JP2008190645A - Vibration reducing mechanism and its specification setting method - Google Patents

Vibration reducing mechanism and its specification setting method Download PDF

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JP2008190645A
JP2008190645A JP2007026477A JP2007026477A JP2008190645A JP 2008190645 A JP2008190645 A JP 2008190645A JP 2007026477 A JP2007026477 A JP 2007026477A JP 2007026477 A JP2007026477 A JP 2007026477A JP 2008190645 A JP2008190645 A JP 2008190645A
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vibration
pendulum
natural frequency
additional
additional mass
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Kazuhiko Isoda
和彦 磯田
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Shimizu Construction Co Ltd
Shimizu Corp
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F7/00—Vibration-dampers; Shock-absorbers
    • F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Vibration Prevention Devices (AREA)
  • Buildings Adapted To Withstand Abnormal External Influences (AREA)

Abstract

<P>PROBLEM TO BE SOLVED: To provide an effective and appropriate vibration reducing mechanism which can be simply installed on a structure, and to provide its specification setting method. <P>SOLUTION: In the vibration reducing mechanism, an added vibration system is added to a structure 1 as a vibration reduced object for vibrating an added mass 2 as a pendulum to synchronize the natural frequency of the added vibration system with the natural frequency of the structure. A shaft spring 5 which is expanded with the vibration of the pendulum to vary the length of the pendulum is incorporated into the added vibration system and a damping device 6 is installed in parallel to the shaft spring so that the natural frequency of the pendulum which is determined by the length of the pendulum and the acceleration of gravity during resting, is synchronized with the natural frequency of the structure to adjust the frequency of the added vibration system which is determined by the added mass and the shaft spring, to be twice the natural frequency of the pendulum. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

本発明は建物等の構造物を対象とする振動低減機構およびその諸元設定方法に関する。   The present invention relates to a vibration reduction mechanism for a structure such as a building and a specification setting method thereof.

構造物の振動を低減するための機構として、たとえば特許文献１に示されているような動吸振器がある。これは所謂チューンド・マス・ダンパー（Tunned Mass Danper：ＴＭＤ）と称されるもので、振動低減対象の構造物にバネおよびダンパーを介して付加マス（付加質量）を相対振動可能に結合し、付加マスとバネにより定まる固有振動数を構造物の固有振動数に同調させる、つまり付加振動系の固有振動数を主振動系のそれに一致させるように調整することにより共振点近傍における振動を吸収して応答を低減するものである。
特開昭６３−１５６１７１号公報 As a mechanism for reducing the vibration of a structure, there is a dynamic vibration absorber as disclosed in Patent Document 1, for example. This is the so-called Tuned Mass Danper (TMD), which is connected to the structure subject to vibration reduction by adding an additional mass (additional mass) via a spring and damper so as to allow relative vibration. The natural frequency determined by the mass and the spring is tuned to the natural frequency of the structure, that is, by adjusting the natural frequency of the additional vibration system to match that of the main vibration system, the vibration near the resonance point is absorbed. The response is reduced.
JP-A 63-156171

特許文献１に示されるような従来一般のＴＭＤは、付加質量を構造物の頂部において水平各方向にスライド可能に設置することが基本であって、通常はＸ方向とＹ方向の双方に自由にスライドしかつ自ずと復元する機構のスライドベース上に付加質量を設置するようにしている。そして、そのためのスライドベースはＸ方向とＹ方向のレールを重ねた構成とされ、かつバネとダンパーとを両方向に作動するように組み込むという複雑な機構のものとなり、そのためにＴＭＤ装置全体が複雑かつ高価とならざるを得ないものであった。   The conventional general TMD as shown in Patent Document 1 is basically installed such that the additional mass is slidable in each horizontal direction at the top of the structure, and usually free in both the X direction and the Y direction. Additional mass is placed on the slide base of the mechanism that slides and restores itself. For this purpose, the slide base has a structure in which rails in the X direction and the Y direction are overlapped, and has a complicated mechanism in which a spring and a damper are assembled so as to operate in both directions. It was unavoidable.

なお、上記のような付加質量を水平各方向にスライドさせるのではなく振り子として振動させる振り子型のＴＭＤも考えられる。
図５はそのような振り子型のＴＭＤの原理を示すモデルであって、振動低減対象の主振動系としての構造物１（図では柱と頂部梁とによる簡略なフレームとして示してある）に対して、付加質量２を吊り材３によって吊り下げることによって振り子として振動するような付加振動系を付加し、その付加質量２の振り子としての固有振動数を構造物１の固有振動数に同調させるようにしたものである。
これによれば、一般的なＴＭＤと同様に付加質量２の振り子振動によって構造物１の共振点近傍の応答を低減できるし、地震による加振入力のみならず風などの加振力による振動も効果的を低減できる効果が期待できる。
しかし、このような振り子型のＴＭＤにおいても、上述した一般的なＴＭＤと同様に外力が大きくなると付加質量２の水平変位（振幅）が過大になるので、図示しているように付加質量２の水平変位を抑制し減衰させるための減衰装置４（ダンパー）が不可欠である。つまり、振り子型といえども付加質量２を単に振り子として設置するだけではなく、その振り子振動を規制するための減衰装置４を付加質量２と構造物１との間に介装する必要がある。しかも全方向の振動を減衰させるためには減衰装置４を少なくともＸ方向とＹ方向の双方に対して設置しなければならないし、振り子長さが長い場合や振幅が大きい場合には建築計画上から減衰装置４の設置自体が困難な場合もあり、その点では特許文献１に示されるような一般的なＴＭＤと同様に、あるいはそれ以上に、複雑な機構とならざるを得ない。 Note that a pendulum type TMD that vibrates as a pendulum instead of sliding the additional mass in the horizontal direction as described above is also conceivable.
FIG. 5 is a model showing the principle of such a pendulum type TMD, and for the structure 1 (shown as a simple frame with columns and top beams) as a main vibration system to be reduced in vibration. Thus, an additional vibration system that vibrates as a pendulum is added by suspending the additional mass 2 with the suspension member 3 so that the natural frequency of the additional mass 2 as a pendulum is synchronized with the natural frequency of the structure 1. It is a thing.
According to this, the response in the vicinity of the resonance point of the structure 1 can be reduced by the pendulum vibration of the additional mass 2 as in general TMD, and not only the vibration input due to the earthquake but also the vibration due to the vibration force such as the wind. The effect which can reduce effectiveness can be expected.
However, even in such a pendulum type TMD, the horizontal displacement (amplitude) of the additional mass 2 becomes excessive as the external force increases, as in the general TMD described above. The damping device 4 (damper) for suppressing and damping the horizontal displacement is indispensable. That is, even if it is a pendulum type, it is necessary not only to install the additional mass 2 as a pendulum but to interpose the damping device 4 for regulating the pendulum vibration between the additional mass 2 and the structure 1. Moreover, in order to attenuate the vibrations in all directions, the damping device 4 must be installed at least in both the X direction and the Y direction. If the pendulum length is long or the amplitude is large, it is necessary from the architectural plan. In some cases, it is difficult to install the damping device 4. In that respect, the mechanism is inevitably complicated as in the case of a general TMD as disclosed in Patent Document 1.

上記事情に鑑み、本発明は構造物に簡略に設置することのできる有効適切な振動低減機構とその諸元設定方法を提供することを目的としている。   In view of the above circumstances, an object of the present invention is to provide an effective and appropriate vibration reduction mechanism that can be simply installed in a structure and a specification setting method thereof.

本発明は、振動低減対象の構造物に付加質量を振り子として振動させる付加振動系を付加して、該付加振動系の固有振動数を構造物の固有振動数に同調させることによって振動低減効果を得る振動低減機構、およびその諸元設定方法であって、前記付加振動系に、振り子振動により半径方向に伸縮して振り子長さを可変とする軸バネを組み込むとともに、該軸バネに並列に減衰装置を設置し、静止時の振り子長さと重力加速度によって定まる振り子の固有振動数を構造物の固有振動数と同調させるとともに、付加質量と軸バネにより定まる付加振動系の振動数を振り子の固有振動数の２倍に調整するようにしたことを特徴とするものである。   The present invention adds an additional vibration system that vibrates an additional mass as a pendulum to a structure that is subject to vibration reduction, and synchronizes the natural frequency of the additional vibration system with the natural frequency of the structure. A vibration reduction mechanism to be obtained and a specification setting method thereof, wherein a shaft spring that can be expanded and contracted in a radial direction by pendulum vibration to change a pendulum length is incorporated in the additional vibration system, and is attenuated in parallel with the shaft spring. Install the device and synchronize the natural frequency of the pendulum determined by the pendulum length and gravitational acceleration when stationary with the natural frequency of the structure, and the frequency of the additional vibration system determined by the additional mass and shaft spring. It is characterized in that it is adjusted to twice the number.

本発明は振り子型のＴＭＤの範疇に属するものであるが、振り子長さを可変とする軸バネとその減衰装置を備えたことにより、水平方向振動に効く減衰装置を省略でき、したがって従来一般の各種のＴＭＤに比べて装置全体の構成の簡略化と小型軽量化を実現できるし、構造物に対してより容易にかつコンパクトに設置することが可能であり、振り子が長い場合や振幅が大きい場合にも容易に対応可能である。
また、付加質量の振幅が大きくなるほど減衰効果が高くなり、したがって大きな入力まで安定的に作動するとともに、過大な入力に対する付加質量の衝突防止や付加質量を支持する部材の疲労負荷低減にも効果的であり、信頼性の高い制振機構とすることができる。
しかも、構造物の水平方向の振動を付加質量の円周方向振動からさらに半径方向振動に変換して増幅し、そのように大きく増幅した振幅に対して減衰装置により振動エネルギーを吸収する機構であるので、非常に効率の高い合理的な制振システムであるといえる。 Although the present invention belongs to the category of the pendulum type TMD, the provision of the shaft spring that makes the pendulum length variable and the damping device thereof eliminates the damping device that works in the horizontal direction. Compared with various TMDs, the overall configuration of the device can be simplified and reduced in size and weight, and it can be installed more easily and compactly with respect to the structure. When the pendulum is long or the amplitude is large Can be easily accommodated.
In addition, the larger the added mass amplitude, the higher the damping effect. Therefore, it operates stably up to a large input, and is effective in preventing the added mass from colliding with an excessive input and reducing the fatigue load of the member supporting the added mass. Therefore, a highly reliable vibration damping mechanism can be obtained.
In addition, the horizontal vibration of the structure is amplified by converting the additional mass from the circumferential vibration to the radial vibration, and the vibration energy is absorbed by the damping device for the greatly amplified amplitude. Therefore, it can be said that it is a very efficient and rational vibration control system.

図１は本発明の振動低減機構の一実施形態を示すものである。これは、図５に示した振り子型のＴＭＤを基本とするものであるが、従来の振り子型のＴＭＤにおいては付加質量２と構造物１との間に介装する必要のあった減衰装置４を省略し、それに代えて、付加質量２を吊り下げる吊り材３に軸バネ５を介装するとともに、その軸バネ５と並列に減衰装置６を設置したものである。   FIG. 1 shows an embodiment of the vibration reducing mechanism of the present invention. This is based on the pendulum type TMD shown in FIG. 5, but in the conventional pendulum type TMD, the damping device 4 required to be interposed between the additional mass 2 and the structure 1. The shaft spring 5 is interposed in the suspension member 3 that suspends the additional mass 2, and the damping device 6 is installed in parallel with the shaft spring 5.

上記の軸バネ５は振り子振動に伴って軸方向（半径方向）に伸縮するものであり、したがってこの付加振動系では振り子振動に伴って振り子長さが刻々と変化するものとなる。
また、減衰装置６は振り子振動に伴う軸バネ５の伸縮に対して減衰を与えるもので、公知の各種ダンパー、たとえばオイルダンパー、シリコンオイル粘性ダンパー、粘弾性ダンパー、摩擦ダンパー等を任意に採用可能である。 The shaft spring 5 expands and contracts in the axial direction (radial direction) along with the pendulum vibration. Therefore, in this additional vibration system, the pendulum length changes every moment along with the pendulum vibration.
Further, the damping device 6 provides damping against the expansion and contraction of the shaft spring 5 due to the pendulum vibration, and various known dampers such as an oil damper, a silicone oil viscous damper, a viscoelastic damper, a friction damper, etc. can be arbitrarily employed. It is.

本実施形態の振動低減機構も、基本的には図５に示したような通常の振り子型のＴＭＤと同様に、静止時における振り子長さと重力加速度により定まる振り子の固有振動数（円周方向の固有振動数）を構造物１の固有振動数と同調させるものであるが、それに加えて、付加質量２と軸バネ５により定まる付加振動系の半径方向の振動数を振り子の固有振動数の２倍に調整するものである。
つまり、構造物１の１次固有角振動数をω１、静止時の振り子長さをＬ、重力加速度をｇ、付加質量２の質量をｍ、軸バネ５のバネ定数ｋ０とした場合、次式が成り立つように調整する。 The vibration reduction mechanism of the present embodiment is basically the same as the normal pendulum type TMD as shown in FIG. 5, and the natural frequency of the pendulum (circumferential direction) determined by the pendulum length and gravitational acceleration at rest. The natural frequency) is synchronized with the natural frequency of the structure 1, but in addition, the radial frequency of the additional vibration system determined by the additional mass 2 and the shaft spring 5 is 2 of the natural frequency of the pendulum. It is to adjust to double.
That is, when the primary natural angular frequency of the structure 1 is ω 1 , the pendulum length at rest is L, the gravitational acceleration is g, the mass of the additional mass 2 is m, and the spring constant k 0 of the shaft spring 5 is Adjust so that the following equation holds.

Figure 2008190645
Figure 2008190645

したがって本実施形態の振動低減機構では、基本的には従来一般のスライド型のＴＭＤや振り子型のＴＭＤと同様に、構造物１の地震や風による水平振動（特に共振点近傍の振動）により付加質量２の振動（円周方向の振り子振動）が励起され、構造物１の振動エネルギーが付加質量２に移動することで振動を有効に低減できるものである。
加えて、本実施形態の振動低減機構では、付加質量２が円周方向に振り子運動で振動した際にはその周期の１／２の周期で変動する遠心力によって軸バネ５が伸縮し、それによって付加質量２は同時に半径方向にも振動するものとなる。
そこで、その半径方向の振動数を円周方向に振動する振り子の固有振動数の２倍となるように調整することにより、付加質量２が円周方向に１往復する間に同時に半径方向には２往復して、付加質量２の振動軌跡は図１（ｂ）に示すように略∞状となる。これは、遊具としてのブランコに乗った人が身体を上下させて揺れを減らす場合の重心位置の軌跡に相当し、共振時には上下運動と遠心力とが１／４周期だけ位相ズレを生じていることになる。
その結果、そのような半径方向の振動が構造物１の振動に共振して減衰装置６により効率的に振動エネルギーが吸収され、優れた制振効果が得られるものである。 Therefore, in the vibration reduction mechanism of this embodiment, basically, it is added by horizontal vibration (particularly vibration near the resonance point) of the structure 1 due to an earthquake or wind of the structure 1 as in the conventional general slide type TMD and pendulum type TMD. The vibration of the mass 2 (circumferential pendulum vibration) is excited, and the vibration energy of the structure 1 moves to the additional mass 2 to effectively reduce the vibration.
In addition, in the vibration reducing mechanism of the present embodiment, when the additional mass 2 vibrates in the circumferential direction by the pendulum motion, the shaft spring 5 expands and contracts due to the centrifugal force that fluctuates in a cycle that is half that cycle. Thus, the additional mass 2 simultaneously vibrates in the radial direction.
Therefore, by adjusting the frequency in the radial direction to be twice the natural frequency of the pendulum oscillating in the circumferential direction, the additional mass 2 is simultaneously moved in the radial direction while making one round trip in the circumferential direction. After two reciprocations, the vibration trajectory of the additional mass 2 becomes approximately ∞ as shown in FIG. This is equivalent to the locus of the center of gravity when a person on a swing as a play equipment moves up and down to reduce shaking, and the vertical movement and centrifugal force cause a phase shift by a quarter period at resonance. It will be.
As a result, the vibration in the radial direction resonates with the vibration of the structure 1, and the vibration energy is efficiently absorbed by the damping device 6, so that an excellent damping effect can be obtained.

本実施形態の振動低減機構によれば以下に列挙するような効果が得られる。
図５に示したような通常の振り子型のＴＭＤと比較すると、付加質量２と構造物１との間に水平方向振動に効く減衰装置４（ダンパー）を省略できることから小型軽量の応答低減機構となり、建築計画的にも配置しやすく、ローコストに設置することが可能となる。
特に、通常の振り子型のＴＭＤでは減衰装置４を水平２方向に設置する必要があるが、本実施形態では鉛直方向の軸バネ５に並列に単一の減衰装置６を設置すれば足り、振り子が長い場合や振幅が大きい場合にも容易に対応可能である。
さらに、付加質量２を水平各方向にスライドさせる形式の最も一般的なスライド型のＴＭＤの場合には、付加質量２を全方向に自由にスライドさせるためにＸ方向とＹ方向の２段のレールや両方向のバネとダンパーを組み込んだスライドベースのような複雑な機構を必要とするが、本実施形態ではそれに比べて機構全体を格段に簡略化することが可能である。 According to the vibration reduction mechanism of the present embodiment, the following effects can be obtained.
Compared with a normal pendulum type TMD as shown in FIG. 5, the damping device 4 (damper) that acts on the horizontal vibration can be omitted between the additional mass 2 and the structure 1, so that a small and lightweight response reducing mechanism is obtained. It is easy to arrange in the architectural plan and can be installed at low cost.
In particular, in a normal pendulum type TMD, it is necessary to install the damping device 4 in two horizontal directions, but in this embodiment, it is sufficient to install a single damping device 6 in parallel with the axial spring 5 in the vertical direction. It is possible to easily cope with a long period or a large amplitude.
Furthermore, in the case of the most common slide type TMD of the type in which the additional mass 2 is slid in each horizontal direction, two-stage rails in the X direction and the Y direction in order to freely slide the additional mass 2 in all directions. In addition, a complicated mechanism such as a slide base incorporating a spring and a damper in both directions is required, but in this embodiment, the entire mechanism can be greatly simplified.

また、本実施形態の振動低減機構では、付加質量２の振幅が大きくなるほど減衰効果が高くなるものであり、したがって大きな加振入力では付加質量２の振幅が通常のＴＭＤの場合よりも抑制されることになる。これにより、より大きな入力にまで安定的に作動するとともに、過大な入力に対する付加質量２の衝突防止や付加質量２を支持する部材の疲労負荷低減にも効果的であり、信頼性の高い制振機構とすることができる。換言すると、振り子の振幅が小さいうちは通常のＴＭＤより応答低減効果が小さいが、揺れが問題になり応答低減したいのは振幅が大きいときであるので、本実施形態の機構はそのような場合に有効な振動対策といえる。
しかも、本実施形態の機構は、構造物１の水平方向の振動を付加質量２の円周方向振動からさらに半径方向振動に変換して増幅し、構造物１自体の振幅よりはるかに大きく増幅した振幅に対して減衰装置６により振動エネルギーを吸収する機構であるので、非常に効率の高い合理的な制振システムであるといえる。
但し、本実施形態の機構においても、図５に示した通常の振り子型のＴＭＤにおける水平方向の減衰装置４を省略することなくそのまま設置することしても良く、そのようにすれば通常の振り子型のＴＭＤと同様に小さな振幅に対しても応答低減効果が有効に得られるものとなる。つまり、図５に示したような水平方向の減衰装置４を備えた通常の振り子型のＴＭＤを基本として、それに軸バネ５と鉛直方向の減衰装置６を付加する構成とすれば、小さな振幅から大きな振幅まで充分な応答低減効果が得られるものとなる。 Further, in the vibration reduction mechanism of the present embodiment, the damping effect increases as the amplitude of the additional mass 2 increases, and therefore the amplitude of the additional mass 2 is suppressed more than in the case of normal TMD with a large excitation input. It will be. As a result, stable operation can be achieved up to a larger input, and it is effective in preventing the collision of the additional mass 2 against an excessive input and reducing the fatigue load of the member supporting the additional mass 2. It can be a mechanism. In other words, while the amplitude of the pendulum is small, the effect of reducing the response is smaller than that of normal TMD. However, the swing is a problem and the response is to be reduced when the amplitude is large. This is an effective vibration countermeasure.
Moreover, the mechanism of the present embodiment converts the horizontal vibration of the structure 1 from the circumferential vibration of the additional mass 2 to a further radial vibration and amplifies it, and amplifies it much larger than the amplitude of the structure 1 itself. Since the vibration energy is absorbed by the damping device 6 with respect to the amplitude, it can be said that this is a very efficient and efficient vibration damping system.
However, also in the mechanism of the present embodiment, the horizontal attenuation device 4 in the normal pendulum type TMD shown in FIG. 5 may be installed as it is without being omitted. As in the case of TMD, a response reduction effect can be effectively obtained even for a small amplitude. That is, if a configuration in which a shaft spring 5 and a vertical damping device 6 are added to a normal pendulum type TMD provided with a horizontal damping device 4 as shown in FIG. A sufficient response reduction effect can be obtained up to a large amplitude.

また、本実施形態の振動低減機構も、基本的には従来一般のＴＭＤと同様に構造物１の共振による応答増大を防止する機構であるので、共振点近傍での応答変位や反力を大きく低減することができ、地下基礎部への負担軽減や浮き上がり防止にも効果的であるし、特に１次モードの振動を大きく低減できるので地震のみならず風揺れの低減効果も有効に発揮することができる。
勿論、本実施形態の機構における振動数調整作業は、通常の振り子型のＴＭＤにおける振り子長さの調整に加えて軸バネ５の調整を追加するだけで良く、設置後の微調整や諸元変更等にも容易に対応することができる。
さらに、新築構造物のみならず既存構造物を対象とする制振化手法としても好適であるし、特に共振問題を生じている既存構造物に対して本実施形態の機構を建築計画上で支障のない箇所に付加することにより、共振問題を有効に解消することができる。 Also, the vibration reduction mechanism of this embodiment is basically a mechanism that prevents an increase in response due to resonance of the structure 1 as in the conventional general TMD, so that the response displacement and reaction force near the resonance point are greatly increased. It can be reduced, and it is effective for reducing the burden on the underground foundation and preventing lifting. Especially, it can greatly reduce the vibration of the primary mode, so it can effectively reduce not only earthquakes but also wind fluctuations. Can do.
Of course, the frequency adjustment work in the mechanism of the present embodiment only needs to add adjustment of the shaft spring 5 in addition to the adjustment of the pendulum length in the normal pendulum type TMD, and fine adjustment and change of specifications after installation. Etc. can be easily handled.
Furthermore, it is suitable as a vibration control method not only for new structures but also for existing structures. In particular, the mechanism of the present embodiment has an obstacle in building planning for existing structures that are causing resonance problems. The resonance problem can be effectively solved by adding it to the place where there is no.

次に、本実施形態の機構の諸元を設定するための設計手法について以下に説明する。
本実施形態の振動低減機構を備えた構造物１を図１に示すような１質点系の振動モデルとし、主振動系としての構造物１の諸元が、質量Ｍ、水平バネ定数Ｋ、１次固有角振動数ω１、減衰係数ｃ、水平方向の変位ｘとする。
付加振動系である振り子としての諸元が、付加質量２の質量ｍ、静止時の振り子長さＬ、軸バネ５のバネ定数ｋ０、減衰装置６の減衰係数ｃ０とする。
また、付加質量２の円周方向振動による鉛直方向からの傾斜角θ、半径方向振動による静止位置からの半径方向変位ｕ、重力加速度ｇとし、加振入力として風などによる次式の加振力f(t)を想定する。 Next, a design method for setting the specifications of the mechanism of the present embodiment will be described below.
The structure 1 provided with the vibration reduction mechanism of this embodiment is a one-mass system vibration model as shown in FIG. 1, and the specifications of the structure 1 as the main vibration system are mass M, horizontal spring constant K, 1 The second natural angular frequency ω 1 , the damping coefficient c, and the horizontal displacement x are assumed.
The specifications of the pendulum as an additional vibration system are the mass m of the additional mass 2, the pendulum length L at rest, the spring constant k 0 of the shaft spring 5, and the damping coefficient c 0 of the damping device 6.
Further, the inclination angle θ from the vertical direction due to the circumferential vibration of the additional mass 2, the radial displacement u from the stationary position due to the radial vibration, and the gravitational acceleration g, and the excitation force of the following expression by wind as the excitation input Assume f (t).

Figure 2008190645
Figure 2008190645

構造物１の加振方向変位をｘとし、静止座標系（絶対変位）における釣合式は次式となる。   The displacement in the vibration direction of the structure 1 is x, and the balance equation in the stationary coordinate system (absolute displacement) is as follows.

Figure 2008190645
Figure 2008190645

付加質量２の円周方向（振り子の振動方向）の釣合いから次式が成り立つ。なお、次式における左辺第３項はコリオリの力を表し、半径方向の速度に比例した円周方向力として作用する。   From the balance of the additional mass 2 in the circumferential direction (vibration direction of the pendulum), the following equation is established. Note that the third term on the left side in the following equation represents the Coriolis force and acts as a circumferential force proportional to the radial velocity.

Figure 2008190645
Figure 2008190645

付加質量２の半径方向（振り子の中心から放射方向）の釣合いから、静止状態を基準として次式が成り立つ。次式における左辺第５項は遠心力を表し、角速度の２乗に比例する。   From the balance of the additional mass 2 in the radial direction (radial direction from the center of the pendulum), the following equation holds based on the stationary state. The fifth term on the left side in the following equation represents centrifugal force and is proportional to the square of the angular velocity.

Figure 2008190645
Figure 2008190645

上記各式からθ、ｕ、ｘを解析することにより本実施形態の機構の諸元を設定することができる。なお、これは線形ではないので単純には解けない（θが微小な場合でも高次の項があるため線形計算とはならない）が、連立微分方程式として時刻歴応答解析して初期値を与えることにより容易に解析することができる。   By analyzing θ, u, and x from the above equations, the specifications of the mechanism of this embodiment can be set. Since this is not linear, it cannot be solved simply (even if θ is very small, there is a high-order term, so it is not a linear calculation), but the initial value is obtained by analyzing the time history response as a simultaneous differential equation. Can be easily analyzed.

なお、本実施形態の振動低減機構は、構造物１の水平方向の振動に伴う振り子の鉛直方向の振動を減衰装置６により吸収し、それによって構造物１の応答を低減させるものであるから、一般的なＴＭＤと同様に付加質量２が大きいほど効果的ではあるが、あまり大きな質量を振り子として設置することは現実的ではなく、通常は構造物１の質量の１〜５％程度とすることが現実的であり、それによっても充分な効果が得られる。
また、付加質量２としては、上記のような振動数の設定が可能であり、そのような振動を許容でき、かつ上記のような所要質量を確保できるものであれば、構造物１内に吊り支持されて設置される各種の設備類や器具類、たとえば建物内に設置される大型のシャンデリア等を利用することも可能である。
また、減衰装置６の減衰係数ｃ０の最適値は付加質量２によって変化し、付加質量２が大きくなるほど減衰係数ｃ０の最適値も大きくなるが、通常は構造物１の１次固有角振動数ω１における減衰定数ｈは下記の範囲で最適値を解析シミュレーションによって定めれば良い。 In addition, since the vibration reduction mechanism of this embodiment absorbs the vibration in the vertical direction of the pendulum accompanying the vibration in the horizontal direction of the structure 1 by the damping device 6, thereby reducing the response of the structure 1. Although it is more effective as the additional mass 2 is larger as in general TMD, it is not practical to install a large mass as a pendulum, and it is usually about 1 to 5% of the mass of the structure 1 However, it is realistic and sufficient effects can be obtained.
Further, as the additional mass 2, it is possible to set the frequency as described above, and to suspend it in the structure 1 as long as such vibration can be allowed and the required mass as described above can be secured. It is also possible to use various types of equipment and instruments that are supported and installed, such as a large chandelier installed in a building.
Further, the optimum value of the damping coefficient c 0 of the damping device 6 varies depending on the additional mass 2, and the optimum value of the damping coefficient c 0 increases as the additional mass 2 increases. The optimum value of the attenuation constant h in the number ω 1 may be determined by analysis simulation within the following range.

Figure 2008190645
Figure 2008190645

以上で本発明の一実施形態を説明したが、図２〜図４に他の実施形態を示す。
図２は構造物１上に剛体振り子を設置したものであって、これは吊り材３に代わる支柱７を、重力に代わる復元力となる回転バネ８を介して構造物１上に設置し、その支柱７に軸方向のみに伸縮変形する軸バネ５と減衰装置６を組み込んだものであって、支柱７が剪断変形を生じることなく直線状態を維持したままで円周方向に振り子として振動し、かつその際に軸バネ５の伸縮によって支柱７の全長が伸縮して付加質量２が半径方向にも振動するようにされているものである。
図３は、図２に示したものと同様に軸バネ５および減衰装置６を組み込んだ支柱７によって付加質量２を半径方向にのみ振動自在に支持するとともに、その全体をケース内に収容して揺動体９を構成し、その揺動体９を構造物１上に設置した球面座１０上において転動あるいは滑動可能に配置して全方向に揺動させるように構成したものである。なお、図示例の揺動体９では、付加質量２をケース側面に対してローラを介して摺動自在に支持することによって、付加質量２のケースに対する相対的な横揺れを拘束しつつ上下方向にのみ振動させるものとしている。
図４は図３における揺動体９を吊り材３によって構造物１から吊り下げた構成のものである。
上記各実施形態のものは、いずれも付加質量２を構造物１に対して直接あるいは揺動体９を介して設置して構造体１との間に軸方向のみに伸縮変形する軸バネ５を直列配置することにより付加質量２が円周方向に振動しつつ半径方向にも振動し、軸バネ５に並列配置した減衰装置６によって効果的に振動エネルギーが吸収されるので、上記実施形態と同様の振動数調整により同様の効果が得られるものである。 Although one embodiment of the present invention has been described above, other embodiments are shown in FIGS.
FIG. 2 shows a structure in which a rigid pendulum is installed on the structure 1, in which a column 7 instead of the suspension member 3 is installed on the structure 1 via a rotating spring 8 serving as a restoring force instead of gravity. The strut 7 incorporates a shaft spring 5 and a damping device 6 that expands and contracts only in the axial direction, and the strut 7 vibrates as a pendulum in the circumferential direction while maintaining a straight state without causing shear deformation. At that time, the full length of the support column 7 is expanded and contracted by the expansion and contraction of the shaft spring 5 so that the additional mass 2 vibrates in the radial direction.
3 is similar to that shown in FIG. 2 in that the additional mass 2 is supported by the support 7 incorporating the shaft spring 5 and the damping device 6 so as to vibrate only in the radial direction, and the entirety thereof is accommodated in the case. The oscillating body 9 is configured, and the oscillating body 9 is configured to be slidable or slidable on the spherical seat 10 installed on the structure 1 so as to oscillate in all directions. In addition, in the oscillating body 9 in the illustrated example, the additional mass 2 is supported slidably on the side surface of the case via a roller, thereby restraining the relative roll of the additional mass 2 relative to the case in the vertical direction. Only to vibrate.
FIG. 4 shows a configuration in which the rocking body 9 in FIG. 3 is suspended from the structure 1 by the suspension member 3.
In each of the above embodiments, the additional mass 2 is installed on the structure 1 directly or via the rocking body 9, and the shaft spring 5 that expands and contracts only in the axial direction between the structure 1 and the structure 1 is connected in series. By arranging, the additional mass 2 vibrates in the radial direction while oscillating in the circumferential direction, and the vibration energy is effectively absorbed by the damping device 6 arranged in parallel with the shaft spring 5. Similar effects can be obtained by adjusting the frequency.

なお、図４に示したように吊り支持した揺動体９内に付加質量２を収容するという構成は、特開２００６−２５８１４１号公報に示されている吸振器の構成と共通する部分がある。しかし、その吸振器は支点から吊り下げられた揺動体（ロープウェイのゴンドラやリフト等）に付加質量を半径方向にのみ移動できるように配置して、それにより揺動体自体の風揺れ（振り子としての円周方向の振動）を低減するものに過ぎない。つまり、その技術はあくまで振り子運動する揺動体の振動を抑制するものであって、本発明のようにその揺動体の振動を利用して構造物の振動を低減させるためのＴＭＤを構成するものではなく、その点で両者は目的や用途が全く異なるものである。   Note that the configuration in which the additional mass 2 is accommodated in the oscillating body 9 that is suspended and supported as shown in FIG. 4 has a portion that is common to the configuration of the vibration absorber shown in Japanese Patent Laid-Open No. 2006-258141. However, the vibration absorber is arranged on an oscillating body (rope gondola, lift, etc.) suspended from a fulcrum so that the additional mass can be moved only in the radial direction. It merely reduces the circumferential vibration). In other words, the technology only suppresses the vibration of the rocking body that moves pendulum, and does not constitute a TMD for reducing the vibration of the structure using the vibration of the rocking body as in the present invention. In that respect, both have completely different purposes and uses.

本発明の一実施形態である振動低減機構を示す図である。It is a figure which shows the vibration reduction mechanism which is one Embodiment of this invention. 同、他の実施形態である振動低減機構を示す図である。It is a figure which shows the vibration reduction mechanism which is other embodiment same as the above. 同、他の実施形態である振動低減機構を示す図である。It is a figure which shows the vibration reduction mechanism which is other embodiment same as the above. 同、他の実施形態である振動低減機構を示す図である。It is a figure which shows the vibration reduction mechanism which is other embodiment same as the above. 従来の振り子型のＴＭＤを示す図である。It is a figure which shows the conventional pendulum type TMD.

符号の説明Explanation of symbols

１ 構造物
２ 付加質量
３ 吊り材
４ 減衰装置
５ 軸バネ
６ 減衰装置
７ 支柱
８ 回転バネ
９ 揺動体
１０ 球面座 DESCRIPTION OF SYMBOLS 1 Structure 2 Additional mass 3 Suspension material 4 Damping device 5 Axial spring 6 Damping device 7 Post 8 Rotating spring 9 Oscillator 10 Spherical seat

Claims (2)

振動低減対象の構造物に、付加質量を振り子として振動させる付加振動系を付加して、該付加振動系の固有振動数を構造物の固有振動数に同調させることによって振動低減効果を得る機構であって、
前記付加振動系に、振り子振動により半径方向に伸縮して振り子長さを可変とする軸バネを組み込むとともに、該軸バネに並列に減衰装置を設置し、
静止時の振り子長さと重力加速度によって定まる振り子の固有振動数を構造物の固有振動数と同調させるとともに、付加質量と軸バネにより定まる付加振動系の振動数を振り子の固有振動数の２倍に調整してなることを特徴とする振動低減機構。 A mechanism that obtains a vibration reduction effect by adding an additional vibration system that vibrates an additional mass as a pendulum to a structure to be reduced in vibration, and synchronizes the natural frequency of the additional vibration system with the natural frequency of the structure. There,
The additional vibration system incorporates a shaft spring that can expand and contract in the radial direction by pendulum vibration to change the pendulum length, and a damping device is installed in parallel with the shaft spring.
The natural frequency of the pendulum determined by the length of the pendulum at rest and the acceleration of gravity is synchronized with the natural frequency of the structure, and the frequency of the additional vibration system determined by the additional mass and the axial spring is double the natural frequency of the pendulum. A vibration reduction mechanism characterized by being adjusted. 振動低減対象の構造物に、付加質量を振り子として振動させる付加振動系を付加して、該付加振動系の固有振動数を構造物の固有振動数に同調させることによって振動低減効果を得る機構の諸元設定方法であって、
前記付加振動系に、振り子振動により半径方向に伸縮して振り子長さを可変とする軸バネを組み込むとともに、該軸バネに並列に減衰装置を設置し、
静止時の振り子長さと重力加速度によって定まる振り子の固有振動数を構造物の固有振動数と同調させるとともに、付加質量と軸バネにより定まる付加振動系の振動数を振り子の固有振動数の２倍に調整することを特徴とする振動低減機構の諸元設定方法。 A mechanism for obtaining a vibration reduction effect by adding an additional vibration system that vibrates an additional mass as a pendulum to a structure to be reduced in vibration and synchronizing the natural frequency of the additional vibration system with the natural frequency of the structure. A specification setting method,
The additional vibration system incorporates a shaft spring that can expand and contract in the radial direction by pendulum vibration to change the pendulum length, and a damping device is installed in parallel with the shaft spring.
Synchronize the natural frequency of the pendulum determined by the pendulum length and gravitational acceleration with the natural frequency of the structure, and double the frequency of the additional vibration system determined by the additional mass and the shaft spring to the natural frequency of the pendulum. A specification setting method of a vibration reduction mechanism characterized by adjusting.
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WO2012090259A1 (en) * 2010-12-27 2012-07-05 三菱重工業株式会社 Vibration control device for windmill for wind-powered electricity generation, and windmill for wind-powered electricity generation
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WO2012090259A1 (en) * 2010-12-27 2012-07-05 三菱重工業株式会社 Vibration control device for windmill for wind-powered electricity generation, and windmill for wind-powered electricity generation
US8322975B2 (en) 2010-12-27 2012-12-04 Mitsubishi Heavy Industries, Ltd. Vibration control apparatus of wind turbine generator and wind turbine generator
EP2746483A1 (en) * 2012-12-21 2014-06-25 Wölfel Beratende Ingenieure GmbH & Co. KG Oscillation damping assembly
CN107060125A (en) * 2017-03-22 2017-08-18 东南大学 A kind of tuned mass damper device
CN107060125B (en) * 2017-03-22 2018-11-27 东南大学 A kind of tuned mass damper device
CN106988592A (en) * 2017-04-06 2017-07-28 东南大学 A kind of swing-type tuned mass damper device
CN106988592B (en) * 2017-04-06 2019-02-01 东南大学 A kind of swing-type tuned mass damper device
CN113167067A (en) * 2018-11-07 2021-07-23 毛雷尔工程有限公司 Mass damper for damping structural vibrations, structure having such a mass damper and method for adjusting the natural frequency of a mass damper
JP2020148339A (en) * 2019-03-16 2020-09-17 株式会社奥村組 Vibration control mechanism
JP7100943B2 (en) 2019-03-16 2022-07-14 株式会社奥村組 Vibration control mechanism

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