention of the invention, it should still be regarded as belonging to the scope of the invention of the invention. In other words, several descriptions in the present invention should be regarded as describing the novel innovative structure and method of this patent case. No matter what kind of piezoelectric material or method is used to obtain the invention, The scope of protection. Summary of the Invention: Following the basic innovation concept of the Republic of China patent application 88 1 1 35 9 1, Ben Ming has developed a series of innovative gain functions but phases can be set separately. Reputation measurement devices, using this series of newly developed design methods Develop different kinds of vibration detection devices of the same kind, and propose how to use these dynamic detection devices to form a vibration detection device with various characteristics. In the following description, the present invention will be described by taking a cantilever beam as an example, and then discussing the structural design of the body of the different vibration detection device and the application of the boundary bar. A series of vibration detection devices with different gain functions but separate phases are designed, and other forms such as free-free beams and fixed fi xed beams can be represented by fourth-order body structure equations. The scope of the invention.

以下說明壓電薄層本構方The piezoelectric thin layer constitutive method is explained below

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505793 五、發明說明（5) TP = chekpEk A = eiqSq^ Ek 或，（3) (4) SP=slqTq + dkpEk A = diqTq+^l Ek 其中i， j， k =1〜3，p， q = 1〜6，Tp、 Sq分別為應力及應變，Ek為電場強度，比是電位移，Cpq、 ε ^、 spq = 、ekp 、dip則分別表示彈性勁度矩陣（elast ic stiffness matrix)、介電常數矩陣（permittivity matrix)、彈性柔度矩陣（eiastic compliance matrix)、壓電應力常數矩陣（piezoelectric stress matrix)，以及壓電應變常數矩陣（piezoelectric strain matrix)。上述標號乃依據美國電子電機協會所訂定之符號（I EEE compact matrix notation)予以定義〇由南斯定律求得經由壓電表面電極所量取到的訊號為： q(t) = \Dda ,(5) 由壓電本構方程式出發，配合上壓電感應子元件所附著的感應子結構本體之變型與應變關係即可取得壓電感應子方程式。以感應子結構本體為同時具有面内應變（i η - p 1 a n e strain)及面外應變（〇ut-of〜plane strain)之二維平坦薄層為例，壓電感應子元件之壓電薄層感應子方程式可以505793 V. Description of the invention (5) TP = chekpEk A = eiqSq ^ Ek or (3) (4) SP = slqTq + dkpEk A = diqTq + ^ l Ek where i, j, k = 1 ~ 3, p, q = 1 ~ 6, Tp, Sq are stress and strain, Ek is electric field strength, ratio is electric displacement, Cpq, ε ^, spq =, ekp, dip respectively represent elastic stiffness matrix (elast ic stiffness matrix), dielectric A permittivity matrix, an elastic compliance matrix, a piezoelectric stress constant matrix, and a piezoelectric strain constant matrix. The above symbols are defined according to the symbol (I EEE compact matrix notation) set by the American Electrical and Mechanical Association. The signal measured by the piezoelectric surface electrode obtained from Nance's law is: q (t) = \ Dda, ( 5) Starting from the piezoelectric constitutive equation, the piezoelectric inductor equation can be obtained by combining the deformation and strain relationship of the inductor substructure body to which the piezoelectric inductor element is attached. Taking the inductive substructure body as a two-dimensional flat thin layer with both in-plane strain (i η-p 1 ane strain) and out-of-plane strain (〇ut-of ~ plane strain) as an example, the piezoelectricity of the piezoelectric inductive element The thin-layer inductor equation can

505793 五、發明說明（6) 表示成： •Jit 12) δκ diln 0V〇 ^31 + e32 + e36 ί气卜叫· 1办 Θκ ) dxdy d2\\ —ψ + 2c 3z 5y2 -31 02W &1" d2\v dKy dxdy 其中式（6 )之第一部份代^ 變（in-plane strain)造 j 壓電感應子本體結構中面造成之反應。若考慮壓電感應子本體結板，則式（6 )可簡化為：^Λ〇 = ~ζΙ jFF〇 s 假設一維的尤拉樑只有X 4 移只和X，t有關，即W = W ( d2w 良壓電感成之反應外應變（構為僅7 ，（6) 應子本體結構中面内應，式（6 )之第二部份代表 ou of-plane strain 受面外應變之二維薄 36 d2w dxdy505793 V. Description of the invention (6) is expressed as: • Jit 12) δκ diln 0V〇 ^ 31 + e32 + e36 ί Qi Biao · 1 office Θκ) dxdy d2 \\ —ψ + 2c 3z 5y2 -31 02W & 1 & quot d2 \ v dKy dxdy where the first part of formula (6) substitutes the in-plane strain to create the response caused by the midplane of the piezoelectric inductor body structure. If the piezoelectric inductor body junction plate is considered, the formula (6) can be simplified as: ^ Λ〇 = ~ ζΙ jFF〇s Assume that the one-dimensional Euler beam has only X 4 and X and t are related, that is, W = W (d2w response to external strain caused by a good voltage inductor (constructed to be only 7), (6) should be in-plane in the body structure, the second part of formula (6) represents ou of-plane strain Dimensions thin 36 d2w dxdy

〖由方向之 X， t) ， I 位：曲式彎下則成，化義簡意可有式形6) 變Κ q{t) = -zQe?.^g(x)^dx 在式（8)中， bn-W2 ,(9) 式（9 )即為有效表面電極€ 電極分佈的函數，而Pi ( X，與b分別表示感應子的長2 感應子結構，皆可應用為，（8) Ϊ勺形狀， y)即代 £和寬度本發明户 T# ί 面，表度效強有化為極 y)的 X，向 FC方中 1 3 I e 其表的設假述上合符何任構結子應感之 -\6T 設〖From the direction of X, t), I position: It is formed by bending down, and the simplified meaning can have the form 6) Change Κ q {t) = -zQe?. ^ G (x) ^ dx in the formula ( In 8), bn-W2, (9) Equation (9) is a function of the electrode distribution of the effective surface electrode, and Pi (X, and b respectively represent the length of the inductor 2 and the inductor structure can be applied as, ( 8) The shape of the spoon, y) is the width and width of the T # ί face of the present invention, which is effectively expressed as X, which is 1 3 I e in the FC side. Fu Heren's Constructor Should Feel-\ 6T Design

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i 505793 五、發明說明（7) 一阻尼為R之一維尤拉樑的統御方程式（governi ng equation)可以表示成下式·· dxA dtdx2 dt2 ，（ 1 0 ) 其中E I為勁度常數；A為結構之截面積；p為密度。其彎曲位移W ( X，t)的解有兩種表示法，其一為符合邊界條件的模態展開式（normal mode expansion)，李世光（C.K.i 505793 5. Description of the invention (7) The governing equation of a Viyula beam with damping of one of R can be expressed as the following formula: dxA dtdx2 dt2, (1 0) where EI is the stiffness constant; A Is the cross-sectional area of the structure; p is the density. The solution of its bending displacement W (X, t) has two representations. One is the normal mode expansion that meets the boundary conditions. Li Shiguang (C.K.

Lee)於其1987年的美國康乃爾大學博士論文 ,f Piezoelectric Laminates for Tort ional and Bending Modal Control: Theory and Experiment” 提出這種均佈型感應子的理念，另一為在無限域上表示之波傳的特徵多Lee) in his 1987 doctoral dissertation of Cornell University, f Piezoelectric Laminates for Tortional and Bending Modal Control: Theory and Experiment "proposed this idea of uniformly distributed inductors, and the other is the wave expressed in the infinite domain Many features

Miller， S. A· Collins and S· P· Peltzman 在1990 年於美國航空與太空協會（A I AA)所發表·的論文（A I AA編號 ΑΙΑΑ-90-1127-cp) "Development of SpatiallyMiller, S. A. Collins and S. P. Peltzman, 1990 paper published by the American Aeronautics and Space Association (A I AA) (A I AA number ΑΙΑΑ-90-1127-cp) " Development of Spatially

Convolving Sensors for Structural Control Appl i cat ions”中提出這種空間型濾波器的理念，這兩種解即為構成本發明之多項發明之最基本的設計工具，其中模悲展開即為模態感應子的設計基礎，其最根本的想法就是利用模態的正交特性來設計感應子，而利用波傳的特徵多項式展開之設計理念即為空間濾波器的根本思路，應用這兩種設計方法理念皆可以提高增益函數但相位可分立設計之振動檢測裝置的可用頻寬，如第1圖的曲線丨2為將本發明所提之空間濾波器引入感應子結構所得的頻寬響應曲"Convolving Sensors for Structural Control Appl i cat ions" put forward the concept of such a spatial filter, these two solutions are the most basic design tools constituting a number of inventions of the present invention, of which modal expansion is the modal inductor The most fundamental idea of the design is to use the orthogonal characteristics of the modal to design the inductor. The design concept of using wave propagation characteristic polynomial expansion is the basic idea of the spatial filter. The available bandwidth of a vibration detection device that can increase the gain function but have a discrete phase design, as shown in the curve in Figure 1 and 2 is the bandwidth response curve obtained by introducing the spatial filter of the present invention into the induction substructure.

第11頁 505793 五、發明說明（8)Page 11 505793 V. Description of the invention (8)

線，由圖中所示可以知道其可用頻寬1 5比單純的感應子結構特性1 1的可用頻寬1 4高了許多，而第1圖的曲線1 6與1 7 則分別表示在加入如曲線1 3的空間濾波器或傳統電子式濾波器時其對原本感應子結構系統相位的影響。由第1圖之曲線1 6可以知道利用本發明所提出之將空間濾波器架構引入點式感應子中，將有可能不會像一般的電子式濾波器隨著對系統增益的影響，遵循因果率來影響整個系統的相位，第2圖的曲線2 2為應用模態感應子於點式感應子的效應，可明顯的看出藉由消除第一模態的效應，其可用頻寬 24比原感應子結構特性2 1所可容許的可用頻寬2 3高出許多，值得注意的乃是此次所選的兩種方法皆具有可調整感應子結構系統增益響應函數，且有可能不遵循如傳統電子濾波器所需依循的因果率來調整相位，其中之一特例即是有可能在不造成感應子系統相位移動的情形下調整系統增益之頻率響應特性。這兩大類壓電感應子於振動檢測裝置之各種架構及其設計理念將會詳細陳述於後。以下說明本發明所採用的空間濾波器：As shown in the figure, it can be known that the available bandwidth 15 is much higher than the available bandwidth 14 of the pure inductive sub-structure characteristic 1 1. The curves 16 and 17 in Figure 1 indicate that For example, the effect of the spatial filter of curve 13 or the traditional electronic filter on the phase of the original inductive substructure system. It can be known from the curve 16 in FIG. 1 that the spatial filter architecture introduced into the point inductor by using the present invention may not follow the cause and effect as the general electronic filter will affect the system gain. Rate to affect the phase of the entire system. The curve 22 in Figure 2 is the effect of applying the modal inductor to the point inductor. It can be clearly seen that by eliminating the effect of the first mode, its available bandwidth is 24 ratios. The permissible available bandwidth of the original substructure 2 1 is much higher than 2 3. It is worth noting that the two methods selected this time have adjustable gain response functions of the system of the substructure and may not follow For example, the traditional electronic filter needs to follow the cause-effect ratio to adjust the phase. One special case is that it is possible to adjust the frequency response characteristic of the system gain without causing the phase shift of the induction subsystem. The various architectures and design concepts of these two types of piezoelectric inductors in vibration detection devices will be described in detail later. The following describes the spatial filter used in the present invention:

假設傳入感應子結構的波為時間簡譜震逯，即 w(x，t)=w(x)ejcdt，其中 j二（-1)-1/2，所以在式（10)中，其波數域k和頻率域ω有下列之頻散關係（d i s p e r s i ο η relationship) · 2ΕΓ 2EI ~ , (11)Assume that the wave introduced into the inductive substructure is a time-spectrum shock, that is w (x, t) = w (x) ejcdt, where j is two (-1) -1/2, so in equation (10), its wave The number domain k and frequency domain ω have the following dispersion relationship (dispersi ο η relationship) · 2ΕΓ 2EI ~, (11)

第12頁 505793 五、發明說明（9) 若R2<4EI p A則波數k可以表示成： k = kR-j k丨，（12) 其中 kR=^-(l~-R2 /SEIpAf2 t ▲ ，= -(i?2/8£/p4)1/2 且C0 =(EI/ p A)1/2。因此若以波傳的特徵多’二13) 結構的彎曲位移進行波傳模態展開可得'夕J、式對感應子 w(x^ t) = [yi^ipeukR^k!)x + wiee(kR^Jks)x ❿ + we~J〇kR~kl)x + w e^(kR^)xi^ ^ re Jo 其中，Wrp分別表示為向左及向右的傳，（14) 的振幅，Wle，Wre分別表示為向左及;;右m叫 μ構的邊界條件不同而異，而這四種油 3奴加4 徑/皮將是本發明之增益细數但相位可分立設計之振動檢測装 4农1的重要的基礎工具之一’以下將有詳盡的說明。把（1 4)式代入第（8 )式中，並忽略麻早古和4 一丄合丨且尼的效應，則壓電感應千方程式可改寫成：自式（15)可看出空間濾波器 ’（15) 來將右丄今币丄 ^ 卜^就疋利用波傳的四個模態 A將有政電極進行特殊轉換，本發明所裎々^ 4與是在益限士七l 4 a . 麵1之波的傳遞貫 &甘…限域上討論，但如式（丨5 ) 有限的，也,、，）所不，可知結構本體是為解決此一 ϋ:異性；本發明引隹 k θ Μ進窗函數的觀念， 505793 五、發明說明（ίο) F · J · H a r r i s於1 9 7 8年在國際電子電機工程師協會的期刊 (Proceedings of the IEEE， Vol. 66， No· 1， January 1978， ρρ·51-83)所發表的 ’’〇η the Use of Windows forPage 12 505793 V. Description of the invention (9) If R2 < 4EI p A, then the wave number k can be expressed as: k = kR-j k 丨, (12) where kR = ^-(l ~ -R2 / SEIpAf2 t ▲ , =-(I? 2/8 £ / p4) 1/2 and C0 = (EI / p A) 1/2. Therefore, if the bending displacement of the structure is more than two, the wave propagation mode is used for the wave propagation mode. Expanding to get 'xi J, the formula pair w (x ^ t) = (yi ^ ipeukR ^ k!) X + wiee (kR ^ Jks) x ❿ + we ~ J〇kR ~ kl) x + we ^ ( kR ^) xi ^ ^ re Jo where Wrp is expressed as a leftward and rightward pass, the amplitude of (14), Wle, Wre are expressed as leftward and right respectively; the right m is called μ-structural boundary conditions are different and different These four types of oil, three and four diameters / skins will be one of the important basic tools for the vibration detection device of the present invention, which has a fine gain but a phase-separate design. The detailed description will be given below. Substituting equation (1 4) into equation (8), and ignoring the effects of Ma Zaogu and 4i, the piezoelectric induction thousand equation can be rewritten as: From (15), the spatial filter can be seen '(15) Come to the right of today's coin 丄 ^ ^ ^ 疋 use the four modal A wave to make special conversion of the political electrode, ^ ^ 4 in the present invention and is in the limit of the 7th l 4 a The transmission of the wave of plane 1 is discussed in the limited region, but as the formula (丨 5) is limited, also ,,,), it can be seen that the structural ontology is to solve this problem: the opposite sex; the present invention cited The concept of 进 k θ Μ window function, 505793 V. Description of invention (ίο) F · J · Harris in the Journal of the International Association of Electrical and Mechanical Engineers (Proceedings of the IEEE, Vol. 66, No. 1, January 1978, ρρ51-83), `` 〇η the Use of Windows for

Harmonic Analysis with The Discrete Fourier Transform” 對窗函數的效應有詳細的討論，利用Harris 的觀念可以看出，在表面電極之方程式上再乘上一個窗函數h (X )，此窗函數h ( X)在結構本體内有值，而在結構本體外則為零值函數，如此乃可使波傳遞的表現形式自有限之結構本體轉化為在無限域上表現，再應用拉普拉斯轉換表為設計工具進一步挑選適合的窗函數，也就是說選擇Η ^ ,/(λ：)= h{xy^{x)y^mI ，（ 1 6 ) 其中Wml為一常數值。綜合言之，式（15)中之每一個波傳常數的相對應項都可以下式總合： ' ，（17) 其中s=jk、-：ik、k、-k，而f(x)為經過窗函數修正過之可於無限域中適用之有效表面電極的函數。 σHarmonic Analysis with The Discrete Fourier Transform "has a detailed discussion of the effect of the window function. Using Harris's concept, we can see that the surface electrode equation is multiplied by a window function h (X). This window function h (X) There is value in the structure body, and it is a zero-value function outside the structure body. In this way, the expression form of wave transmission can be transformed from the finite structure ontology to the infinite domain, and then the Laplace conversion table is used for design. The tool further selects a suitable window function, that is, selects Η ^, / (λ :) = h {xy ^ {x) y ^ mI, (1 6) where Wml is a constant value. In summary, formula (15 The corresponding terms of each wave propagation constant in) can be summed up as follows: ', (17) where s = jk,-: ik, k, -k, and f (x) is the one modified by the window function. Function of effective surface electrode applicable in infinite domain. Σ

本新發明之增益函一個重要設計目標叶一個特殊渡波器份，但不會影響相但相位可分立設計不用考慮一般電子數但相位可分立設計乃是希望以空間濾·波 ’其可改變系統頻率位，如此一來乃可以之振動檢測裝置的可濾波器進行增益調整之振動檢測裝置之，相關之理念來設鲁應函數之增益部取得提高增益函數 1頻寬之好處，而時隨之而來之相位An important design goal of the gain function of this new invention is a special wavelet component, but it will not affect the phase, but the phase can be separated. The design does not need to consider the general number of electrons, but the phase can be separated. The design is to use space filtering and waves to change the system In this way, the vibration detection device that can adjust the gain of the vibration detection device can be adjusted. The related idea is to set the gain part of the response function to obtain the benefit of increasing the bandwidth of the gain function 1 and then follow Coming phase

第14頁 505793Page 14 505793

五、發明說明（11) 延遲的缺點，（如第1圖）為基礎，而提出之一系歹,J 下面將詳細的敘述本發明以波振動檢測裝置。本發明所：J r出數但相位可分立設計之第3圖所示，其中31為感動裝置的基本架構如 32、Μ、34、U分$ & φ〇構本肢，壓電感應子元件田表面電極36、37、38、Μ、Ή 0、 311、312、313及壓電材料薄層314、315、316 31二同構成。表面電極36至313之功效在經由接觸選擇性麼電材料薄層受應變所產生的電荷傳至用來界面壓電感應子的界面電路，又若將表面電極36、39，31〇、313接於介面電路之地極（Ground)，則也可用來作電磁頻障（£^夏 shielding)，10和20則表示各種不同結構的邊的設計方法將陳述於後。 ^ ^ 本案所述空間遽波可分立設計之振動點的挑選、波傳設性、映像原理、界選頻感應薄層的挑進行設計，以下謹下。器架構，基本上為構檢測裝置之基本要素計理念、空間濾波器面電路的配合、邊界選、波傳振動的應用將上述所有設計要素成增益函數但相位，其可利用設計原的基底、疊加特條件的應用、空間與迴授控制理論等配合圖式分述如V. Description of the invention (11) The disadvantages of delay (as shown in Fig. 1) are based on one of them. J The following will describe in detail the wave vibration detection device of the present invention. The present invention: Figure 3 shows the number of J r but the phases can be separated. Among them, 31 is the basic structure of the moving device, such as 32, M, 34, and U points. The element field surface electrodes 36, 37, 38, M, Ή 0, 311, 312, 313 and the piezoelectric material thin layers 314, 315, 316 31 are both formed in the same way. The effects of the surface electrodes 36 to 313 are transferred to the interface circuit used to interface the piezoelectric inductor through the strain generated by the contact-selective thin layer of the electrical material. If the surface electrodes 36, 39, 31, and 313 are connected, The ground of the interface circuit can also be used for electromagnetic shielding (£ ^ 夏 shielding). 10 and 20 indicate that the design methods of edges of various structures will be described later. ^ ^ The spatial wave described in this case can be designed separately by selecting the vibration points, wave transmission properties, mapping principles, and boundary frequency-selective sensing thin layers. The device architecture is basically the basic element calculation concept of the detection device, the cooperation of the space filter surface circuit, the boundary selection, and the application of wave transmission. All the above design elements are gain functions but phases. They can use the original design basis, The application of superimposed special conditions, space and feedback control theory, etc.

(1 )空間濾波器之設計原點的挑選·· 505793 五、發明說明（12)(1) Selection of design origin of spatial filter 505793 V. Description of invention (12)

換的原點0，是為空間濾波器的設計原點。適當的選擇此設計原點在感應子結構上的位置’將可挑選出各種不同空間濾波效應，以下將會--詳細陳述依此設計理念所的也之一系列之不同特性的增益、相位可分立設計之虹4產測裝置。 ^ 由式（1 5 )中可知，空間濾波器在設計時，是針對波數域4 計，再由式（11)的頻散關係轉回頻率域，並利用此關係^ 達到對感應子結構系統頻率響應函數之控制。由式（1 5 )中玎知，本發明所提各種設計均假設為時間簡諧振盪，亦即刻意忽略e—1 的項，但在設計空間濾波器時，其設計原點The origin 0 of the change is the design origin for the spatial filter. Appropriate selection of the position of the design origin on the inductive substructure will select a variety of different spatial filtering effects. The following will detail the gains and phases of different characteristics of one of the series based on this design concept. The discretely designed Rainbow 4 production test device. ^ As can be seen from equation (1 5), the spatial filter is designed for the wave number domain 4 when designing, and then the dispersion relationship of equation (11) is returned to the frequency domain, and this relationship is used to achieve the inductive substructure. Control of system frequency response function. It is known from equation (1 5) that the various designs proposed in the present invention are assumed to be simply resonant in time, that is, the term of e-1 is deliberately ignored, but when designing the spatial filter, its design origin

案：不在感應成相差’但應子結構頻子結此相率響改設計原點將不。惟一需考量性電感應子對象。另外值網：不會有結效應’易言置，所量測原點不同所廢電感應子真體表現。外加得一* 構振之，得到產生系統構的振動源上，則以時間簡諧振盪將會形差在每個頻率皆為定值，因此其對整個感應效應之影響可用線性疊加重建，因此更會影響整個空間濾波器的基本設計與特的乃是在選擇不同的設計原點時，整體壓振動源之響應將有不同的相位轉移的現提的是若特意選擇設計原點在振動源，則動所造成時間差而產生壓電感應手相差以振動源為設計原點所設計的振動檢測裝的訊號將不會含有振動源所在位置與設计之相差’因此在此設計條件下，所完成之之頻率響應將完全只是感應子結構特性之Case: Do not induce phase difference ’, but the frequency of the sub-structure should be changed. This phase response will not change the design origin. The only thing that needs to be considered is the electrical induction object. Another value net: there will be no knot effect. It is easy to set, the measured electric power is different from the original point, and the actual performance of the waste electricity sensor. In addition, a * structure is obtained to obtain the vibration source that generates the system structure. The simple harmonic resonance in time will form a difference at each frequency. Therefore, its influence on the entire induction effect can be reconstructed by linear superposition, so What will affect the basic design and characteristics of the entire spatial filter is that when selecting different design origins, the response of the overall piezo-vibration source will have different phase shifts. The current mention is that if the design origin is deliberately selected at the vibration source , The time difference caused by the movement will cause the phase difference of the piezoelectric sensor. The signal of the vibration detection device designed with the vibration source as the design origin will not contain the difference between the location of the vibration source and the design. Therefore, under this design condition, all The completed frequency response will be nothing more than the characteristics of the induced substructure

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I 505793 五、發明說明（13) (2 )波傳的設計理念：以懸臂襟為例，油傳在以厭Φ # 、、古哭沾人2 \ ί 感應子元件所構成之空間濾，:看:到ί :咸；、ΐ就是當波在結構中來回傳遞•，不停的件，再力=t ί ΐ缚層與表面電極共同形成的壓電感應子元庫子心太-堅電材料的7軸方向的不同寬度來對傳入感 ί=4:之Λ來提供權重函數，以達到空間渡波的效設計原點，42為感應子結構本體，發明創新發明所設計之一種空間渡波器而 4刀:表示固定端和自由端’從式(15)中，可以知道，* 間濾波器可以針對波的特徵多項 ^ :來進行設計。雖然結構本體為有限•，但t 發明將取窗函數來使設計點移至無限域上，此一映本雙邊拉普拉斯轉換為工具，纟設計出各種跳脫： I良制之感應子，如具增益變化但無相位變動手即為一重要標的。 I冤感應子 ▲波傳到感應子結構的邊界（b 〇 u n d a r y )時，會因尺不同而有相位移動或能量消耗的現象，最常見二邊界界的為自由端（free end)和固定端（f ixed end)，其典型|條件的、、'°構就是懸臂薄板（cantilever plate)。於1975年气表 F· Graff 的著作 ’’Wave Motion in Elastic Soiu 映像（image)的觀念，討論波傳由有限域轉到無限^就以對應關係，由此傳統波傳理念來看，波傳在自由/上的寻相位不會有任何改變，故除行進方向相反以外 /、夜其波仍I 505793 V. Description of the invention (13) (2) Design concept of wave transmission: Take the cantilever as an example, the oil transmission is based on the space filter formed by the inductive element Φ # ,，古哭着人 2 \ ί, See: ί: salty; ΐ is when the wave passes back and forth in the structure, non-stop pieces, re-force = t ί piezoelectric sensor element library formed by the binding layer and the surface electrode together The different widths in the 7-axis direction are used to provide a weight function for the incoming sense, ί = 4: 之 Λ, to achieve the effective design origin of the space wave, 42 is the inductive substructure body, and a space wave device designed by the invention and innovation And 4 blades: the fixed end and the free end. From Eq. (15), we can know that the filter between * can be designed for the characteristic multiples of the wave ^ :. Although the structural ontology is limited, t has invented a windowing function to move the design point to an infinite field. This map translates bilateral Laplacian into a tool to design a variety of escapes: I well-made inductors For example, a hand with gain change but no phase change is an important target. I Inductor ▲ When the wave reaches the boundary (b undund) of the inductive substructure, there will be phase shift or energy consumption due to different scales. The most common two boundary boundaries are the free end and the fixed end. (F ixed end), its typical | conditional, '° structure is a cantilever plate. In 1975, F. Graff's book "Wave Motion in Elastic Soiu image" discussed the concept of wave transmission from a finite field to an infinite one. From the traditional wave transmission concept, the wave transmission There will be no change in the seek phase on freedom /, so except that the direction of travel is reversed

第17頁 505793 五、發明說明（14) 為連續。但波傳到固定端時就將有1 8 0度的相位轉變，所以若空間濾波器的原點設計在自由端如第5圖，其中5丨為以自由端為設計原點之空間濾波器，52為感應子結構，對波而言，其在無限域上所看到的空間濾波器將為如第6圖所示之偶函數，若如第7圖以固定端為設計原點，其中7 ^ 為以固定端設計之空間濾波器，72為感應子結構本體，則波在無限域上所看到的空間濾波器即為如第8圖所示之奇幽數’因此可以利用如上所述之映像原理來充分應用不同的邊界條件，以將原本於有限域感應子結構本體傳遞之波視為在無限域上傳遞，第9圖即為以固定端為設計原點所建構完成之空間濾波器在無限域上檢視的示意圖，其中粗 $91為結構本體中波的傳遞示意圖，92為由壓電感應子本 ⑻所在之有限域利用映像原理展開成無限域波傳的示意圖i而曲線9 3即表示波在結構中來回傳遞時所見到空間濾 ^ 的…思圖’其圖形清楚顯示其在無限域上的展開為奇第1 0圖即表示以自由端為設計原點所設計的空間濾 ' 曲線1 0 1及1 0 2分別表示感應子結構本體内部及利用圖伶原理沿拓邊界條件至無限域上以檢視波傳效應的米意 :’由曲線1 03可知此類其空間濾波器在無限域上的展開性Γ由數’此一理念與體認實為本發明所提多種具不同特勺）日显跑數但相位可分立設計之振動檢測裝置之一個重要的基本設計方法與架構。 (3 )工間渡波器的基底：Page 17 505793 V. Description of Invention (14) is continuous. However, when the wave reaches the fixed end, it will have a phase transition of 180 degrees, so if the origin of the spatial filter is designed at the free end as shown in Figure 5, where 5 丨 is the spatial filter with the free end as the design origin , 52 is an inductive substructure. For waves, the spatial filter seen in the infinite domain will be an even function as shown in Fig. 6. If the fixed origin is used as the design origin in Fig. 7, where 7 ^ is a spatial filter designed with a fixed end, and 72 is the body of the inductive substructure, then the spatial filter seen by the wave in the infinite domain is an odd number as shown in Figure 8 and therefore can be used as above The mapping principle described above is used to fully apply different boundary conditions to treat the waves originally transmitted in the finite field induction substructure ontology as transmitting in the infinite domain. Figure 9 is the space constructed with the fixed end as the design origin. The schematic diagram of the filter viewed in the infinite domain, where the rough $ 91 is the schematic diagram of the wave transmission in the structure body, 92 is the schematic diagram of the infinite domain wave propagation developed from the finite field where the piezoelectric inductor is located, and curve 9 3 means that the wave comes in the structure Seeing the spatial filter ^ when thinking back, the figure clearly shows that its expansion on the infinite domain is odd. Figure 10 shows the spatial filter designed with the free end as the design origin. Curve 1 0 1 and 1 0 2 represents the interior of the body of the inductive substructure and uses Turing's principle to extend the boundary conditions to the infinite domain to view the wave propagation effect: 'From curve 103, we can see the expansion of this type of spatial filter on the infinite domain. The concept of “number by number” is an important basic design method and structure of a vibration detection device with a daily running number but a discrete phase design. (3) The base of the workshop wave:

第18頁 505793 五、發明說明（15) 如前所述應子結構本體上傳遞妆斯轉換表即成為有理念基礎為波，而以遞’皮’其表示式都是極中是有以自然對數間濾、波器的特性。易何，就可以知道這個所需之壓電感應子條感應子，就可以輕易可分立設計之振動檢方向的波，和X < Q 用於空間濾波器設計響：窗函數或邊之波改成在力的設計蒼薄板結構來自然對數的為其基底的言之，只要空間濾波器件，挑選不的製造出所測装置。下 $向的波以 B寺將對整個界條件來將無限域上探考，因空間看，不論是指數形式，函數，即能知道表面電的特性，同同的基底，需特性之增列表1及表2 及其内所列感應子系統討時，濾波器消散波所以當有效的極的基樣的只選配出益1¾數分別代各種基所造成有限感則拉普的設計或是傳表面電控制空底為要依照特定的但相位表X > 底在運的影Page 18 505793 V. Description of the invention (15) As mentioned above, the transfer table of the makeup structure onto the body of the substructure becomes a wave of ideas, and the expression of "skin" is extremely natural. Logarithmic filter and wave filter characteristics. Yi He, we can know that the required piezoelectric sensor strip inductor can easily separate the wave of the vibration direction of the discrete design, and X < Q is used for the design of the spatial filter: window function or edge wave Change to the design of the force of thin plate structure to naturally logarithmically speaking, as long as the space filter device, choose not to make the device under test. The wave in the $ direction will explore the infinite field for the entire boundary condition. Because of the space, whether it is an exponential form or a function, it can know the characteristics of the surface electricity, the same basis, and the list of required characteristics. 1 and Table 2 and the induction subsystems listed therein, the filter dissipates the wave. Therefore, when only the effective base samples are selected, the benefits are only 1 ¾. The number of generations of the various bases is limited. The surface electric control of the bottom is based on the specific but phase table X >

表1空間濾波器在X > 的基底Table 1 The basis of the spatial filter at X >

第19頁 505793 五、發明說明（16) 系統中的基底基底在系統中的含意 e s - a e ca 5 + Or - .} a eJ'ax s-(a+ ja) 5 + (a + j a ) 2i s + a 2 s sin ⑽） cos(cx) sinh(c^) cosh(cit) sm(^) λ cos(你） β"^Λ smh(^) e 'λ cosh(/fe) a / + a' s_+a4 a L^-a2 Λ a β (s+a) (s-haf +/j (s-aY+l β (Sa^ts)-β)({α+ε) + β) a + s (ia+s)- β)((αΛ-ε) + /]) 表2 空間濾波器在X < 0的基底 iBii 第20頁 505793 五、發明說明（17) 系統中的基底基底在系統中的含意 e' ePage 19 505793 V. Description of the invention (16) Base in the system Meaning of base in the system es-ae ca 5 + Or-.} A eJ'ax s- (a + ja) 5 + (a + ja) 2i s + a 2 s sin ⑽) cos (cx) sinh (c ^) cosh (cit) sm (^) λ cos (you) β " ^ Λ smh (^) e 'λ cosh (/ fe) a / + a' s_ + a4 a L ^ -a2 Λ a β (s + a) (s-haf + / j (s-aY + l β (Sa ^ ts) -β) ((α + ε) + β) a + s (ia + s)-β) ((αΛ-ε) + /]) Table 2 Bases of spatial filters at X < 0 iBii Page 20 505793 V. Description of the invention (17) Bases in the system Bases in the system Meaning of e 'e

(XX α λ- s j (a + ja) - s (a + jcx)+ 5 2i a Φ 2s sin(osx) a cos(ax) s 4- a 1 sinh(〇ix) a Λ a cosh(ci3r) s2 - a? sm(0x) β [a + s)2 + β2 p ~ax cos(你） s) (a +5Υ£ + β^ n ! sinh(A) β ((α+ε) — β)(Χα + ε) + β) cosh (你） ο^Λ-ε 由表1、2中可明顯的看出，'雙邊拉普拉斯轉換的左邊和右(XX α λ- sj (a + ja)-s (a + jcx) + 5 2i a Φ 2s sin (osx) a cos (ax) s 4- a 1 sinh (〇ix) a Λ a cosh (ci3r) s2-a? sm (0x) β (a + s) 2 + β2 p ~ ax cos (you) s) (a + 5Υ £ + β ^ n! sinh (A) β ((α + ε) — β) (Χα + ε) + β) cosh (you) ο ^ Λ-ε It is obvious from Tables 1 and 2 that the left and right sides of the bilateral Laplace transform

第21頁 505793 五、發明說明（18) 邊的轉移函數（t rans f er f t i on )剛好自動相位相反，而互相抵消，而空間濾波器本身並非真正跳脫因果律的限制’其在X > 0及X < 〇方向上的訊號仍符合因果律，口是在兩個方向上所得到的訊號，其相位剛好相反，而自動互相抵消，並不影響整個感應子的相位，並且可在空間中加入；慮波的效應’所以空間濾波器是在空間中兩個方向上因果律互相加成後的成果，本發明所提之設計架構之一即為應用此一特性，巧妙的設計出無相位轉變之空間濾波器。在以表1及表2這些基底為設計基礎的空間率濾波器中:可矛丨J用如弟6圖所表TfC之^ A·/ / r , · \ =口 J衣丁夂偶幽數（even function)的表面電極炎〇，/、所產生對點式均佈式感應子之頻率響，-個-4麵ecade的低通濾波器，若數（odd function)爽# - ^ 特疋可跑即f(x) = f+(x)若X > 1電極$構成空間濾波器，以相近偶函數來建構之矣）=+(χ).右Χ/〈 0，則其會比、古叫、士 γ 表面電極對感應子系統的傳#油和消散波個別提供-個零點的傳遞波和 f(x)”“x)若 X < η 丨丄…ΐΛχ’ 右X > 〇，消散波在2傳遞波而言此零點為jk，對生額外之零點，且會0有感個應子夂構的頻率響應函數上產办I心〜、曰有一個與波數相關△ (k)的辦只。舲月在應用本發明說明時，…使用者Vr，，:擇不同的表面電極來構成处、而求 k擇位可分立1計二a1 /慮波為，以求在增益函數但相特定的效；進：:裝置的頻率響應函數… 置的性能如在月：發明w 、感應子結構本體之頻率響應函數中Page 21 505793 V. Description of the invention (18) The side transfer function (t rans f er fti on) happens to have the opposite automatic phase and cancel each other out, and the spatial filter itself does not really break away from the limitation of causality. It's in X > The signals in the 0 and X < 〇 directions are still in accordance with the law of causality. The signals obtained in the two directions have exactly opposite phases and automatically cancel each other out, which does not affect the phase of the entire inductor and can be in space. Add; consider the effect of waves', so the spatial filter is the result of the mutual addition of causal laws in two directions in space. One of the design architectures mentioned in the present invention is to apply this feature and design a phase-free transition. Spatial filter. In the space rate filter based on the bases of Tables 1 and 2, the following can be used: 矛 J uses TfC as shown in Figure 6 ^ A · // r, (Even function) surface electrode inflammation 0, /, the frequency response of the point-type uniformly distributed inductor, a low-pass filter with a 4-sided facade, if the number (odd function) is cool #-^ 特疋It can be run, that is, f (x) = f + (x) if X > 1 electrode $ constitutes a spatial filter, which is constructed by a close even function) = + (χ). Right X / <0, it will be compared with, The ancient name, Shi γ surface electrode to the transmission subsystem of the induction # oil and dissipated waves individually provide a zero-point transmission wave and f (x) "" x) if X < η 丨丄 ... 丄 Λχ 'right X > 〇 The zero point of the dissipated wave is 2 for the transmitted wave, and the extra zero point is opposite, and the frequency response function of the structure of the sensor should be zero. There is a correlation with the wave number △ ( k). In applying the description of the present invention, ... the user Vr ,: chooses different surface electrodes to form a place, and finds the k-selection can be divided into two counts a1 / wave as, in order to find the gain function but phase-specific The frequency response function of the device: The performance of the device is as described in the month: invention w, the frequency response function of the inductive substructure ontology

505793 五、發明說明（19) 產生帶不通頻率效應來降低共振的效應，以提高可用頻寬等，即經常為一重要之設計目標。整合前述兩種設計理念，對空間濾波器的設計原點而言，其對設計原點兩邊所分別傳來的向左和向右的同類形的消散波或傳遞波，所產生的訊號影響相同，同樣的兩個分別離開中心的波，其產生的訊號亦相同。空間濾波器之所以可以達到對感應子結構本體之頻率響應函數產生增益之影響而不會變動相位的成因，就是對設計原點而言，其過去、現在、未來的資訊都存在，因此才可以達到增益改變而相位不動之設計需求。所以若空間濾波器，其中心點左右兩邊的有效表面電極形狀對稱的話，則式（1 5 )可以改寫成： q(k) = -zle3lk2 -{Wip + Wrp) J f(XykX dx + + Wre)] ^ ，（18) 位系 fsfe/ JA^* 無更〆只出將。計器係設波關以濾之可間率就空頻，之與 X)殊位 f(特相數一其函此響極，影電器會面波不表濾而的型，當間值適空益擇的增選換的若變統 (4 )空間濾波器的疊加特性：從式（1 8 )，可依據上述討論可知空間濾波器可以利用線性疊加來完成，易言之，可以將表面電極的形狀改寫成各種已知功能之空間濾波器函數的加成，唯一需注意的乃是這505793 V. Description of the invention (19) It is an important design goal to generate the band-effect effect to reduce the effect of resonance to increase the available bandwidth. Integrating the two aforementioned design concepts, the design origin of the spatial filter has the same effect on the left and right homogenous dissipative or transmitted waves from the two sides of the design origin. The same two waves that leave the center respectively produce the same signal. The reason why the spatial filter can achieve the effect of gain on the frequency response function of the inductive substructure without changing the phase is that for the design origin, its past, present, and future information exists, so it can only To meet the design requirements of gain change without phase change. So if the spatial filter has symmetrical shapes of the effective surface electrodes on the left and right sides of the center point, then equation (1 5) can be rewritten as: q (k) = -zle3lk2-{Wip + Wrp) J f (XykX dx + + Wre )] ^, (18) bits are fsfe / JA ^ * No more, just come out. The counter is designed to set the wave filter to filter the space rate to the air frequency, which is the same as X) and the special f (the number of special phases is a function of which is extremely important. The video appliance meets the wave without filtering, and the current value is suitable for the air. The superimposed characteristics of the spatial filter (4) of the increasing, changing, and changing: From equation (18), according to the above discussion, it can be known that the spatial filter can be completed by linear superposition. In other words, the shape of the surface electrode can be changed. Rewrite into the addition of spatial filter functions of various known functions, the only thing to note is this

第23頁 505793 五、發明說明（20) 些函數本身或其加成後的結果，可在無限域上定義，則本發明所提之空間濾波器的設計理念都可整合應用，據此理念，式（18)可改寫成： ck ，（19)Page 23 505793 V. Description of the invention (20) The functions themselves or the result of their addition can be defined in the infinite domain, then the design concepts of the spatial filter mentioned in the present invention can be integrated and applied. According to this concept, Equation (18) can be rewritten as: ck, (19)

其中a ’和-a ’分別代表以空間濾波器設計原點左右之長度，& ( X)代表第i個空間濾波器表面電極的形狀，假設兩空間濾波器的轉移函數（t r a n s f e r f u n c t i ο η )分別為Zi ( s ) / P! ( s )和Z2 ( s ) / P2 ( s )，其表面電極的形狀分別為& (x)及 R2 ( x )則整個點式均佈型感應子的轉移函數可以改寫成： £2* <d(^) = -^le3ik2[~{wir *+· wrP) ] Rxix^dx 4- j R2{x)e^dx 或 + (w!e + wrg) a aJ R,{x^dx + J Κ2(χ^ ，dx (20) • La(^) P2,U)\\ ，（ 2 1 ) 其中下標的p及e分別代表傳遞波及消散波的轉移函數，若每一個轉移函數或合成後為一沒有相位轉移的濾波器，則其加成的結果亦為一無相位轉移的空間型濾波器，又式 q{k) - -z^k2 ~(W!P+W^) P\p{^) P2p(^)Where a 'and -a' respectively represent the lengths around the origin of the spatial filter design, & (X) represents the shape of the surface electrode of the i-th spatial filter, assuming the transfer function of the two spatial filters (transferfuncti ο η) Zi (s) / P! (S) and Z2 (s) / P2 (s). The shape of the surface electrode is & (x) and R2 (x). The transfer function can be rewritten as: £ 2 * < d (^) =-^ le3ik2 [~ {wir * + · wrP)] Rxix ^ dx 4- j R2 {x) e ^ dx or + (w! E + wrg ) a aJ R, {x ^ dx + J Κ2 (χ ^, dx (20) • La (^) P2, U) \\, (2 1) where the subscripts p and e represent the transfer of the transmission wave and the dissipation wave, respectively Function, if each transfer function or synthesis is a filter without phase shift, the result of its addition is also a spatial filter without phase shift, and the formula q {k)--z ^ k2 ~ ( W! P + W ^) P \ p (^) P2p (^)

(2 1 )可以改寫成：(2 1) can be rewritten as:

第24頁 505793 五、發明說明（21) q(k) = -z°ke3lk2[-(wlp + >n；Page 24 505793 V. Description of the invention (21) q (k) = -z ° ke3lk2 [-(wlp + >n;

Plp(^)P2pU) (22)Plp (^) P2pU) (22)

Pu(s)p2g(s) y \ u L ) 從上式可以知到，加成德的介劭、、索、、士。。从俊的工間應波态，其極點（po丨e)的位置及特性不會改變，但零點（zero)必須經通分後才能確定其特性，所以只須在空間上使構成空間濾波器之壓應子元件上的有效表面電極（effectlve surface ^ electrode)的函數相加，在頻率域上的極點（叫丨幻就3 接相加，可以一直提高其濾波的效應。疋應用這個設計理念，可以應用這個方法，製造一系列通濾波g§(band-pass fiiter)，在感應子結構振動、π 右各加上有阻尼效應的空間濾波器，即空間濾波器、古左 e^x或e jαλ的—基底，如第11圖，可以有效的拉長帶通涛器的有效頻寬，如第12圖，其中124、125和126分別=^ 原系統，一次濾波及二次濾波的可用頻寬，如曲線1 2 β不不這幾次濾波均不會影響整個系統的特性。同樣的在所 4波為上亦可以提高其可用頻寬而不影響整個系咬的通生’由第12圖可以明顯的看出，應用空間滤波器加寺性’可以有效的降低增益函數但相位可分立設=特 :裝置共振的效應，進而提高整個壓電感應子的功能動檢 =設=增益函數但相位可分立振動署叉表面Λ極的正負號轉變太多或太密，特別是含有二V 6的土 &如此將使得感應子之製作程序變得非常繁Pu (s) p2g (s) y \ u L) As can be seen from the above formula, the suffixes, suo, and shi of Jiachengde. . Congjun ’s work should be in a wave state. The position and characteristics of its poles (po 丨 e) will not change. However, the zero point (zero) must be determined after passing through points. Therefore, it is only necessary to make a spatial filter in space. Adding the function of the effective surface electrode (effectlve surface ^ electrode) on the pressure element, the poles in the frequency domain (called 丨 magic 3 connection) can always improve the filtering effect. 疋 Apply this design concept , You can apply this method to make a series of pass filtering g§ (band-pass fiiter), and add a damping effect to the inductive sub-structure vibration, π to the right, namely the spatial filter, the ancient left e ^ x or e jαλ-the base, as shown in Figure 11, can effectively lengthen the effective bandwidth of the bandpass device, as shown in Figure 12, where 124, 125 and 126 respectively = ^ original system, primary and secondary filtering available The bandwidth, such as curve 1 2 β, does not affect the characteristics of the entire system. The same can be done on the 4th wave without affecting the overall bandwidth of the entire system. Figure 12 clearly shows that the application space The wave device can be used to effectively reduce the gain function, but the phase can be separated. = Special: the effect of the device resonance, thereby improving the function of the entire piezoelectric inductor. Set = the gain function but the phase can be separated. The sign of the pole is changed too much or too dense, especially the soil containing two V 6 & this will make the production process of the inductor very complicated

画11_ 第25頁 505793 五、發明說明（22) 複，但應用空間濾波器加成的特性，把表面電極加上另一個沒有正負號轉變的空間濾波器，使其經疊加所合成之表面電極皆為同號如第1 3圖，如此一來不但不會影響原設計之濾波的特性，還可以提高整個濾波效應的功能，而且製作簡便。若所設計的空間濾波器為一次系統，即其所應用之基底中不含ejkx及e_jkx時，以f (x) = tne~alx丨為例，由表1及表2可知 x>0及x<0在感應子的系統中所產生的效應為： «! «! (a-hsy (a-s)n ,(23) 則其轉移函數（transfer function)可以表示成下式 T(s) « nl (u)”+1 + 〇 W+1 (a2 ~/γ+ι ，（24) 可以發現其分子的s奇次方自動消去，只剩下s2k項的加成，由式（1 5 )中可知，消散波的s為k和-k，而傳遞波的s 為jk和-jk，由式（24)可知，此類空間濾波器其在極點時 s二k或-k，亦即代表消散波趨近於無限大，易言之，極點的特性乃為消散波所形成。在零點時，因只有s為j k或 - jk，才能產生零點，而消散波之值為k或-k之特性，永遠只能在分子產生大於0的值，所以由一階系統所形成的零點，其特性均為s = j k或-j k之傳遞波的效應。其實這一系列由一階系統所設計之空間濾波器，其表面電極e_“lxl的含意就是，在空間頻率α時表面電極把傳遞波Draw 11_ Page 25 505793 V. Description of the invention (22) Complex, but apply the characteristics of the spatial filter addition, add the surface electrode to another space filter without sign transition, and superimpose the synthesized surface electrode All have the same number as in Figure 13 so that not only will not affect the filtering characteristics of the original design, but also improve the function of the entire filtering effect, and the production is simple. If the designed spatial filter is a primary system, that is, if the applied base does not include ejkx and e_jkx, take f (x) = tne ~ alx 丨 as an example. From Tables 1 and 2, we can know that x > 0 and x < 0 The effect in the system of the inductor is: «!«! (A-hsy (as) n, (23), then its transfer function can be expressed as the following formula T (s) «nl ( u) ”+ 1 + 〇W + 1 (a2 ~ / γ + ι, (24) It can be found that the s odd power of the molecule is automatically eliminated, leaving only the addition of the s2k term, which can be known from formula (1 5) , The s of the dissipated wave is k and -k, and the s of the transmitted wave is jk and -jk. It can be known from equation (24) that this type of spatial filter has s two k or -k at the pole, which means the dissipated wave Approaching infinity, in other words, the characteristics of the poles are formed by the dissipating wave. At zero, only zero s can be generated because s is jk or-jk, and the value of the dissipating wave is k or -k. A value greater than 0 can always be generated in the molecule, so the zero point formed by the first-order system has the characteristics of the transmission wave effect of s = jk or -jk. In fact, this series of spatial filtering designed by the first-order system Device, its surface Pole e_ "lxl meaning that, when the spatial frequency of the transmitted wave surface electrode α

11111111

第26頁 505793 五、發明說明（23) 的分佈和消散波的振形一樣，會提出消散波的效應。若表面電極的基底只含有Nkx及elkx，則可產生二次系統，以！（乂）=6_—|3111(/3\)的為例，由表1及表2中，可知其在感應子系統中所造成的效應為： Γω-τ;>0(>Η?;<〇ω β β + (a~sy -l· (a + sf ,(25) 其轉移函數可表示成： Τ(8).β--^-- (s + 2as + or )(S - 2as + α ) ，（ 2 6 ) 若再配合xn的基底，則f ( x) = xn e_ alxl s i n ( yS x )其轉移函數可由以各種下式的型式合成： (S2 + 2aS+a2 )k + (S2 -2aS+ a2 )k (S2 + 2aS+a2 )k (S2 - 2a5+ a2 f ，（ 2 7 ) 其中整數k<n，由式（26)中可以很明顯的看出，因正弦函數為奇函數，其會產生一個零點s，又由式（2 7 )可以發現，其分子的展開式亦為s的偶數次方的合成，其零點的特性和一次系統相同，空間濾波器的零點亦為傳遞波所形成，但其極點的特性為兩種波的共同形成。本發明所應用之空間濾波器的疊加特性只能確定其極點的特性，但其零點必須通分以後才能確定，但若每一種空間滤波器本身或合成後沒有相位，其加成的效應亦不會影響整個系統相位的頻率響應函數特性，同時也不會使及原設計之空間濾波器之相位不變特性受到影響。Page 26 505793 V. Description of the invention (23) The distribution of the dissipated wave is the same as that of the dissipated wave, and the effect of the dissipated wave will be proposed. If the substrate of the surface electrode only contains Nkx and elkx, a secondary system can be generated, so that (乂) = 6_— | 3111 (/ 3 \) is taken as an example. From Tables 1 and 2, it can be known that the effect it causes in the induction subsystem is: Γω-τ; > 0 (>Η?; < 〇ω β β + (a ~ sy -l · (a + sf, (25) The transfer function can be expressed as: Τ (8) .β-^-(s + 2as + or) (S -2as + α), (2 6) If the basis of xn is further matched, f (x) = xn e_ alxl sin (yS x) and its transfer function can be synthesized by various types of formula: (S2 + 2aS + a2) k + (S2 -2aS + a2) k (S2 + 2aS + a2) k (S2-2a5 + a2 f, (2 7) where the integer k < n can be clearly seen from equation (26), because of the sine function It is an odd function, which will generate a zero point s, and it can be found from the formula (2 7) that the molecular expansion is also a synthesis of the even power of s. The characteristics of the zero point are the same as those of the primary system. The zero point of the spatial filter It is also formed by the transmitted wave, but the characteristics of its poles are the joint formation of two kinds of waves. The superimposed characteristics of the spatial filter applied by the present invention can only determine the characteristics of its poles, but its zero point must be determined after passing through points, but If each spatial filter is itself or synthesized No phase, an addition effect of the entire system will not affect the frequency characteristics of the phase response function, and at the same time does not make the original design of the spatial phase filter of invariant properties are affected.

第27頁 505793Page 505793

(5)映像原理在空間濾波器上的應用由前述理，可明，討 (cosin 後之值分立設數展開在波傳數，在 (sine) 開到無數，而限域上的展開應用映結合乃圖及第固定端依前所其仍然狀，而的設計理念，可知應用波傳及映像（ima 以把波傳由有限域轉到無限域的原論利用幻及表2巾的正弦函數（sine)和 = e)兩個空間據波器的基底，其經 ^ 計之振動檢测裂置’此類感應子完全不須;:目位' ’即可經由映像的原理自動展開到無限域上。的設計理念中’可知自由端的空間濾波器為偶函固定端為奇函數，所以若表面電極中含有正弦或餘弦函數（cosine)，不須外加—個窗函數使其展限域上，只須在自由端時其函數為偶函數之餘弦函在固定端時為奇函數之為正弦函數，即可自動在無展開成完整的正弦或餘弦函婁文，如第！ 4圖為懸臂樑示意圖’14 1為以結構長度為1/4週期的正弦函數，像（image)的原理再加上邊界的應用，兩者之巧妙可直接把壓電感應子由有限域轉到盔限 5 16圖分別表示結構兩端為自由端 ' ^ ^ 時此類感應子的應用方法。…及結構兩端為述雙邊拉普拉斯的值為0 ’如正弦及餘弦函數，但改變了固感應H統之設計以及表面之形其之所以可以不對整個系統產生影響(5) The application of the mapping principle to the spatial filter is explained by the foregoing principles. It can be seen that the value after cosin is discretely set to the wave propagation number, opened to (sine) to innumerable, and the application of the map to the limited area is expanded. Combining the design of Naito and the fixed end as before, the wave propagation and mapping (ima are used to transform the wave propagation from the finite field to the infinite field, using the illusion and the sine function of the table 2 ( sine) and = e) The basis of the two spatial data wave receivers, whose vibration detection is split, 'these inductors are not required at all ;: the target position' can be automatically expanded to the infinite domain through the principle of mapping In the design concept of ', we know that the free-end spatial filter is an even function and the fixed end is an odd function, so if the surface electrode contains a sine or cosine function (cosine), you do n’t need to add a window function to make it spread over the limit range. As long as the cosine function whose function is an even function at the free end is a sine function which is an odd function at the fixed end, it can be automatically expanded into a complete sine or cosine function without Wen Wen. Schematic '14 1 is the length of the structure The sine function of 1/4 period, the principle of image plus the application of the boundary, the cleverness of the two can directly transfer the piezoelectric inductor from the finite field to the helmet limit. 5 16 The figures show that the two ends of the structure are free ends. '^ ^ Is the application method of this type of inductor .... and the two ends of the structure are described as bilateral Laplace values of 0' such as sine and cosine functions, but the design of the solid induction H system and the shape of the surface are changed. So it does n’t affect the whole system

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在感應子的糸統中各產生又極點和零點的择戶问特性的極點和零點，因此不會影響原有&茂φ &特丨生相反而互相抵消，處中口八右二壓電感應子特性。若空間滹、法哭的其底中-3有14兩個函數，因其值：、波”的基波的效果，但可結人並 /、本身不會有濾到濾波的效果。口一，於表1及表2之感應子函數來達基於此二可以不須論，而不性。以下界的值不之兩種設將其轉到及映像原上，此處將原設計種函數相可順利之濾波器的數修改成種幽數的特性，再加In the sensor system, the poles and zeros of the user-selection characteristics of the poles and zeros are generated, so they will not affect the original & Mao φ & characteristics, and they will cancel each other out. Electrical inductor characteristics. If there is space in the bottom of the space and the law is crying, -3 has two two functions, because of its value: the effect of the fundamental wave, but it can be combined and / or it will not have the effect of filtering itself. The induction sub-functions in Tables 1 and 2 can be achieved based on these two. It is not necessary to talk about them. They are not inexhaustible. The values of the lower bounds are set to the original and the mapping. Here, the original design functions are used. The number of smooth filters can be modified to the characteristics of a faint number, plus

透過窗函數的μ呼τ目二間濾波為的疊加原理會影響原設mi力就可以轉到無限域上假設一空Γ；、ίί：：間滤'波器及原感應子結構的 Απ #間濾波益的基底挑選為e-仏I，Α #邊為，故無法直接推展到益限域。依太路、在邊無限域上，之應用窗函數的效應，理，利用正L 用空間渡波器加成的特‘ 气认如仃Γ 餘弦函數來將其推展到無限域。“如何應用後者來進行無限域的推展。的空間濾波哭，力、喜R 丄減，使复ΐ :“ 和這正弦與餘弦| 二：的值為0，所形成之表面電極即擴展到無限域上，而完全奋旦 ρThe superposition principle of the two-pass filtering between μ and τ through the window function will affect the original mi force and can be transferred to the infinite domain. Assuming an empty Γ; The base of the filtering benefit is selected as e- 仏 I, and the Α # edge is, so it cannot be directly extended to the benefit limit region. The application of the window function on the edge infinite domain according to Tailuo is based on the use of the special ‘Qi such as 仃 Γ cosine function added by the positive L with a space waver to extend it to the infinite domain. "How to apply the latter to the extension of infinite domains. The spatial filtering of Cry, force, and R are reduced to make complex ΐ:" and the sine and cosine | two: the value of 0, the surface electrode formed is extended to infinity Over the domain, but completely strenuously

并百銮變廄" 而兀王不會影響原設計之空I銮百銮变廄 " But Wu Wang will not affect the original design I

Α二:〜，對自由端而言，若將其表面電極的】下式· (28) /(乂) ：= ΠΊ — q C〇S(K) 其中α為所設計之轉角頻率（使cos在有限的結構上完成一 corner frequency )，沒1 為個1/4倍數週期的係數，Cl為Α 二: ~, for the free end, if the surface electrode of it is as follows: (28) / (乂): = ΠΊ — q C〇S (K) where α is the designed corner frequency (make cos Complete a corner frequency on a finite structure, where 1 is a coefficient of 1/4 multiple period, and Cl is

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使此表面電極的函數在邊界的推展到無限域上。或是對固定端而言若將修改為：將表面電極函數 /Cv)=^坤丨一C2sin[/?2(v+r。)] ，（μ) 其中万2為使sin在有限域上完使表面電極函數在邊界的值為 (29)代入式（18)中，可看出^匕數，完全不會對空間慮波器之以下再深入的探討式（2 9 )中之響，由第14圖到第16圖中可知為正弦函數，且在固定端的值函數的效應，此時若再一次引函數稍微移動^下，使其在邊函數反貼回來，即可達成目的定端及自由端為設計原點所設及式（2 9 )其所產生的濾波效應成1 / 4倍數週期的係數，^為零的權重函數。將式（2 8 )及二表面電極所加成之正弦函頻率效應產生任何影響。正弦函數平移之應用與影對固定端而言，若表面電極為零，將無法用以消除一些入映像的設計理念，把正弦界有值，並把未完成的正弦第1 7圖及第1 8圖為分別以固計之空間濾波器，由式（2 8 ) TV):The function of this surface electrode is extended to the infinite domain at the boundary. Or for the fixed end, if it is modified as follows: change the surface electrode function / Cv) = ^ 坤丨 a C2sin [/? 2 (v + r.)], (Μ) where 2 is to make sin in a finite field After substituting the value of the surface electrode function at the boundary into (29) and substituting into (18), it can be seen that the number of ^ k will not affect the following in-depth discussion of the space filter (2 9). From Figures 14 to 16, the sine function can be seen, and the effect of the value function at the fixed end. At this time, if the function is moved slightly again, and it is pasted back on the edge function, the fixed end of the purpose can be achieved. The sum of the free end is the sum of the formula (2 9) set at the design origin, and the filtering effect produced by it is a coefficient with a multiple of 1/4, and ^ is a weight function of zero. Add the formula (2 8) and the sine function frequency effect of the two surface electrodes to any effect. Application and shadowing of sine function translation. For the fixed end, if the surface electrode is zero, it will not be able to eliminate some design concepts that are reflected in the image. The sine boundary is valued, and the unfinished sine is shown in Figure 1 and Figure 1. Figure 8 shows the fixed spatial filters, respectively, by formula (2 8) TV):

，（30), (30)

所以應用映像及加成的觀念，可以不必經過窗函數，就可以直接由有限域轉到無限域上，因此可以發展出一系列不同特性之增益函數但相位可分立設計之振動檢測裝置。Therefore, by applying the concepts of reflection and addition, it is possible to directly transfer from the finite field to the infinite field without going through the window function. Therefore, a series of vibration detection devices with gain functions of different characteristics but separate phases can be developed.

綜合表1及表2所列以及前面所闡述的各種設計理念，可知若欲得到無相位延遲現象的空間濾波器，必須同時得到X 1 m _ I Η 第30頁 505793 五、發明說明（27) >0及X < 0的訊號，才會形成所須之空間濾波的效應，以下歸納出每一種基底對感應子結構本體頻率響應函數之影響： (a)若構成空間濾波器之表面電極中含有e αχ或e- αχ就會對感應子結構本體頻率響應函數提供兩個一次的極點 (pole)，如e-wi所產生的極點為1/( y —S2)。Based on the various design concepts listed in Tables 1 and 2, and the previous description, it can be seen that if you want to obtain a spatial filter without phase delay, you must also obtain X 1 m _ I 页 page 30 505793 V. Description of the invention (27) > 0 and X < 0 signals will form the required spatial filtering effect. The following summarizes the influence of each type of substrate on the frequency response function of the inductive substructure body: (a) If the surface electrode constituting the spatial filter Including e αχ or e- αχ will provide two-order poles for the frequency response function of the body of the inductive substructure. For example, the pole generated by e-wi is 1 / (y — S2).

(b) 若構成空間濾波器之表面電極中含有ej αΧ或e-』αΧ就會對感應子結構本體頻率響應函數提供一個二次的極點 (?〇16)，並會在系統中產生阻尼，如6-4\|以11(/5又）所產生的極點為 4 α 召s/(s2 + 2as+a2)( s2 - 2as+a2)。 (c) 若構成空間濾波器之表面電極中含有χη，則代表提高空間漶波器對感應子結構本體頻率響應函數影響之極點 (pole)的次數，如xn eiUI所產生的效應為…[(a— n+1-( a +s)n+1 ]/ ( a2 — s2)n+1 〇(b) If the surface electrode constituting the spatial filter contains ej α × or e- ″ α ×, it will provide a quadratic pole (? 〇16) to the frequency response function of the body of the inductive substructure, and it will generate damping in the system. For example, 6-4 \ | calls s / (s2 + 2as + a2) (s2-2as + a2) with a pole of 11 (/ 5 again). (c) If the surface electrode constituting the spatial filter contains χη, it represents the number of times to increase the pole of the spatial response of the frequency response function of the inductive substructure. For example, the effect of xn EIUI is ... [( a— n + 1- (a + s) n + 1] / (a2 — s2) n + 1 〇

(d)若將兩個代表不同空間濾波器之表面電極的基底互相加減來形成新的空間濾波器，則在新的空間濾波器中將4 有原先各單—空間濾波器之基底，並將有新的零點（ze ro 產2生2，如e—αΙΧΙ+ e-mi，因其所合成的效應為[(a2-s2) + ( 点212) ]/ [( a2-s2) ( /5Ls2)]，故將分別產生 1/( =2 — s2)和1八/32-s2)的濾波特性。構成二間渡波裔之表面電極可由奇函數表示，則其 ::ί應Γ結構本體之頻率響應函數之影響將比利用、相、〗構本r:ί為表面電極所形成之空間渡波器對原感應子$ 丑 < 頰率響應函數之影響多一個零點S，如ei(d) If two substrates representing the surface electrodes of different spatial filters are added and subtracted from each other to form a new spatial filter, the new spatial filter will have 4 substrates of the original single-space filters, and There are new zeros (ze ro produces 2 births 2, such as e-αΙχΙ + e-mi, because the combined effect is [(a2-s2) + (point 212)] / [(a2-s2) (/ 5Ls2 )], So it will produce 1 / (= 2 — s2) and 1/8 / 32-s2) filtering characteristics. The surface electrode constituting the two crossing waves can be represented by an odd function, then :: the impact of the frequency response function of the structure of the structure will be more than the utilization, phase, and structure. The effect of the original sensor $ ugly < cheek rate response function has an additional zero S, such as ei

第31頁 505793 五'發明說明（28) --- ⑴sin(川所產生的效應為4α〜（州as+a2+e)( S2-2as+f+/S2)，因 sin 函數本身 (S +( αΗ 占 i)/(SH2 心“2+ 万”（s2_2 as+ α2”2)，可知其極點的特^完全相同，僅只因為則（州為奇函數而Sln(AUI)，對應之偶函數的關係、，所之頻率響應函數將多一個零點5， ϋ 構相同。除此之外’其零點並不 ⑴由設計原點的挑選和邊界條件的配合，亦可本架構出奇函數或偶函數的感應:二 ”定端為設計原點的即為奇函數的特性的感應子，。由私為設計原點2即為偶函數的點式均佈型感應子。 γ右以-個e-或―為基底來構成空間濾波器，則此* 間濾波益將對感應子頻率響應函數提工 (P，’但此一增加之極點將含有虛部，因此將=子之頻率響應函數之增益與相位均有影響。于戍炙子 (h) ^表面電極的方程式中只含可使雙邊拉普拉斯轉換的值為0值’如正弦及餘弦函數，由表丨及表2中得知如、其他的基底配合時’仍可彳旱到益如 Π 佈型感應子。 Τ仔到無相位延遲現象的的點式均 (1)應用映像的原理及映像（image)的觀念，在有限正弦或餘弦的函數在無限域上展開，再應用空間濟皮哭= 加的特性，可以不透過窗函數就可以直接把空間遽^ ς 開到無限域上討論，而對原設計之感應子系統及空間^ 505793 五、發明說明（29) 器的效應均不會產生影響。 (6)高通（high pass)，帶通（band pass)濾波器的設計：别面所k出之全新增盈函數但相位可分立設計振動檢測襄置的設計理念，都是針對低通渡波刀器(1乂= f i 1 ter )而設計，在本發明中應用前述一系列的理論，巧妙的運用如懸臂樑等的各種邊界條件，波傳的理論，和基底的選用，再加上感應子界面電路的配合，即可應用空間濾波器，設計出一系列的高通濾波器（high — pass filter)，帶通濾波器（band_pass fUter)，或帶不通滹 ^器（band - rejected fllter)，下面將詳細敘明所提與此相關之一系列全新的點式均佈型感應子。不&月厅於空間遽波器的基底中已提出奇函數的空^滤應之偶函數的空間濾波器在成岸子；;相對應，相對Γ可「函數而言，則其頻率響應函數可表示成： q{k) = -ζα,3Λ2 [-K + -.)[(^)G (,)] + K + w J[(/c)^ ω , =-ζ^3Λ2Δ(λ)[-(% + (J)]+κ + , 但對於與奇函數對庫之 …」，（31 ) 的頻率響應函數可表示成幽數，其整個振動檢測裝置价斗鳥+')巧味其中Gp⑷代表傳遞波原偶函數空間遽波器二函數Page 31 505793 Description of the Five 'Invention (28) --- ⑴sin (Sichuan's effect is 4α ~ (state as + a2 + e) (S2-2as + f + / S2), because the sin function itself (S + ( αΗ occupies i) / (SH2 heart "2+ ten thousand" (s2_2 as + α2 "2), it can be seen that the characteristics of its poles are exactly the same, only because then (state is an odd function and Sln (AUI), corresponding to the relationship of the even function Therefore, the frequency response function will have an additional zero point 5, and the structure is the same. In addition, its zero point is not determined by the selection of the design origin and the cooperation of boundary conditions. The architecture can also induce the induction of odd or even functions. : Two "fixed end is the design origin of the inductor which is the characteristic of the odd function. From the private design origin 2 is the point-type uniformly distributed inductor of the even function. Γ right with-e-or- To form a spatial filter for the base, then the filtering benefit will improve the frequency response function of the inductive element (P, 'but this added pole will contain the imaginary part, so the gain and phase of the frequency response function of the element will be = In the equation of the surface electrode (h) ^ only the value that can make the bilateral Laplace transform is 0, such as sine and The cosine function is shown in Tables 丨 and 2 that when the other substrates are combined, they can still be used to benefit from Π cloth-type inductors. Point-to-point types without phase delay (1) Application image The principle of the image and the concept of image (exp), the function of the finite sine or cosine function is expanded on the infinite domain, and then the feature of the space is used to add the space, and the space can be directly opened to infinity without passing through the window function. It will be discussed in the field, but it will not affect the original design of the induction subsystem and space ^ 505793 V. Invention Description (29) The effect of the device will not affect. (6) High pass, band pass filter Design: The design concept of all newly added profit functions but separate phases for vibration detection and design is designed for low-pass wave cutters (1 乂 = fi 1 ter). The aforementioned application is applied in the present invention. A series of theories, clever use of various boundary conditions such as cantilever beams, the theory of wave propagation, the selection of the substrate, and the cooperation of the inductive sub-interface circuit can apply a spatial filter to design a series of high-pass Filter (high — pas s filter), band-pass filter (band_pass fUter), or band-rejected fllter (band-rejected fllter), the following will describe in detail one of the new series of point-type uniformly distributed inductors related to this. & Moon Hall has proposed an odd function of the space filter in the base of the space wave filter, and the spatial filter of the even function is in the bank; correspondingly, in terms of the Γ function, its frequency response function Can be expressed as: q {k) = -ζα, 3Λ2 [-K +-.) [(^) G (,)] + K + w J [(/ c) ^ ω, = -ζ ^ 3Λ2Δ (λ) [-(% + (J)] + κ +, but for the library with odd functions ... ", the frequency response function of (31) can be expressed as a faint number, and its entire vibration detection device is worth fighting bird + ') Where Gp⑷ represents the original function of the transmitted wave

第33頁 505793 五、發明說明（30) (transfer function)， Ge(s)代表傳遞波原偶函數空間Page 33 505793 V. Description of the invention (30) (transfer function), Ge (s) represents the space of the original and original function of the transfer wave

濾波器的轉移函數（transfer functi〇n)，Mk)代表利用奇函數將比利用偶函數設計之振動檢測裝置多出一個與波相關之增益值，由式（3 1 )與式（3 2 )可以知道奇函數對傳遞波所產生的零點比消散波的零點多一個j，因此將提供個9 0度的相差，因此在系統中會產生額外的零點，所以在第一個零點產生前，整個以奇函數所設計之振動檢測系統的頻率響應函數和偶函數的完全相同，只是在增益部分& 一個20dB/decade的Mk)函數而已，並沒有相位轉移二二應，但值得注意的是，若感應子結構物為簡支樑（sim > support beam)，則其只有傳遞波的效應，則奇函數比以相對應之偶函數設計的振動檢測系統多一個零點〗k运而本發明高通及動檢測自由端自由端相反的已提到波與消因ilb以個偶函零點出應用此低通濾装置，時的含為設計，對固過，其散波的懸臂樑數的振現以前對應奇偶函波器特性之前面已在波意’對自由原點，其波定端而言為在兩種波上效應分別比為感應子結動檢測裝置比偶函數的增益函傳的理端而言所看到奇函數所提供偶函數構物可性，乃可設數但相位可念提出，波，波為連續的空間濾波，而在空間的效應，奇分立設計之振傳到固定端和的’所以若以益為偶函數，慮波器的基底函數針對傳遞多提供一個零點j k和k 自動提供一個奇函數及 ’利用懸臂樑的奇多一個△ ( k )函數函數感應子在 ’把兩個訊號The filter's transfer function (Mk) represents that using an odd function will have one more wave-related gain value than a vibration detection device designed using an even function. It is expressed by equations (3 1) and (3 2) It can be known that the zero point generated by the odd function for the transmitted wave is one more j than the zero point of the dissipated wave, so it will provide a 90 degree phase difference, so an extra zero point will be generated in the system, so before the first zero point is generated, the entire The frequency response function and the even function of the vibration detection system designed by the odd function are exactly the same, but in the gain part & a 20dB / decade Mk) function, there is no phase shift binomial response, but it is worth noting that If the inductive substructure is a simple support beam (sim > support beam), it only has the effect of transmitting waves, and the odd function has one more zero point than the vibration detection system designed with the corresponding even function. Detection of the free end The opposite of the free end has been mentioned. The wave and the decontamination ilb are applied to this low-pass filter device with a zero-point even function. The appearance of the number of beams previously corresponds to the characteristics of the parity function wave. The wave front's free point of origin, the fixed end of the wave is the ratio of the effect on the two waves to the even function of the inductor junction detection device. As far as the rationale of the gain function is concerned, the evenness of the even function provided by the odd function can be set, but the phase can be set. Waves and waves are continuous spatial filters, and the effects in space are odd and discrete. The vibration is transmitted to the fixed-end sum, so if the benefit is an even function, the base function of the wave filter provides an additional zero point for the transfer, jk and k automatically provide an odd function and 'use an odd one of the cantilever beam △ (k) Function function inductor in 'put two signals

第34頁 505793 五、發明說明（31) 相加可自動形成一個帶通渡波器，再加上界面電路的配合，將可以輕易的架構出一個高通濾波器，又若以簡支樑為感應子結構物，因其並無消散波的存在，所以比偶函數的頻率響應函數多一個j k而已，所以可以輕易的在任意的頻率内架構出具帶通或高通濾波器的增益函數但相位可分立設計之振動檢測裝置，本發明將以懸臂樑為例，提出一系列的帶通濾波器及高通濾波器。所以在一個懸臂樑的感應子結構上，在自由端和固定端分別加上同一型的空間濾波器如第1 9圖，其中曲線1 9 1表示以固定端為設計原點所設計之空間濾波器，其數學表示式 1 f丨（X )可依（1 6 )式定義之，曲線1 9 2表示以自由端為設計原點所設計之空間濾波器，其數學表示式f2 (X)亦可依式 (1 6 )定義之，把這兩個訊號分別取出相加，就可以直接在 ‘ 系統中提供一個零點（ze r〇 )，利用界面電路的頻率增益 -1 9 3或構成空間濾器之表面電極尺寸來控制依自由端和依固定端所設計之兩個空間濾波器的相對增益，就可以控制這個零點s的位置，如此也就可以配合空間濾波器的轉角頻率，製造出一個如第2 0圖中之曲線的帶通濾波器（ba nd p a s s f i 11 e r )，例如，若構成空間濾波器之表面電極f 丨_ (乂）可表示為丨1(\)+%(乂），則可得如曲線201及2 02之帶通濾波器的頻率響應函數，易言之，整個系統可以表示成： Φ)=[-(Μν+(*〇]+(>% + ^j[(^-(*s)]] ，（ 3 3 ) 其中σ之主要目的乃在於調整依自由端和依固定端所設計 -Page 34 505793 V. Description of the invention (31) Addition can automatically form a band-pass wave waver, and with the cooperation of the interface circuit, a high-pass filter can be easily constructed, and if a simply supported beam is used as an inductive substructure Because there is no dissipative wave, it is only one jk more than the frequency response function of the even function, so it is easy to construct a vibration function with a bandpass or high-pass filter at any frequency, but the phase can be designed separately. As a detection device, the present invention will use a cantilever beam as an example to propose a series of band-pass filters and high-pass filters. Therefore, on a cantilever beam inductive substructure, the same type of spatial filter is added to the free end and the fixed end, as shown in Figure 19, where the curve 191 represents the spatial filter designed with the fixed end as the design origin. Device, its mathematical expression 1 f 丨 (X) can be defined according to (1 6), the curve 1 9 2 represents the spatial filter designed with the free end as the design origin, and its mathematical expression f2 (X) also It can be defined according to formula (1 6). By taking out and adding these two signals separately, a zero point (ze r0) can be directly provided in the 'system, and the frequency gain of the interface circuit is −193 or a spatial filter is formed. The surface electrode size is used to control the relative gain of the two spatial filters designed according to the free end and the fixed end, so that the position of this zero point s can be controlled. In this way, the corner frequency of the spatial filter can be matched to produce a filter such as The bandpass filter (ba nd passfi 11 er) of the curve in Fig. 20, for example, if the surface electrode f 丨 _ (乂) constituting the spatial filter can be expressed as 丨 1 (\) +% (乂), Then a band-pass filter like curve 201 and 202 can be obtained Frequency response function, in other words, the entire system can be expressed as: Φ) = [-(Μν + (* 〇] + (>% + ^ j [(^-(* s)]]), (3 3) The main purpose of σ is to adjust the design of the free end and the fixed end-

第35頁 505793 五、發明說明（32) 之兩空間濾波器的相對增益，值得一提的是，σ所代表的相對增ϋ ’除可如上述讨論利用空間電極之相對尺寸來達成外，亦可以用兩空間濾波器之界面電路的相對電子增益來達成。由於傳遞波的s為j k及-j k，消散波的s為k及_ k，兩者均會產生額外的零點，但在第一個零點出現以前，皆可任意調變空間濾波器的轉角頻率及外加：t曾益值σ ，_才鼻出具帶通濾波特性的增益函數但相位可分立設計之振動檢測裝置。 "" 局通濾端的訊荷放大應子系第21圖荷放大目的實整零點的增益乃可以波器的設計是延續帶通濾波器的理各，口炻六m〜須在固定號接電流放大器（current amplifer)，自由端接電器（charge amplifer)，這樣就可以很方便的在感統之頻率響應函數中再加上一個零，（zer〇)(失^ 及第22®) ’其中211和212分別為電流放大器^ 器，而2 1 3為針對電流放大器所外加之增益值，盆為調整電流放大器及電荷放大器之相料 2 ^ 之位置。弟22圖中之曲線221及222為+古、、 ^ 和相位示意圖，整個系統依式（3丨）:1通濾波态表示成：及式（32)之合成同樣的只要調變空間濾波器的轉角頻查R t ，（ 3 4 ) n午及外加辦2从可以任意設計出所需之高通濾波器（h彳^ 9鼓值，就 11 ^π pass f · 1 而在系統中所造成的兩個零點，在固6 1 1 t e r )，疋立而的焚愛j；山不會使感應子之頻率響應函數在增益嘴以 π ‘，、、5出現前將曰| ,變時了乂肩面對相位Page 35 505793 V. The relative gain of the two spatial filters in the description of the invention (32). It is worth mentioning that the relative increase represented by σ 'can be achieved by using the relative size of the space electrodes as discussed above. This can be achieved by the relative electronic gain of the interface circuit of the two spatial filters. Because s of the transmitted wave is jk and -jk, and s of the dissipated wave is k and _ k, both will generate additional zeros, but the corner frequency of the spatial filter can be arbitrarily adjusted before the first zero appears. And plus: t has a benefit value σ, _ Cai nose produces a vibration detection device with a gain function of band-pass filtering characteristics but a phase that can be designed separately. " " The signal amplification of the local pass filter should be based on the real zero point gain of Figure 21 for the purpose of amplification. The design of the wave filter is to continue the principle of the band pass filter. Connect the current amplifier (charge amplifer), and freely terminate the appliance (charge amplifer), so you can easily add a zero to the frequency response function of the sense system, (zer〇) Among them, 211 and 212 are current amplifiers respectively, and 2 1 3 is the gain value applied to the current amplifier, and the basin is to adjust the position of the current amplifier and the charge amplifier 2 ^. The curves 221 and 222 in Fig. 22 are schematic diagrams of + ancient,, ^, and phase. The entire system is expressed according to formula (3 丨): 1 pass filter state is as follows: and the synthesis of formula (32) is the same as long as the spatial filter is modulated Corner frequency check R t, (3 4) n noon and extra office 2 can design the required high-pass filter (h 彳 ^ 9 drum value, just 11 ^ π pass f · 1 and caused in the system The two zeros of the two are fixed at 6 1 1 ter), and the love of j stands upright; Shan will not make the frequency response function of the inductor before the gain mouth appears with π ',, 5, | Face-to-face

505793 五、發明說明（33) 會循因果率而移動的傳統問題。 .tt 設的器波慮間空之點原 -tt 設為界心中構結 kh 的而若器，但波稱，濾對件間為條空極的制電稱控面對效表了有效供欲有提若的已，邊就念兩界理點邊計原及設計心的設中樑使構臂須結懸必在面 ώζ 點前，原續應計延效設不在這些位置上，就必須補回所失去的訊號，換句話說，就是在結構上再加上未完成之表面電極，把失去的訊號加 | 回去，使波在無限域上探討。 1 在懸臂樑的感應子結構上，如第23圖及第24圖，可以知道若設計原點不在結構中心的話，就無法完全的使空間濾波器的表面電極左右對稱，應用波傳的理念，因在自由端的 > 波為連續，所以只要把未完成的表面電極回貼，把失去的 · 訊號加回去就可以保持原設計之空間濾波器如第2 5圖，其中2 5 1和2 5 2分別表示原設計之空間濾波器及加貼之空間濾波器包含壓電薄層及表面電極，而構成兩個空間濾波器之壓電薄層上之π + π號乃表示於原先極化時所施加的正電場電極位置，而兩個壓電薄層之” + π號均朝上，乃表示此二 I 空間濾波器之極化方向相同，第2 6圖及第2 7圖分別表示另外兩種的製作方式，第2 6圖為外加一回貼之壓電薄膜，第 2 7圖表示直接把回貼的部分加入2 6 1的表面電極函數中，虛線2 7 1即表示尚未外加回貼之表面電極函數的形狀。同樣的情形若使用在固定端，把未完成之表面電極回貼，即505793 V. Description of Invention (33) The traditional problem that moves according to the cause and effect ratio. .tt set the wave point to consider the original point of the space -tt is set to the structure of kh in the heart of the world, but Bo said that the filter for the space between the pieces of electric control system has an effective supply table If you want to mention something, read the rationale of the two realms, calculate the original and design the center beam so that the arm must be suspended in front of the surface, and the original accrual extension effect is not in these positions. The lost signal must be replaced, in other words, an unfinished surface electrode is added to the structure, and the lost signal is added back | so that the wave can be explored in the infinite domain. 1 On the inductive substructure of a cantilever beam, as shown in Figures 23 and 24, it can be known that if the design origin is not in the center of the structure, the surface electrodes of the spatial filter cannot be fully symmetrical to the left and right, and the concept of wave propagation is applied. Since the> wave at the free end is continuous, as long as the unfinished surface electrode is pasted back and the lost signal is added back, the original space filter can be maintained as shown in Figure 25, of which 2 5 1 and 2 5 2 indicates that the originally designed space filter and the attached space filter include a piezoelectric thin layer and a surface electrode, and the π + π number on the piezoelectric thin layer constituting the two spatial filters is indicated when the original polarization The position of the applied positive electric field electrode, and the "+ π" of the two piezoelectric thin layers are facing upwards, which means that the polarization directions of the two I-space filters are the same. Figures 26 and 27 respectively show the other There are two kinds of manufacturing methods. Figure 26 shows the piezoelectric film with an additional paste, and Figure 27 shows that the posted part is directly added to the surface electrode function of 2 61. The dashed line 2 7 1 indicates that it has not been added. The shape of the electrode function on the surface. If this situation is used at the fixed end, put the unfinished surface electrode back, that is,

第37頁 505793 五、發明說明 (34)Page 37 505793 V. Description of the Invention (34)

可有相同f性之空間渡波器，但波在固定端所看到之空間滤波器為：函妻欠，所以其回貼之表面電極的極化方向必須相反’如弟28圖到第同八σι 士 - 皮釦…冗圖表不三種不同的製作方式，其中2 9 1矛2 9 2分別表示原設古十*門滤波器，…間滤波貼之空間反，才能使波傳現象清楚的在無限域上；::、極化方向相 (8)不同邊界條件空間濾波器的設計：在某二、，’。構中，其邊界條件含有如阻尼竣〜懸臂樑的結構，使得當波傳到邊界時其反百寻不同於都會改變，但壓電薄膜只能用極化方向，振幅及相位正負號的轉變，而這個方法在自由端和c提-個來使波傳轉到無限域上討論，但其他的邊衣二11丁以應用用這個設計架構，但幾乎所有這種結構都可2 無法應表達： Γ以下式來近似 mx cx + kx q ，（35) 其中代表位移，代表加速度，m為質量，c代夺 k代表勁度（stlffness)所以其基本設計方法和懸=二:2 全一樣的，在本發明中，巧妙的應用外加之界*疋完得其波傳可在無限域上討論，假設一增益函數但相路j使立設計之振動檢測裝置的結構如第3 2圖，其邊界I分定端或自由端，在這種結構中只須在邊界再〔同於固々上兩片同一There can be a space wave waver of the same f nature, but the space filter seen by the wave at the fixed end is: the letter is owed, so the polarization direction of the surface electrode posted by it must be opposite. σι 士-leather buckle ... There are no three different ways to make redundant charts, of which 2 9 1 spear 2 9 2 represents the original ancient ten * gate filter, and the space of the filter paste can be reversed to make the wave propagation phenomenon clearly visible. Infinite domain; ::: Design of spatial filters with different boundary conditions (8) with different polarization conditions: In some two, '. In the structure, the boundary conditions include structures such as damping and cantilever beams, so that when the wave reaches the boundary, its inverse 100% change will change, but the piezoelectric film can only use the polarization direction, amplitude and phase sign change And this method is discussed on the free end and c to make the wave transfer to the infinite domain, but the other side garments are used to apply this design architecture, but almost all of this structure can be expressed. : Γ The following formula is used to approximate mx cx + kx q, (35) where represents displacement, acceleration, m is mass, and c represents kst stands for stiffness, so its basic design method is the same as the suspension = 2: 2 In the present invention, the clever application plus the bounds * 疋 is complete, and its wave propagation can be discussed in the infinite domain. Assume that the structure of a vibration detection device with a gain function but phase path j design is shown in Figure 32. The boundary I is divided into a fixed end or a free end. In this structure, it is only necessary that

第38頁 505793 五、發明說明（35) 性質空間率波器，把其訊號分別提出，一個接電流放大器 (current ampl 1 f er)並反貼’使其訊號自動轉27〇度，即和另外一片的同形的波差- 9 〇度的相角，而另一片只接電荷放大器（charge amplifer) ’這時只須在電流放大器或電荷放大器乘上一個增益值再相加，使其在複數平面上的虛部為零，且其實部的值和相對於原設計的空間濾波器的值相同，但沒有相差，其設計架構如第33圖，其中331為電流放大裔’ 3 3 2及3 3 3電荷放大器，3 3 4及3 3 5為外加之增益值’使兩回貼之空間濾波器33 7及338的值和原未完成之空間濾波器3 36相同，但其並沒有相差，即可輕易的由有限的結構轉到無限域上，其在複數平面上的含意如第3 4 圖’其中341為假設空間濾波器3 36的相位為零的相對複數平面，342為337的訊號，其因邊界的效應而有差^的相角差，3 4 3的訊號和3 4 2的訊號完全相同，但本發明結合界面電路的應用，並利用壓電材料反面貼時會自動提供一個 180度的相差，所以訊號342及34 3自動相差90度，再加上外加增益值，使其虛部的值為0，實部的量和原曲到之3 4 2 Λ 5虎強度相同即可’訊5虎3 4 4及3 4 5即外加增益後的效鹿，如此一來，在具阻尼的邊界條件出現時仍可保持原設計之空間滤波為’而保有原有設計的空間遽波的效應。 (9)空間選頻感應薄層及波傳振動的應用：在薄板型增益函數但相位可分立設計之振動檢測裂置中，Page 38 505793 V. Description of the invention (35) The nature of the space rate wave device, put its signal separately, one connected to the current amplifier (current ampl 1 f er) and paste it to make its signal automatically turn 27 degrees, that is, and other One piece has the same wave difference-a phase angle of 90 degrees, while the other one is only connected to a charge amplifier. At this time, you only need to multiply the current amplifier or the charge amplifier by a gain value and add them to make it on the complex plane. The imaginary part is zero, and the value of the real part is the same as the value of the original designed spatial filter, but there is no difference. The design architecture is as shown in Figure 33, where 331 is the current amplifier '3 3 2 and 3 3 3 Charge amplifier, 3 3 4 and 3 3 5 are the added gain values, so that the values of the two space filters 33 7 and 338 posted are the same as the original uncompleted space filters 3 36, but there is no difference between them. It can be easily transferred from a finite structure to an infinite field. Its meaning on the complex plane is as shown in Figure 3 4 'where 341 is a relative complex plane assuming that the phase of the spatial filter 3 36 is zero, and 342 is a signal of 337. Different phase angle due to boundary effect The signal of 3 4 3 and the signal of 3 4 2 are completely the same, but the present invention combines the application of the interface circuit and the piezoelectric material will automatically provide a 180 degree phase difference when it is pasted on the reverse side, so the signals 342 and 34 3 automatically differ. 90 degrees, plus the added gain value, so that the value of the imaginary part is 0, and the amount of the real part is the same as that of the original song. 3 4 2 Λ 5 Tiger strength can be the same. After the gain is added, the original design's spatial filtering can still be maintained when the damped boundary conditions appear, while the original design's spatial chirp effect is maintained. (9) Application of spatial frequency-selective induction thin layer and wave-transmitted vibration: In the vibration detection split of thin-plate gain function but phase separation design,

第39頁Page 39

(36) 505793 五、發明說明（36) 其共振的效應是由傳遞波和消散波的波形的合條件時即為其共振頻，但可應用表面電極的挑數的配合，針對其中一種波形設計，可以單獨一種波的共振頻的效應提出，利用波傳共振的統中製造出外加的極點或零點。以懸臂樑為例，其共振時的彎曲位移的方程式 cosh(卞)-cos(~^) — 〇·加nh(·^) — sin(ii)) JL· 其中可看出消散波形成的振動為： cosh(^) ~ 〇*. sinh(i^) L L ，（37) 傳遞波形成的振動為： ^ it 5ιϊ u共振的杈其中某特性，,1' 在系為：(36) 505793 V. Explanation of the invention (36) The resonance effect is the resonance frequency of the combined conditions of the waveforms of the transmitted wave and the dissipated wave. However, the cooperation of the surface electrode can be applied to one of the waveform designs. It is possible to propose the effect of the resonance frequency of a single wave, and use the system of wave resonance to create an extra pole or zero. Taking a cantilever beam as an example, the equation for the bending displacement at resonance is cosh (卞) -cos (~ ^) — 〇 · 加 nh (· ^) — sin (ii)) JL It is: cosh (^) ~ 〇 *. Sinh (i ^) LL, (37) The vibration formed by the transmitted wave is: ^ it 5ιϊ One of the characteristics of the resonance branch, 1 'in the system is:

.λ Λ 一 COS(—丄 L 其中在懸臂其共振頻的振形各種的振振形動的態時反，為奇 )-f cr, Sin(i^).λ Λ-COS (— 丄 L where the form of the resonant frequency of the cantilever and the various modes of the vibration are inverse in time, as odd) -f cr, Sin (i ^)

L 為此一結樑共振模態的形，50及60為一模態兩種波模態兩種波的以看出，其振的，在第一模第二模態則相數，而傳遞波，（3 8 ) 構的特徵值（e i g e n v a 振形如附第3 5圖到第 ’（B)及（C )分別為傳波的振形和原結構的形，第36圖及第37圖 ’假設以結構中心為模態是兩種波形以奇其消散波為偶函數，所以在奇數模態時，函數，而在偶數模態 1 ue)， 37圖，遞波和位置，分別為原點，偶函數傳遞波消散波 B夺為相這兩種波傳其中（A)為消散波的波第35圖為第第二及第三則從圖中可白勺交替產生為奇函數，皆為偶函反，但產生L is the shape of the resonant mode of a knotted beam. 50 and 60 are two modes of one mode and two waves. It can be seen that the vibration is transmitted in the first mode and the second mode. The characteristic values of the (3 8) structure (eigenva shape as shown in Figures 3 to 5) (B) and (C) are the shape of the transmitted wave and the shape of the original structure, Figure 36 and Figure 37, respectively. 'Assuming that the center of the structure is the mode, the two waveforms are odd and their dissipated waves are even functions, so in the odd mode, the function is, but in the even mode 1 ue), Figure 37, the recursive wave and the position are the original Point, even function transfer wave, dissipated wave B, is phase. These two waves are transmitted. (A) is the wave of dissipated wave. Figure 35 is the second and third. From the figure, it can be alternately generated as an odd function. Anti-even function, but produces

505793 五、發明說明（37) 共振的因素為兩種波在邊界的合成符合共振的條件時，即節點（固定端）及腹點（自由端），就會形成共振。由結構共振的特性，可以知道其傳遞波本身尚未在結構中形成共振條件時，就和消散波形成結構的共振，利用這個觀點，本發明結合了空間選頻感應薄層的設計和奇偶函數的應用，可以在系統中提供外加的極點和零點，提高增益函數但相位可分立設計之振動檢測裝置的性能。由式（1 4)可知，本發明所提之各種四階的系統皆為這四個波所合成，可把每一個波所提供的訊號視為系統中的s，由前面所提出之奇偶互換的性質，可以知道每達到一個共 | 振模態時只有一種波的效應被提出，產生一個二次系統，到下一個模態就演變成另一種波，所以可以利用表面電極的挑選及奇偶函數的挑選，在其共振頻進行換波的動作， ~ 但前面已提過，當結構達到共振頻時，為兩種波的合成符 -合共振條件時就會形成，其傳遞波尚未完全形成偶函數或奇函數，所以改變有效表面電極的奇偶函數，在傳遞波形成奇偶函數的頻率時進行換波的動作，此一系列的增益，相位可分立設計之振動檢測裝置的基本架構為第4圖，只有以結構中心為設計原點才可使用此種設計方法，以下幾 | 點是應用這種設計理念在感應子系統中提供外加的極點和零點： (A) 表面電極為含有e —α|χ|的偶函數： (a ) 在奇數模悲時’消散波因表面電極函數的權重e a 1x1 ，所以其值很小，所以其二次系統的效應被消去，而傳505793 V. Explanation of the invention (37) The resonance factor is that when the combination of two waves at the boundary meets the conditions of resonance, that is, the node (fixed end) and the ventral point (free end), resonance will form. From the characteristics of structural resonance, it can be known that when the transmitted wave itself has not formed a resonance condition in the structure, it forms structural resonance with the dissipated wave. Using this viewpoint, the present invention combines the design of the spatial frequency selective induction thin layer and the parity function. Applications can provide additional poles and zeros in the system to improve the performance of a vibration detection device with a gain function but a discrete phase design. It can be known from formula (1 4) that the various fourth-order systems mentioned in the present invention are synthesized by these four waves, and the signal provided by each wave can be regarded as s in the system, which can be exchanged by the parity proposed previously. It can be known that every time a common mode is reached, the effect of only one wave is proposed, generating a quadratic system, and it evolves into another wave in the next mode, so the selection of the surface electrode and the parity function can be used. The selection of the wave is to change the wave at its resonance frequency, but as mentioned earlier, when the structure reaches the resonance frequency, it will be formed when the two waves are synthesized and combined with the resonance condition, and the transmitted wave has not yet completely formed the even wave. Function or odd function, so change the parity function of the effective surface electrode, and perform the wave changing operation when the frequency of the transmitted wave forms the parity function. The basic structure of this series of vibration detection device with discrete gain and phase design is shown in Figure 4. This design method can only be used with the structural center as the design origin. The following | points are the application of this design concept to provide additional poles and zeros in the induction subsystem. (A) The surface electrode is an even function containing e —α | χ |: (a) In the odd-numbered mode, the 'dissipated wave' has a small value due to the weight of the surface electrode function ea 1x1, so its secondary system effect Eliminated, and passed

第41頁 505793 五、發明說明（38) 遞波因為奇函數，其值為零，在系統中形成一個零點。 (b ) 在偶數模態時，消散波為奇函數其值為零，而傳遞波為偶函數，其效應被保留，所以會延長偶數模態影響的頻率範圍，但不會產生額外的1 8 0度的相位轉移。 (B) 表面電極為含有e - α 1x1的奇函數： (a) 在奇數模態時，消散波因表面電極函數為e ι|χ|的奇函數，變成奇函數，其值很小，所以消散波的二次系統的效應被消去，而傳遞波則被改為偶函數，其效應被提出，在系統中形成一個二次系統的極點。 (b) 在偶數模態時，消散波被改為偶函數，但因表面電極函數為e - aU1，其效應被消去，而傳遞波改為奇函數，其值為零，在系統中產生一個零點。應用這個方法我們可以在特定頻率製作帶通濾波器，或加上一個帶不通濾波器，提高增益函數但相位可分立設計之振動檢測裝置之可用頻寬。 (1 0 )窗函數及空間濾波器的設計：前面已提到，應用空間濾波器的基底，可以確定空間濾波器的效應，而引入窗函數的觀念，可使波傳轉到無限域上討論，再加上空間濾波器疊加的特性，將可應用空間濾波器的基底來設計窗函數，如此一來就可以確定加入窗函數對原空間濾波器設計的影響，換句話說，窗函數的效應被一起設計到整個增益函數但相位可分立設計之振動檢測裝Page 41 505793 V. Explanation of the invention (38) Because the wave is odd, its value is zero, which forms a zero point in the system. (b) In the even mode, the dissipated wave is an odd function and its value is zero, while the transmitted wave is an even function, and its effect is retained, so the frequency range affected by the even mode is extended, but no additional 1 8 is generated. 0 degree phase shift. (B) The surface electrode is an odd function containing e-α 1x1: (a) In the odd mode, the dissipated wave becomes an odd function because the surface electrode function is an odd function of e ι | χ |, and its value is very small, so The effect of the secondary system of the dissipating wave is eliminated, while the transmission wave is changed to an even function, and its effect is proposed to form a pole of the secondary system in the system. (b) In the even mode, the dissipated wave is changed to an even function, but because the surface electrode function is e-aU1, its effect is eliminated, and the transmitted wave is changed to an odd function, with a value of zero. Zero. By applying this method, we can make a band-pass filter at a specific frequency, or add a band-pass filter to increase the available bandwidth of a vibration detection device with a gain function but a discrete phase design. (1 0) Design of window function and spatial filter: As mentioned earlier, the effect of the spatial filter can be determined by applying the basis of the spatial filter. The introduction of the concept of the window function enables the wave to be transferred to the infinite domain for discussion. , Coupled with the characteristics of the spatial filter superposition, the basis of the spatial filter can be used to design the window function, so that the effect of adding the window function on the original spatial filter design can be determined, in other words, the effect of the window function A vibration detection device that is designed together to the entire gain function but with a discrete phase design

505793 五、發明說明（39) 置中’如此一來可以使波傳可在無限域上設計，而且可以確定窗函數對空間濾波器的影響’還可以提高整個系統的性此。下面將會詳細介紹應用這幾種全新的設計理念，所設計出之一系列的增益函數但相位可分立設計之振動檢測裝置。從表1表2中’可以知道若表面電極中有e_a|x| ，直轉角頻率在波數a ，而且會產生l/( a2-s2)的極點（p〇le)，為一個-40dB/deCade的低通濾波器，其實它本身就是一種補償器（compensator)，但結構是有限的，無法製作e_a|x|的完整的表面電極，所以引入窗函數的設計理念，從基底的特性中可以發現在e-αμ的前面加一個tn可以提高叫k的次數’但不破壞原極點（po丨e )的特性，假設中心距邊界的長度為a，依據上面的特性，選用下面的窗函數： | 、 k|V — α’」，（39 ) 使其在邊界的值為零，並用e- aui的有效表面控制轅g斗s、玄，, . 、極形狀來得角頻率（corner frequency)的位置，α 頻率之值，所以空間濾波器的表面電 :此轉角505793 V. Description of the invention (39) Centering ‘In this way, the wave propagation can be designed in the infinite domain, and the influence of the window function on the spatial filter can be determined. It can also improve the performance of the entire system. The following will introduce in detail the application of these new design concepts, one of a series of vibration detection devices designed for gain function but phase separation design. From Table 1 and Table 2 'it can be known that if there is e_a | x | in the surface electrode, the right angle frequency is at the wave number a, and it will produce a pole (p0le) of 1 / (a2-s2), which is a -40dB / DeCade's low-pass filter is actually a kind of compensator, but its structure is limited. It is impossible to make a complete surface electrode of e_a | x |, so the design concept of window function is introduced. It is found that adding a tn in front of e-αμ can increase the number of times called k, but does not destroy the characteristics of the original pole (po 丨 e). Assuming the length of the center distance boundary is a, according to the above characteristics, the following window function is selected: |, K | V — α '″, (39) make the value of the boundary at zero, and use the effective surface of e-aui to control 斗 g bucket s, xuan,.,, And pole shape to obtain the corner frequency (corner frequency) Position, the value of α frequency, so the surface charge of the spatial filter: this corner

UI 「/ 、一让旧w歌改寫成： -冲| 所以，（40) 轉移函數，每一個波經空間濾波器，對系統所產生的可以表示成下式：UI "/ ，一 Let the old song be rewritten as: -rush | So, (40) the transfer function, each wave passing through the spatial filter, can be expressed as follows for the system:

第43頁 505793 五、發明說明（40)Page 43 505793 V. Description of the invention (40)

2a(a2 - s2)n2a (a2-s2) n

+ (a+s广1 (a2 -s2)n+l (41 ) 從式（4 1 )分子的第二項可以看出，其s的奇數次方的自動消去，只留下偶次式，所以若其量比第一項小很多的話，則不會破壞第一項分子的展開式，且其會很接近轉角頻率 α ，可以改寫成下式： Π (^2 - s2f(s2 - fH s2 + a}s++ (a + s 广 1 (a2 -s2) n + l (41) As can be seen from the second term of the numerator of formula (4 1), the odd-numbered power of s is automatically eliminated, leaving only the even-numbered formula, So if its amount is much smaller than the first term, it will not damage the expansion of the first molecule, and it will be close to the corner frequency α, which can be rewritten as: Π (^ 2-s2f (s2-fH s2 + a) s +

(42) 其中，L、nii和h分別是由式（4 1 )分解的結果，c是α的函數，從式（42)中可以很明顯的發現，這是一個沒有相位延遲現象的-40dB/decade的低通濾波器，下表是這一系類同類型的空間濾波器的效應： Η的次數P 轉角頻率的位置與表面電極的長度仏：f5 感應子特性- n— αα > 1 為一相位不動的感應子令j Η Ο ·*.·.、** ·* a a < 1 在極低頻會存在一個零點， n-l / V3 e f aa 厂 » 0.922 \in \ n ) 為一相位不動的感應子(42) Among them, L, nii, and h are the results of decomposition by equation (4 1), c is a function of α, and it can be clearly found from equation (42) that this is a -40dB without phase delay / decade low-pass filter, the following table is the effect of this type of spatial filter of the same type: the number of P P the position of the corner frequency and the length of the surface electrode 仏: f5 inductor characteristics-n— αα > 1 Let j 不 Ο · *. ·., ** · * aa < 1 be a zero point at a very low frequency, nl / V3 ef aa factory »0.922 \ in \ n) Sensor

從表中可知，只要調變三個設計參數，轉角頻率α 、感應子長度a及η的次數，就可以調變出擁有不同特性的增益函數但相位可分立設計之振動檢測裝置。在這一系列的增益函數但相位可分立設計之振動檢測裝置As can be seen from the table, as long as the three design parameters are adjusted, the frequency of the corner frequency α, the length of the inductor a and η, it is possible to tune a vibration detection device with different gain functions but separate phases. Vibration detection device in this series with gain function but discrete phase design

第44頁 505793 五、發明說明（41) 中，某些狀況下在低頻一個1 8 0度的相位轉變係，改變感應子結構的降低其對增益函數但相響。所以只要妥善的應用本益函數但相位可分立設須特性之感應子。前面分立設計之振動檢測裝象不重要時，但若阻尼可知，由空間濾波器所左邊移動而已，並不影計0 會有零點的存在，使得系統中形成 1此時可以應用式（1 1 )的頻散關特性，把零點提到極低頻的位置，位可分立設計之振動檢測裝置的影發明所提出的全新之理念來設計增計之振動檢測裝置，就可以得到所所提出之一系列增益函數但相位可置的設計方法乃為假設結構阻尼現必須考慮時，由式（11)之頻散關係提供的極點及零點只是向頻率域的響整個空間濾波器在頻率域上的設但在有阻尼的感應子結構中，空間濾波器在波數域上的設計之無相位轉移的增益函數但相位可分立設計之振動檢測裝置，在頻率域上可能會受到阻尼的影響，會有相位的轉變，由式（1 1 )之頻散關係可以明顯的發現，當從頻率域轉到波數域上時，因結構阻尼的效應而往負的實數軸上偏移，假設一空間濾波器對消散波設計一個轉角頻率在α的零點，即（s2 - α2)的兩個一次系統，其相位在波數域上的相位為零，但轉到波數域上時，會引出阻尼的效應，其關Page 44 505793 5. In the description of the invention (41), under certain conditions, a phase transition system of 180 degrees at low frequencies changes the structure of the inductive sub-structure to reduce its effect on the gain function. So as long as the proper application of the benefit function but the phase can separate the characteristics of the inductor. When the vibration detection device of the previous discrete design is not important, but if the damping is known, it is only moved by the left side of the spatial filter, and it does not affect the existence of zero, so that 1 can be applied in the system at this time (1 1 The characteristic of the dispersion closeness, the zero point is referred to the extremely low frequency position, and the new concept proposed by the invention of the vibration detection device with discrete design can be used to design an additional vibration detection device. One of the proposed solutions can be obtained. The design method of the series gain function but the phase can be set is to assume that when structural damping must now be considered, the poles and zeros provided by the dispersion relationship of equation (11) only affect the frequency domain. The design of the entire spatial filter in the frequency domain However, in a damped inductive substructure, the design of the spatial filter in the wavenumber domain without a phase transfer gain function, but the phase-separated design of the vibration detection device may be affected by the damping in the frequency domain. The phase transition can be clearly found from the dispersion relationship of formula (1 1). When changing from the frequency domain to the wavenumber domain, it is negative due to the effect of structural damping. Offset on the real number axis. Suppose a spatial filter designs a dissipative wave with a zero corner frequency at α, that is, two primary systems of (s2-α2). The phase of the phase in the wavenumber domain is zero, but When it is in the wavenumber domain, it will lead to the effect of damping.

第45頁 505793 五、發明說明（42) 係可表示成下式 a2 2ΕΓPage 45 505793 V. Description of the invention (42) can be expressed as the following formula a2 2ΕΓ

2EI ，（43) 令2EI, (43) Order

R (AEIpA-R2)m 2EI , 2EI 則式（4 1 )可改寫成：二+ 仍")仍 (44) +' ，（45) 由式（4 3 )可以看出阻尼對整個空間濾波器在頻率域上的影響，但由表1和表2空間濾波器的基底中，可知若基底中存在ealxl和ej α|χΐ或e— α|χΐ和e_j α|χ|可以設計出兩個一次的系統，可應用此基底的特性，製造出和由阻尼效應相同的特性的系統，換言之，使α2改成α2( ，則當轉回頻率域時，就不會有阻尼的效應，仍可設計出一無相位延遲現象的空間濾波器。模態感應子理論：由式（8 )模態感應子的基本理論架構在於表面電極的形狀。藉由空間權重函數和極化強度的選擇再配合結構橫向變位及共振態之間的正交，選則不同共振頻時的模態形狀R (AEIpA-R2) m 2EI, 2EI The formula (4 1) can be rewritten as: two + still ") still (44) + ', (45) From the formula (4 3), we can see that the damping filters the entire space. Effect in the frequency domain, but from the bases of the spatial filters in Tables 1 and 2, we can see that if there are ealxl and ej α | χΐ or e— α | χΐ and e_j α | χ | A one-time system can apply the characteristics of this substrate to make a system with the same characteristics as the damping effect. In other words, change α2 to α2 (, when the frequency domain is switched back, there will be no damping effect, and A spatial filter without phase delay is designed. Modal inductor theory: The basic theoretical structure of the modal inductor from equation (8) lies in the shape of the surface electrode. Through the choice of spatial weight function and polarization intensity, it is matched The transverse displacement of the structure and the orthogonality between the resonance states, and the modal shapes at different resonance frequencies

第46頁 505793 五、發明說明（43) 再將表面電極做成模態形狀二次微分的形狀便可以量取特定模態的訊號。對於懸臂樑為例，其模態之間相互正交，於〗9 8 5， Blevins在其著作丨’Formulas for Natural Frequency and Mode Shape n有詳細的討論，其模態形狀可以表示為：Page 46 505793 V. Description of the invention (43) The surface electrode can be made into a modal secondary differential shape to measure the signal of a specific modal. For a cantilever beam as an example, the modes are orthogonal to each other. On 9 8.5, Blevins has a detailed discussion in his book 丨 Formulas for Natural Frequency and Mode Shape n. The modal shape can be expressed as:

(46) 其中’又i為此一結構的特徵值（e i g e η ν a 1 u e ) ; σ i為自然頻率參數（parameter)可以表示為：OinhL -Sin;t i )/(cosh λι +cos入太）；a代表樑的長度。利用此一模態(46) where 'i is the characteristic value of this structure (eige η ν a 1 ue); σ i is the natural frequency parameter (parameter) which can be expressed as: OinhL -Sin; ti) / (cosh λι + cos 入太); A represents the length of the beam. Use this mode

彼此正交的特性，可推導得：The orthogonal properties can be derived as follows:

，（47) 其中5mn為計〇116〇:1^『del ta。所以，為了製做模態感應子，將有效表面電極形狀製成： "^(x)=^d^x)λη cbc ，（48) 其中//n為電極設計時的比例常數；下標η則表示第n個模態。可以得到模態感應子方程式·· 果, (47) where 5mn is a total number of 116116: 1 ^ "del ta. Therefore, in order to make a modal inductor, the effective surface electrode shape is made: " ^ (x) = ^ d ^ x) λη cbc, (48) where // n is the proportionality constant at the time of electrode design; subscript η represents the nth mode. You can get the modal inductor equation ...

i(t) = ce31nr u 八 nil dt 其中c為比例常 (49)從（4 9 )式中可以清楚的看出壓電才莫i (t) = ce31nr u eight nil dt where c is a constant ratio (49) It can be clearly seen from the formula (4 9)

第47頁 505793 五、發明說明（44) 感應子可直接量測特定模態座標（m 〇 d a 1 c 〇〇 r d i n a t e )的微分’換言之’模態感應子將沒有模態溢出的效應。若欲去除某一特定模態對結構體的影響時若根據以上的推導只需要選擇不同模態的有效表面電極即可，但是於較高的模.賤時其低頻響應不佳，所以可依據線性疊加理論將其餘的模態電極依某一特定比例相加以得到較佳低頻響應的表面電極，此一將模態間相互加減的電極即為零值模態一感應子 (Nil-mode 1 sensor)。而第（50)式便是零值模態一感應子的表面電極形狀，第（5 1 )式便是其相對應的壓電感應子方程式。 ^(x) = Σ C A4nPage 47 505793 V. Description of the invention (44) The inductor can directly measure the differential of the specific modal coordinates (m d a 1 c 〇 r d i n a t e). In other words, the modal inductor will not have the effect of modal overflow. If you want to remove the influence of a specific mode on the structure, you only need to select the effective surface electrode of different modes according to the above derivation, but in higher modes, its low frequency response is not good, so it can be based on The linear superposition theory adds the remaining modal electrodes according to a certain ratio to obtain a surface electrode with better low frequency response. This electrode that adds and subtracts between modes is a zero-value mode-inductor (Nil-mode 1 sensor ). Equation (50) is the shape of the surface electrode of the inductor in the zero-value mode, and equation (5 1) is the corresponding piezoelectric induction equation. ^ (x) = Σ C A4n

，（50) 9(0 = kC nezxAn{i) ， (51) 定一特定之C2所 ’ 3 8 1為所設計第3 8圖中的是綜合上述的理論依式（4 8 )選製作之第二模態感應子的表面電極的形狀之第二模態感應子。以模態感應子設計之點式感應子從以上的模態感應子理論出發，本發明中將合％ ^ 、村曰砰細地介紹弟〜模態感應子（mode 2 sensor )及零值模離一 ,Μ . 、心、欺* 應、 dll mode 1 sensor)的設計理念。、(50) 9 (0 = kC nezxAn {i), (51) Specify a specific C2 place '3 8 1 is designed. Figure 3 8 is a combination of the above theoretical formula and (4 8). The second modal inductor has a shape of a surface electrode of the second modal inductor. The point-type inductor based on the modal inductor is based on the above modal inductor theory. In the present invention, we will introduce the modal ~ mode 2 sensor and the zero-valued mode in detail. Liyi, M., heart, bullying, dll mode 1 sensor) design philosophy. ,

5〇5793 五、發明說明（45) 第二模態感應子之設計：5〇5793 5. Description of the invention (45) Design of the second modal inductor:

為了設計一應用範圍較傳統的點式感應子與均佈型感應子廣泛的增益函數但相位可分立設計之振動檢測裝置，其第一個步驟需要先設計一個簡單的感應子結構，再利用此一結構來设計其相對應的模態感應子。在此便以一簡單的懸臂樑結構為例（CantUever beam)，其共振模態的形狀如第3 5 (A )圖所示，而其相對應的第二模態表面電極形狀如第38圖所示，其中〜、+表示電極的極化方向。零值模態一感應子之設計：In order to design a vibration detection device with a wider range of gain functions but a discrete gain phase design than traditional point inductors and uniformly distributed inductors, the first step requires designing a simple inductor structure and then using this A structure to design its corresponding modal inductor. Here we take a simple cantilever beam structure as an example (CantUever beam), the shape of its resonance mode is shown in Figure 3 5 (A), and the shape of the corresponding second mode surface electrode is shown in Figure 38 As shown, where ~, + indicate the polarization direction of the electrode. Design of zero-value mode-inductor:

零值模態一感應子最主要的應用便是可以用來消除結構第一共振態的影響，也就是說在表面電極的各種模態組合中’並沒有含有模態一的函數。為了設計一應用範圍較傳統的點式感應子與均佈型感應子廣泛的增益函數但相位可分立設計之振動檢測裝置，其第一個步驟需要先設計一個間早的感應子結構’再利用此一結構來設計其相對應的模態感應子。以懸臂樑為例（cantil eve]r beam)，其第〆t 振模態的形狀如第35 (A)圖所示。根據線性疊加理論，零值模態一感應子表面電極的形狀可以懸臂樑基本結構扣除第一模態後的任意模態形狀相疊合，而在此以選取第三模怨及第五模態為主來疊加表面電極，其形狀如第3 9圖所不’其中一、+表示電極的極化方向。The most important application of the zero-valued mode-inductor is to eliminate the influence of the first resonance state of the structure, that is, in the various mode combinations of the surface electrode ', there is no function of mode-one. In order to design a vibration detection device that has a wider range of gain functions but a discrete gain phase than traditional point inductors and uniformly distributed inductors, the first step requires the design of an early inductor substructure. This structure is used to design its corresponding modal inductor. Taking a cantilever beam as an example (cantil eve) r beam, the shape of the 〆t-vibration mode is shown in Figure 35 (A). According to the theory of linear superposition, the shape of the surface electrode of the zero-value mode-inductor can be superimposed on the shape of an arbitrary mode after the first mode is subtracted from the basic structure of the cantilever beam. The surface electrode is superimposed on it, and its shape is as shown in Fig. 39. One of them, + indicates the polarization direction of the electrode.

505793505793

五、發明說明（46) 再藉由使用電流放大器（current ampl if ier)做為界面電路，便可以輕易的把增盈函數但相位可分立設計之振動松測裝置做為一個加速度率計（acceleration rate s e n s o r )。如果能再進一步的結合半導體的製程方法便可以更加精確地研製壓電模態感應子，可以縮小本身結構的體積，使應用範圍更為廣泛。主動式點式感應子的設計：V. Explanation of the invention (46) By using a current amplifier (current ampl if ier) as the interface circuit, the vibration loosening device with a gain function but a discrete phase design can be easily used as an accelerometer. rate sensor). If the semiconductor manufacturing method can be further combined, the piezoelectric modal inductor can be more accurately developed, the volume of its structure can be reduced, and the application range can be wider. Design of active point inductor:

由壓電互補定理（reciprocal relationship)可以得知，若以一特定的壓電薄層作為致動器，可產生特定之形變及位移時’將此一相同的壓電薄板作為振動檢測裝置，便可以ΐ測到相對應的物理量。以此一定理，乃可更進一井《的引入控制理論以设计補償器（c 〇 n t r ο 1 1 e r、It can be known from the piezoelectric complementary theorem (reciprocal relationship) that if a specific piezoelectric thin layer is used as an actuator, a specific deformation and displacement can be generated. 'If the same piezoelectric thin plate is used as a vibration detection device, then The corresponding physical quantity can be estimated. With this theorem, we can go one step further and introduce the control theory to design the compensator (c 0 n t r ο 1 1 e r,

compensator)，配合壓電感應子及壓電致動器完成如第4 圖的主動感應子迴路系統，其中4〇1及4〇2分別為壓電感」子及致動為，403為感應子結構物，408為一最基本之^ 幽數但相位可分立設計之振動檢測裝置的架構，4 〇 4，: _ 及40 5分別為界面電路及補償器，4〇7為被測之結構物 I9。增Λ函數但相位可分立設計之振動檢測裝置田正们振動檢測裝置受到振動時，壓電感應子备. 生變形經由界面電路（interface circuit)便可以、口^ 動訊號’將此-所得的振動訊號連接到設計好的補償哭' 而連接到補償器的訊號在送至壓電致動器產生相對應：,compensator), cooperate with piezoelectric inductors and piezoelectric actuators to complete the active inductor sub-loop system as shown in Figure 4, where 401 and 402 are piezo inductors and actuators respectively, and 403 are inductors Structure, 408 is the most basic structure of a vibration detection device with a discrete number but a phase that can be designed separately. 4 04, _ and 40 5 are the interface circuit and compensator, and 4 07 is the structure to be measured. I9. Vibration detection device with increasing Λ function but separate phase design. When the vibration detection device is subjected to vibration, the piezoelectric inductor is prepared. The deformation can be obtained through the interface circuit. The vibration signal is connected to the designed compensation cry, and the signal connected to the compensator is corresponding to the piezoelectric actuator :,

第5◦頁 505793Page 5◦ 505793

益函數但相位可分立設計五、發明說明（47) 形，如此一來便完成了主動式增之振動檢測裝置的迴路設計。、/ 應用壓電互補定理，可以輕易的建構出迴4又控制系Benefit function, but the phases can be designed separately. 5. Description of the invention (47) shape, thus completing the circuit design of the active vibration detection device. // Application of the piezoelectric complementarity theorem can be easily constructed

統，不同於傳統的迴授控制理論，本案所沒2之增盈與相位函數可分立設計之振動檢測裝置的設計理念是以波傳理論為基礎進行設計的，所以此一主動式增益與相位函數可分立設計之振動檢測裝置是迴授結構之波傳效應’即抑制結構的振動以達到迴授控制的效應，如第3 9圖’其中有效表面電極3 9 1與3 9 2分別為依據本案所揭示的增盈與相位函數可分立設計之振動檢測裝置，所設計之感應子與致動器於無限域上的示意圖，X。代表致動器之設計原點和感應子設計原點的距離，則感應子所看到的波傳即結構本身受至 =來振動所產生之波傳再減去致動器所提供之反向的波壯罟所以此纟=式增显與相位函數可分立之振動檢牙衣置的感應子方程式改寫成：伽+4伽（52) 其中f s (X )代表感應子有效表面電極的形狀，f “ χ )代表致 =器的表面電極的形狀，其中下標χ。代表致動器的設計原 ”、、“巨感應子設計原點X◦的位置，Α為回授控制回路之增益值^式（52)的含意即結構波傳的權重函數含有一外加回授之權重-A fa ( X )，由於向左向右傳遞的波形振幅由設計原點的挑選而定，且所產生的濾波效應是存在於無限域，所 505793 五、發明說明（48) 以欲把製動器的座標軸移到感應子的的部伤為波傳的振幅而已，則式（4 2 ) q(k) - + £[;; (x)_ 易言之，結構波傳的權重函數被改為 /:〇·)- 4/:(久）所以借由回授控制的原理，波傳的權值得 >主意的是迴授增益可為一固定的的補償器。由式（5 3 )可知，不同於傳改便整個系統原有之特性，本發明所才目位函數分別獨立之振動檢測裝置，特性之中，外加一系列具不同特性的之低通’高通，帶通及帶不通之濾波測裝置。座標輛時，可改寫成·· 所需移動下式：重可以再重放大倍率或統的回授控設計之主動可直接在感增益與相位特性的主動 (53) (54) 新調整，任何型式制系統會式增益與應子結構函數獨立型振動檢Different from the traditional feedback control theory, the design concept of the vibration detection device with separately designed gain and phase functions in this case is based on wave propagation theory, so this active gain and phase The vibration detection device with a separately designed function is the wave propagation effect of the feedback structure ', that is, the effect of suppressing the vibration of the structure to achieve feedback control, as shown in Figure 39, where the effective surface electrodes 3 9 1 and 3 9 2 are respectively based on The vibration detection device disclosed in this case can be designed separately for the gain and phase functions. The schematic diagram of the designed inductor and actuator on the infinite domain, X. Represents the distance between the design origin of the actuator and the design origin of the inductor, then the wave transmission seen by the inductor is the structure itself receiving the wave transmission generated by the coming vibration minus the reverse provided by the actuator Therefore, the formula of the inductor of the vibrating dental set with discrete phase function and phase function can be rewritten as: +4 + (52) where fs (X) represents the shape of the effective surface electrode of the inductor, f "χ) represents the shape of the surface electrode of the actuator, where the subscript χ. represents the design origin of the actuator", "Position of the origin of the giant inductor design X◦, A is the gain value of the feedback control loop ^ The meaning of formula (52) is that the weight function of structure wave transmission contains an additional feedback weight-A fa (X), because the amplitude of the waveform transmitted to the left is determined by the selection of the design origin, and the resulting The filtering effect exists in the infinite domain, so 505793 V. Description of the invention (48) The amplitude of the wave propagation is the partial injury that wants to move the coordinate axis of the brake to the inductor, and then the formula (4 2) q (k) -+ £ [;; (x) _ In other words, the weight function of structure wave transmission is changed to: /: 〇 ·)-4 /: (long time) Therefore, by the principle of feedback control, the weight of wave transmission is worth> the idea is that the feedback gain can be a fixed compensator. As can be seen from equation (5 3), it is different from the original characteristics of the entire system. In addition, a series of low-pass, high-pass, band-pass, and band-pass filter test devices with different characteristics are added to the characteristics of the vibration detection device independently of the eye position function of the present invention. When the vehicle is coordinated, it can be rewritten as · · The following formula for the required movement: The re-magnification or the feedback control design of the system can be directly adjusted to the active gain and phase characteristics. (53) (54) New adjustment. Any type of system can adjust the gain and response. Substructure function independent vibration detection

505793 圖式簡單說明圖式之簡單說明：第1圖：將空間濾波器引入感應子結構所形成的頻寬響應曲線。第2圖：將模態感應子引入感應子結構所形成的頻寬響應曲線。第3圖：增益函數但相位可分立設計之振動檢測裝置的基本設置架構。第4圖：增益函數但相位可分立設計之振動檢測裝置設計原點挑選之示意圖。第5圖：以自由端為設計原點，且具偶函數特性之增益函數但相位可分立設計之振動檢測裝置的示意圖。第6圖··以自由端為設計原點，且具偶函數特性在無限域上的示意圖。第7圖：以固定端為設計原點，且具奇函數特性之增益函數但相位可分立設計之振動檢測裝置的示意圖。第8圖：以固定端為設計原點，且具奇函數特性在無限域上的示意圖。第9圖：以固定端為設計原點所建構完成之空間濾波器在無限域上檢視的示意圖。第1 0圖：以自由端為設計原點所建構完成之空間濾波器在無限域上檢視的示意圖。第1 1圖：應用空間濾波器的疊加特性所設計的相位可分立設計帶通濾波器示意圖。505793 Brief description of the diagram Brief description of the diagram: Figure 1: The bandwidth response curve formed by introducing a spatial filter into the inductive substructure. Figure 2: The bandwidth response curve formed by introducing a modal inductor into the inductor structure. Fig. 3: Basic setup architecture of a vibration detection device with gain function but discrete phase design. Figure 4: Schematic diagram of origin selection of vibration detection device design with gain function but discrete phase design. Fig. 5: Schematic diagram of a vibration detection device with a free end as the design origin and a gain function with even function characteristics but a discrete phase design. Figure 6 ... Schematic diagram with the free end as the design origin and the characteristic of an even function on an infinite domain. Fig. 7: Schematic diagram of a vibration detection device with a fixed end as the design origin and a gain function with odd function characteristics but a discrete phase design. Figure 8: Schematic diagram of the fixed end as the design origin and an infinite domain with odd function characteristics. Figure 9: Schematic view of the spatial filter constructed with the fixed end as the design origin in the infinite domain. Figure 10: Schematic view of the spatial filter constructed on the free end as the design origin in the infinite domain. Figure 11: A phase-separated design of a bandpass filter designed by applying the superposition characteristics of a spatial filter.

第53頁 505793 圖式簡單說明第1 2圖：應用設計之具二次第1 3圖：應用向轉變的裝置第1 4圖：應用域上的示意圖第1 5圖：應用到無限域上的第1 6圖：應用開到無限域上第1 7圖：以懸圖。第1 8圖：以懸圖。第1 9圖：以懸益特性但相位第2 0圖：以懸的帶通濾波器第2 1圖：以懸的南通；慮波器第2 2圖：以懸的高通濾波器第23 、24圖：表面電極設計空間滤波Is的豐加特性所設計的相位可分立以上低通濾波增益特性的示意圖。空間濾波器的疊加特性所設計之不具極化方設計不意圖。映像原理於懸臂樑以把正弦函數展開到無限〇映像原理於自由-自由樑以把正弦函數展開示意圖。映像原理於固定-固定樑上以把正弦函數展的示意圖。臂樑的固定端為空間濾波器設計原點的示意臂樑的自由端為空間濾波器設計原點的示意臂樑為感應子結構所設計之具帶通濾波器增可分立設計的架構圖。臂樑為感應子結構所設計之相位可分立設計頻率響應函數曲線的示意圖。臂樑為感應子結構所設計之相位可分立設計特性架構圖。臂樑為感應子結構所設計之相位可分立設計頻率響應函數曲線示意圖。設計原點不在結構中心或邊界之不對稱有效示意圖。Page 53 505793 Brief description of the diagrams Figure 12: Application design with secondary Figure 13: Application to the transformation of the device Figure 14: Schematic diagram of the application domain Figure 15: The application to the infinite domain Figure 6: The application is opened to the infinite domain. Figure 17: The hanging picture. Figure 18: Overhang. Figure 19: Suspended characteristics but phase Figure 20: Suspended band-pass filter Figure 21: Suspended Nantong; Wave filter 2 Figure 2: Suspended high-pass filter 23, Figure 24: Schematic diagram of the low-pass filtering gain characteristics of the surface electrode design of the spatial filtering Is enrichment characteristics. The design of the superposition characteristic of the spatial filter is not polarized. The design is not intended. The mapping principle is applied to a cantilever beam to expand the sine function to infinity. The mapping principle is applied to a free-free beam to expand the sine function. Schematic diagram of the principle of mapping on a fixed-fixed beam to spread the sine function. The fixed end of the boom is the schematic of the origin of the spatial filter design. The free end of the boom is the schematic of the origin of the spatial filter design. Schematic diagram of phase-separate design frequency response function curve of the boom designed for the inductive substructure. Phase-discrete design feature architecture diagram of the boom designed for the inductive substructure. Schematic diagram of the frequency response function curve of the phase discrete design of the boom designed for the inductive substructure. Asymmetrical effective schematic diagram with design origin not at the center or boundary of the structure.

第54頁 505793 圖式簡單說明第2 5、2 6、2 7圖：應用有效表面電極可疊加特性，來突破設計原點偏向懸臂樑自由端之不對稱有效表面電極設計。第2 8、2 9、3 0、3 1圖：應用有效表面電極可疊加特性，來突破設計原點偏向懸臂樑固定端之不對稱有效表面電極設計。第3 2圖：邊界條件非固定端或自由端之感應子結構示意圖。第3 3圖：針對非固定端及自由端的結構，整合有效表面電極挑選和界面電路應用，所設計完成之增益函數但相位可分立設計的檢測系統。第34圖：針對非固定端及自由端的結構，整合有效表面電極挑選和界面電路應用，所設計之增益函數但相位可分立設計的檢測系統在複數平面上之示意圖。第3 5、3 6、3 7圖：分別表示懸臂樑的第一、第二及第三模態的振形與傳遞波和消散波的效應。第38圖：懸臂樑第二模態感應子的示意圖。第3 9圖：懸臂樑零值第一模態感應子的示意圖。第4 0圖：增益函數但相位可分立設計之檢測系統之基本架構。本發明圖示中所包含之重要元素如下：Page 54 505793 Brief description of the diagrams Figures 2, 5, 6, and 7: Applying the superimposed characteristics of effective surface electrodes to break through the asymmetric effective surface electrode design where the design origin is biased toward the free end of the cantilever beam. Figures 28, 29, 30, 31: Applying the superimposed characteristics of effective surface electrodes to break through the asymmetric effective surface electrode design where the design origin is biased toward the fixed end of the cantilever beam. Figure 32: Schematic diagram of inductive substructure with non-fixed or free end boundary conditions. Figure 33: For the structure of non-fixed and free ends, the integration of effective surface electrode selection and interface circuit applications, the designed gain function, but the phase can be separately designed detection system. Figure 34: Schematic diagram of the detection system with a gain function but a phase-separate design for the structure of non-fixed and free ends that integrates effective surface electrode selection and interface circuit applications. Figures 3, 5, 6, and 7: The shapes of the first, second, and third modes of the cantilever beam, and the effects of the transmitted and dissipated waves, respectively. Figure 38: Schematic diagram of the second modal inductor of a cantilever beam. Fig. 39: Schematic diagram of zero-valued first modal inductor of a cantilever beam. Figure 40: The basic structure of a detection system with a gain function but a discrete phase design. The important elements contained in the diagram of the present invention are as follows:

第55頁 505793 圖式簡單說明不同結構的邊界1 0、2 0 固定端3 0 自由端40 設計原點1 > 335 71 、 141 、 171 、 181 、 191 、 ' 336 、 337 〜338 ' 381 ' 391 電流放大器2 1 1、3 3 1 電荷放大器2 1 2、3 3 2、3 3 3 外加之增益193、213、334 空間選頻感應薄層4 1、5 1、 192 〜261、2 62 ^ 281 >291 401 ' 402 °Page 55 505793 The diagram briefly illustrates the boundaries of different structures 1 0, 2 0 fixed end 3 0 free end 40 design origin 1 > 335 71, 141, 171, 181, 191, '336, 337 ~ 338' 381 ' 391 Current amplifier 2 1 1, 3 3 1 Charge amplifier 2 1 2, 3 3 2, 3 3 3 In addition to gains 193, 213, 334 Spatial frequency selective induction thin layer 4 1, 5 1, 192 to 261, 2 62 ^ 281 > 291 401 '402 °

第5(i頁P. 5 (i

Claims

505793 六、申請專利範圍 1. 一種增益函數但相位可分立設計之一選頻點式量測之檢測裝置，可供量測一待測結構物上之一點之外來振動訊號，該檢測裝置可依需要設計出具不同特性之低通、帶通、頻阻及高通渡波效應的一選頻量測裝置，該檢測裝置之基本架構為：一具有彎曲效應之感應子結構本體，該感應子結構本體可用四次本體結構方程式表示；至少一層具不同渡波特性之一壓電選頻感應子薄層設置於該感應子結構本體上，該壓電選頻感應子薄層可針對該感應子結構之傳遞波、消散波及該感應子結構的邊界條件進行設計，該選頻感應子薄層可依所需挑選一不同寬度，一不同極化或一有效表面電極之一權重函數；一界面電路配合該選頻感應子薄層選定，該界面電路可為一電流放大器，一電荷放大器，一電壓放大器，一補償器或各該界面電路的組合。 2. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為以移動一設計原點與應用其左右對稱特性，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 3. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為以波傳理論與窗函數將有限的感應子結構本體拓展至無限域，形成增益函數具有低通或帶通或頻阻或高通濾波特性。505793 VI. Application for patent scope 1. A detection device with a gain function but a phase-separated design, which is a frequency-selective point-type measurement device that can measure vibration signals outside a point on a structure to be measured. It is necessary to design a frequency selective measurement device with different characteristics of low-pass, band-pass, frequency resistance, and high-pass crossing wave effects. The basic structure of the detection device is: an inductive sub-structure body with a bending effect. The inductive sub-structure body can be used. The quartic body structure equation is expressed; at least one piezoelectric frequency selective inductor thin layer having different crossing wave characteristics is arranged on the induction substructure body, and the piezoelectric frequency selective inductor thin layer can be directed to the transmitted wave of the inductor substructure. The dissipation conditions and the boundary conditions of the inductive substructure are designed. The thin layer of frequency-selective inductive sub-layers can be selected according to the weight function of a different width, a different polarization, or an effective surface electrode; an interface circuit cooperates with the frequency selection The thin layer of the inductor is selected. The interface circuit can be a current amplifier, a charge amplifier, a voltage amplifier, a compensator, or the Combination of surface circuits. 2. The detection device of the frequency-selection point measurement according to the gain function described in item 1 of the scope of patent application but with a phase separated design, wherein the detection device is formed by moving a design origin and applying its left-right symmetry characteristics. The gain function has low-pass or band-pass or frequency-impedance or high-pass filtering. 3. The detection device of the frequency-selective point measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device is a body of limited inductive substructures based on wave propagation theory and window function Extending to the infinite domain, forming a gain function with low-pass or band-pass or frequency-impedance or high-pass filtering characteristics.

第57頁 505793 六、申請專利範圍 4. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為以波傳理論與映像原理將有限的感應子結構本體拓展至無限域，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 5. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置應用正弦和餘弦函數之映像效應將有限的感應子結構本體拓展至無限域，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 6. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置以懸臂樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 7. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置以自由 -自由樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 8. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃以固定-固定樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 9. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為挑選Page 57 505793 VI. Application for patent scope 4. As a gain detection function described in item 1 of the patent application scope but with a phase-separate design, a frequency-selective point-type detection device, wherein the detection device is based on wave propagation theory and The mapping principle extends the limited inductive substructure onto infinite domain, forming a gain function with low-pass or band-pass or frequency-resistance or high-pass filtering characteristics. 5. The detection device of the frequency-selective point-type measurement according to the gain function described in item 1 of the patent scope but with a phase separable design, wherein the detection device applies the mapping effect of the sine and cosine functions to the finite induction substructure ontology Extending to the infinite domain, forming a gain function with low-pass or band-pass or frequency-impedance or high-pass filtering. 6. The detection device of the frequency-selective point-type measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device uses a cantilever beam as an inductive substructure to form a gain function with low pass Or bandpass or frequency resistance or high-pass filtering characteristics. 7. The detection device according to the gain function described in item 1 of the patent application, but with a phase-separate design, which is a frequency-selective point-type measurement device, wherein the detection device uses a free-free beam as an inductive substructure to form a gain function having Low-pass or band-pass or frequency-impedance or high-pass filtering. 8. The detection device of the frequency-selective point type measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device uses a fixed-fixed beam as an induction substructure to form a gain function With low-pass or band-pass or frequency resistance or high-pass filtering characteristics. 9. The detection device of the frequency-selection point measurement according to the gain function described in item 1 of the scope of patent application, but the phase can be discretely designed, wherein the detection device is selected

第58頁 505793 六、申請專利範圍空間濾波器的基底，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 10. 如申請專利範圍第1項所述之益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為應用不同邊界條件的特性與設計原點的挑選，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 11. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置以振動源為一設計原點，形成增益函數具有低通或帶通或頻阻或高通濾波特性而不具時間沿遲。 12. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為結合界面電路與不同的邊界條件，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 13. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置為應用空間濾波器的疊加特性，形成增益函數具有兩次以上的低通或帶通或頻阻或高通濾波特性。 14. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃以挑選表面電極為偶函數，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 15. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃以Page 58 505793 VI. Scope of patent application The base of the spatial filter that forms a gain function with low-pass or band-pass or frequency-impedance or high-pass filtering characteristics. 10. The detection device according to the benefit function described in item 1 of the scope of patent application, but with a phase-separate design, which is a frequency-selection point-type measurement device, wherein the detection device is selected by applying characteristics of different boundary conditions and design origins. The gain function has low-pass or band-pass or frequency-impedance or high-pass filtering. 11. The detection device of the frequency-selection point type measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device uses a vibration source as a design origin to form a gain function with low pass Or band-pass or frequency-impedance or high-pass filtering without delay. 12. The detection device of the frequency-selective point-type measurement according to the gain function described in item 1 of the patent application but with a phase separated design, wherein the detection device is a combination of interface circuits and different boundary conditions to form a gain function with low Pass or band pass or frequency resistance or high pass filtering characteristics. 13. The detection device of the frequency-selective point-type measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device is a superposition characteristic of applying a spatial filter, and the gain function is formed twice. The above low-pass or band-pass or frequency-impedance or high-pass filtering characteristics. 14. The detection device of the frequency-selective point measurement according to the gain function described in item 1 of the scope of patent application but with a phase separable design, wherein the detection device selects a surface electrode as an even function and forms a gain function with a low pass Or bandpass or frequency resistance or high-pass filtering characteristics. 15. A detection device with a gain function as described in item 1 of the scope of patent application, but with a discrete phase design, which is a frequency selective point measurement, wherein the detection device is based on

第59頁 505?93 六、申請專利範圍懸臂樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 16. 如申請專利範圍第1 5項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該懸臂樑乃以自由端為一設計原點之一具偶函數特性，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 17. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃以自由-自由樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 18. 如申請專利範圍第1 7項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該自由-自由樑乃以自由端為設計原點之具偶函數特性，形成增益函數具有低通或帶通或頻阻或高通濾、波特性。 19. 如申請專利範圍第1項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃應用迴授控制理論與壓電材料的互補特性，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 2 0. 如申請專利範圍第1 9項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃由挑選不同濾波特性之感應子與致動器，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 21. 如申請專利範圍第2 0項所述之增益函數但相位可分立設計之一選頻點式量測之檢測裝置，其中該檢測裝置乃在Page 59 505? 93 6. Scope of patent application Cantilever beam is an inductive sub-structure, forming a gain function with low-pass or band-pass or frequency-resistance or high-pass filtering characteristics. 16. The detection device of the frequency-selective point-type measurement according to the gain function described in item 15 of the scope of patent application but with a phase separable design, wherein the cantilever beam has a free function with a free end as a design origin and an even function Characteristics, forming a gain function with low-pass or band-pass or frequency-resistance or high-pass filtering characteristics. 17. The detection device according to the gain function described in item 1 of the patent application, but with a phase-separate design, which is a frequency selective point measurement, wherein the detection device uses a free-free beam as an inductive substructure to form a gain function. With low-pass or band-pass or frequency resistance or high-pass filtering characteristics. 18. The detection device of the frequency-selective point-type measurement according to the gain function described in item 17 of the scope of patent application but with a phase separable design, wherein the free-free beam is a dual function with the free end as the design origin. Characteristics, forming a gain function with low-pass or band-pass or frequency-resistance or high-pass filtering and wave characteristics. 19. The detection device of the frequency-selective point measurement according to the gain function described in item 1 of the scope of patent application but with a phase separated design, wherein the detection device is based on the complementary characteristics of the feedback control theory and the piezoelectric material to form The gain function has low-pass or band-pass or frequency-impedance or high-pass filtering. 2 0. The detection device of the frequency-selective point-type measurement according to the gain function described in item 19 of the scope of patent application, but the phases can be separated, wherein the detection device is made by selecting inductors and actuators with different filtering characteristics. , Forming a gain function with low-pass or band-pass or frequency resistance or high-pass filtering characteristics. 21. A detection device with a gain-selective function as described in item 20 of the scope of patent application, but with a phase that can be separated, wherein the detection device is at

第60頁 505793 六、申請專利範圍迴授控制中加入補償器，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 22. 一種增益函數但相位可分立設計之震動檢測裝置，係一感應子為量測一柔性結構全面或部份之振動訊號，該檢測裝置可依所需設計出具不同特性之低通、帶通、頻阻及高通濾波效應的一選頻量測裝置，該檢測裝置之基本架構為：一具有彎曲效應之一柔性待測結構本體，該柔性待測結構本體可用一四次本體結構方程式表示；至少一層具不同濾波特性之一壓電選頻感應子薄層設置於該待測結構本體上，該壓電選頻感應子薄層可針對該感應子結構之傳遞波、消散波及該感應子結構的邊界條件進行設計，該選頻感應子薄層可依所需挑選一不同寬度，一不同極化或一有效表面電極之一權重函數；一界面電路配合該選頻感應子薄層選定，該界面電路可為一電流放大器，一電荷放大器，一電壓放大器，一補償器或各該界面電路的組合。 23. 如申請專利範圍第2 2項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置為以移動一設計原點與應用其左右對稱特性，形成增益函數具有低通或帶通或頻阻或高通滤波特性。 24. 如申請專利範圍第2 2項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置為以波傳理論與窗函數將有限的感應子結構本體拓展至無限域，形成增益函Page 60 505793 6. Scope of patent application A compensator is added to the feedback control to form a gain function with low-pass or band-pass or frequency resistance or high-pass filtering characteristics. 22. A vibration detection device with gain function but separate phase design. It is an inductor to measure the full or partial vibration signal of a flexible structure. The detection device can be designed with low-pass and band-pass with different characteristics as required. A frequency-selective measurement device with frequency resistance and high-pass filtering effects. The basic structure of the detection device is: a flexible test structure body with a bending effect. The flexible test structure body can be represented by a four-times body structure equation; At least one piezoelectric frequency selective inductor thin layer with different filtering characteristics is disposed on the body of the structure under test. The piezoelectric frequency selective inductor thin layer can be used for the transmitted wave, the dissipative wave and the inductor substructure of the inductor substructure. The boundary conditions of the frequency selective sublayer can be selected according to the needs of a different width, a different polarization or a weight function of an effective surface electrode; an interface circuit selected in conjunction with the frequency selective sublayer, the The interface circuit may be a current amplifier, a charge amplifier, a voltage amplifier, a compensator, or a combination of the interface circuits. 23. The vibration detection device with a gain function as described in item 22 of the scope of patent application, but with discrete phases, wherein the detection device is to move a design origin and apply its left-right symmetry characteristic to form a gain function with low-pass or Bandpass or frequency-impedance or high-pass filtering. 24. The vibration detection device with gain function but phase separation design as described in item 22 of the scope of patent application, wherein the detection device is based on the wave propagation theory and window function to extend the finite inductive substructure onto the infinite domain to form Gain function

第61頁 505793 六、申請專利範圍數具有低通或 2 5· 如申請專設計之震動檢像原理將有限轟數具有低通 26. 如申請專設計之震動檢數之映像效應成增盈函數具 27. 如申請專設計之震動檢結構物，形成特性。帶通或頻阻利範圍第2 2 測裝置，其的感應子結或帶通或頻利範圍第2 2 測裝置，其將有限的感有低通或帶利範圍第2 6 測裝置，其增益函數具或高通濾波項所述之立曾中該檢測裝構本體拓展阻或高通濾項所述之增中該檢測裝應子、结4 t 通戒頻阻或項所述之增中該檢測裝有低帶特性。盈函數但相置為以波傳至無限域，波特性。益函數但相置應用正弦體拓展至無高通攄波特盈函數但相置以懸臂樑通或頻阻或位可分立理論與映形成增益位可分立和餘弦函限域，形性。位可分立為感應子向通）慮波 2 8 ·如申請專利範圍第2 6項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置以自由—自由樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 2 9·如申請專利範圍第2 β項戶斤述之增盈函數但相位可分立設計之震動檢測裝置，其中該檢測裝置乃以固定—固定樑為感應子結構物，形成增益濟數具有低通或帶通或頻阻或高通濾波特性。 3 0.如申請專利範圍第2 6項戶斤述之增盈函數但相位可分立設計之震動檢測裝置，其中該檢測裝置為挑選空間濾波器的基底，形成增益函數具有低通或帶通或頻阻或高通濾波 505793 六、申請專利範圍特性。 31. 如申請專設計之震動檢件的特性與設通或頻阻或高 3 2.如申請專設計之震動檢原點，形成增性而不具時間 33. 如申請專設計之震動檢不同的邊界條高通濾波特性 34. 如申請專設計之震動檢的疊加特性，濾波特性。 3 5. 如申請專設計之震動檢為偶函數，形波特性。 36. 如申請專設計之震動檢子結構物，形利範圍第2 2項所述之增測裝置，其中該檢測裝計原點的挑選，形成增通濾波特性。利範圍第2 2項所述之增測裝置，其中該檢測裝益函數具有低通或帶通沿遲。利範圍第2 2項所述之增測裝置，其中該檢測裝件，形成增益函數具有〇利範圍第2 2項所述之增測裝置，其中該檢測裝形成增益函數具有低通利範圍第2 2項所述之增測裝置，其中該檢測裝成增益函數具有低通或利範圍第2 2項所述之增測裝置，其中該檢測裝成增益函數具有低通或益函數但相位可分立置為應用不同邊界條益函數具有低通或帶益函數但相位可分立置以振動源為一設計或頻阻或高通濾波特益函數但相位可分立置為結合界面電路與低通或帶通或頻阻或益函數但相位可分立置為應用空間濾波器或帶通或頻阻或高通益函數但相位可分立置乃以挑選表面電極帶通或頻阻或高通濾益函數但相位可分立置乃以懸臂標為感應帶通或頻阻或高通濾Page 61 505793 6. The number of patent applications has a low pass or 2 5 · If the application of a specially designed vibration detection principle will have a limited number of low-pass 26. If the application of a specially designed vibration detection, the imaging effect becomes a gain function 27. If you apply for a specially designed vibration inspection structure, form characteristics. Band-pass or frequency-impedance range No. 2 2 measuring device, its inductive junction or band-pass or frequency-range range No. 2 2 measuring device, which will have a limited sense with a low-pass or band-range No. 2 6 measuring device, which The gain function or the high-pass filter term described in the test device body expansion resistance or the high-pass filter term increase the detection device, the 4 t pass or frequency resistance or the increase described in the term. Detection is equipped with low-band characteristics. The profit function but the phase is set to pass to the infinite domain with waves, the wave characteristics. The sine body is applied to the benefit function, but the phase is extended to no high-pass 摅 Potter. The profit function is but cantilevered to pass or the frequency resistance or the potential is discrete. The theory and mapping form the gain, the discrete, and the cosine function. The position can be separated into the direction of the inductor.) Wave 2 8 · The vibration detection device with the gain function as described in item 26 of the patent application scope but with discrete phases, wherein the detection device uses the free-free beam as the inductive substructure. It has low-pass or band-pass or frequency-impedance or high-pass filtering characteristics. 2 9 · If the gain function described in item 2 of the patent scope of the patent application is a vibration detection device with a discrete phase design, the detection device uses a fixed-fixed beam as an inductive sub-structure, which has a low gain. Pass or band pass or frequency resistance or high pass filtering characteristics. 30. If the gain function described in item 26 of the patent application scope is a vibration detection device with a discrete phase design, the detection device is the basis for selecting a spatial filter to form a gain function with low-pass or band-pass or Frequency-resistance or high-pass filtering 505793 6. Characteristics of patent application scope. 31. If you apply for a specially designed vibration inspection part, the characteristics and settings or frequency resistance or high 3 2. If you apply for a specially designed vibration inspection origin, form the increase without time 33. If you apply for a specially designed vibration inspection different Boundary bar high-pass filtering characteristics 34. For example, the superimposed characteristics of vibration detection applied for specially designed, filtering characteristics. 3 5. If the specially designed vibration detection is an even function, the wave characteristics. 36. If you apply for a specially designed vibration detector structure, the augmentation device described in item 22 of the scope of interest, wherein the selection of the origin of the inspection device forms the enhancement filtering characteristics. The increase detection device according to Item 22, wherein the detection benefit function has a low-pass or band-pass edge. The increasing measuring device according to item 22 of the profit range, wherein the detecting device forms a gain function having the increasing measuring device according to item 22 of the profit range, wherein the detecting device forms a gain function having a low gain range. The increase measurement device according to item 2, wherein the detection is configured as a gain function having a low pass or profit range. The increase measurement device according to item 22, wherein the detection is configured as a gain function having a low pass or benefit function but the phase is Discrete application is the application of different boundary stripe functions with low-pass or band-effect functions, but the phases can be separated. The vibration source is a design or frequency resistance or high-pass filtering special function, but the phases can be separated to combine the interface circuit with the low-pass or band. Pass or frequency resistance or benefit function but phase can be separated to apply spatial filter or bandpass or frequency resistance or high pass benefit function but phase can be separated to select surface electrode bandpass or frequency resistance or high pass filter function but phase can be separated Discrete placement is based on cantilever marking as inductive bandpass or frequency resistance or high-pass filter

第63頁 505793 六、申請專利範圍波特性。 37. 如申請專利範圍第3 6項所述之增益函數但相位可分立設計之震動檢測裝置，其中該懸臂樑乃以自由端為一設計原點之一具偶函數特性，形成增益函數具有低通或帶通或頻阻或高通滤波特性。 3 8. 如申請專利範圍第2 2項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置乃以自由-自由樑為感應子結構物，形成增益函數具有低通或帶通或頻阻或高通濾、波特性。 3 9. 如申請專利範圍第3 8項所述之增益函數但相位可分立設計之震動檢測裝置，其中該自由-自由樑乃以自由端為設計原點之具偶函數特性，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 40. 如申請專利範圍第2 2項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置乃應用迴授控制理論與壓電材料的互補特性，形成增益函數具有低通或帶通或頻阻或高通滤波特性。 41. 如申請專利範圍第4 0項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置乃由挑選不同濾、波特性之感應子與致動器，形成增益函數具有低通或帶通或頻阻或高通濾波特性。 42. 如申請專利範圍第4 1項所述之增益函數但相位可分立設計之震動檢測裝置，其中該檢測裝置乃在迴授控制中加入補償器，形成增益函數具有低通或帶通或頻阻或高通濾Page 63 505793 VI. Patent application scope Wave characteristics. 37. The vibration detection device with a gain function as described in item 36 of the scope of patent application, but with discrete phases, wherein the cantilever beam has a free function as one of the design origins and has an even function, forming a gain function with low Pass or band pass or frequency resistance or high pass filtering characteristics. 3 8. The vibration detection device with gain function as described in item 22 of the scope of patent application, but with separate phases, wherein the detection device uses a free-free beam as an inductive sub-structure to form a gain function with low-pass or band Pass or frequency resistance or high pass filtering, wave characteristics. 3 9. The vibration detection device with a gain function as described in item 38 of the scope of patent application, but with separate phases, wherein the free-free beam has a dual function characteristic with the free end as the design origin, and the gain function has Low-pass or band-pass or frequency-impedance or high-pass filtering. 40. The vibration detection device with a gain function as described in item 22 of the scope of patent application, but with discrete phases, wherein the detection device uses the complementary characteristics of feedback control theory and piezoelectric materials to form a gain function with low-pass or Bandpass or frequency-impedance or high-pass filtering. 41. The vibration detection device with a gain function as described in item 40 of the scope of the patent application, but with a discrete phase design, wherein the detection device is formed by selecting inductors and actuators with different filtering and wave characteristics to form a gain function. Low-pass or band-pass or frequency-impedance or high-pass filtering. 42. A vibration detection device with a gain function as described in item 41 of the scope of patent application, but with discrete phases, wherein the detection device is added with a compensator in the feedback control to form a gain function with low-pass or band-pass or frequency. Blocking or high-pass filtering

第64頁 505793 六、申請專利範圍波特性。〇 Φ 第65頁Page 64 505793 VI. Patent application scope Wave characteristics. 〇 Φ page 65