CN113297907B - Nonlinear damping identification method based on data driving under pulse excitation - Google Patents
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Abstract
The invention relates to a nonlinear damping identification method based on data driving under pulse excitation, which comprises the following steps: generating a pulse signal, acting on a two-degree-of-freedom nonlinear vibration system to obtain tested response, obtaining characteristic displacement and characteristic speed by utilizing actual measurement transient response, extracting instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency; and providing a corresponding dynamic model according to the obtained damping-speed curve, defining damping according to the dynamic model, fitting with the damping-speed curve, and determining unknown damping parameters of the system based on a mode searching algorithm. The invention obtains the output signal based on measurement, effectively identifies the nonlinear parameters of the system based on a mode search algorithm through data processing of actual measurement transient response, determines the unknown damping parameters of the two-degree-of-freedom nonlinear vibration system, and has practical engineering significance.
Description
Technical Field
The invention relates to the technical field of nonlinear system parameter identification methods, in particular to a nonlinear damping identification method based on data driving under pulse excitation.
Background
The purpose of nonlinear system parameter identification is to estimate model parameters that describe the dynamics of the system. With the rapid development of engineering machinery, the parameter identification and analysis of a linear vibration system gradually tend to be mature. However, in practical engineering applications, many systems exhibit complex nonlinear behavior due to multiple physical interactions, and thus efficient nonlinear parameter identification methods are needed to describe nonlinear system dynamics.
Disclosure of Invention
The invention provides a nonlinear damping identification method based on data driving under pulse excitation, and aims to effectively identify nonlinear damping parameters.
The technical scheme adopted by the invention is as follows:
the method for identifying the nonlinear damping based on the data driving under the pulse excitation is used for identifying a multi-degree-of-freedom nonlinear vibration system, wherein the multi-degree-of-freedom nonlinear vibration system comprises a linear structure and a nonlinear structure, and the nonlinear structure comprises a damping item and a linear stiffness item which are connected in parallel:
the identification method comprises the following steps:
(1) A pulse signal is acted on the multi-degree-of-freedom nonlinear vibration system, actual measurement transient response after the pulse signal is acted is obtained, characteristic displacement and characteristic speed are obtained by utilizing the actual measurement transient response, instantaneous frequency is extracted, and a damping-speed curve is obtained according to the characteristic displacement and the instantaneous frequency;
(2) And establishing a corresponding dynamic model according to the damping-speed curve, defining damping according to the dynamic model, fitting with the damping-speed curve, and finally obtaining the unknown damping parameters of the nonlinear structure.
The further technical scheme is as follows:
the step (1) specifically comprises the following sub-steps:
11 A pulse signal is applied to a two-degree-of-freedom nonlinear vibration system to obtain actual measurement transient response after action, and characteristic displacement delta c is defined according to response data:
Wherein T represents time, x (T), y (T) are displacements of the nonlinear structure and the linear structure respectively, δ (T) =x (T) -y (T) is a relative displacement between the nonlinear structure and the linear structure, Δt is a period of the lowest frequency involved in measurement response, and δ c (T) is a maximum value of |δ (T) | in Δt time;
12 Time-frequency analysis is carried out on the relative displacement delta (t), instantaneous frequency is extracted according to a time-frequency analysis chart obtained by wavelet transformation, and damping zeta c (t) related to time t is obtained according to the characteristic displacement and the instantaneous frequency:
Where δ c is the characteristic displacement, ω c is the instantaneous frequency, For the first derivative of the characteristic displacement delta c with respect to time,/>Is the first derivative of the instantaneous frequency omega c with respect to time;
in combination with the speed of the nonlinear structure, a damping-speed curve is established.
The step (2) specifically comprises the following sub-steps:
21 Establishing a kinetic equation characterizing a two-degree-of-freedom nonlinear vibration system in a nonlinear structure:
Wherein m and x are the mass of the nonlinear structure and the displacement of the nonlinear structure respectively, and delta is the relative displacement between the nonlinear structure and the linear structure; k2, A linear stiffness term and a damping term of the nonlinear structure respectively;
And damping term Represents a nonlinear damping term/>And linear damping term c;
22 Record(s) δ＝0.85δc、/>From the kinetic equation (3), a damping function relation is derived for the characteristic velocity:
Wherein δ c is the characteristic displacement and v c is the characteristic velocity;
23 Fitting equation (4) to the damping-speed curve, and finally determining the unknown damping parameters C and C of the system based on a mode search algorithm.
The beneficial effects of the invention are as follows:
The present invention utilizes only the measured transient response and associated quality without prior knowledge of the parent structure. Based on the measurement, an output signal is obtained, and the nonlinear damping parameters of the system are effectively identified through data processing of actual measurement transient response, so that the unknown damping parameters of the two-degree-of-freedom nonlinear vibration system are determined, and the method has practical engineering significance.
Drawings
Fig. 1 is a schematic structural diagram of a nonlinear vibration system according to an embodiment of the present invention.
FIG. 2 is a graph comparing a measured damping-velocity curve with a fitted damping-velocity curve according to an embodiment of the present invention.
Detailed Description
The following describes specific embodiments of the present invention with reference to the drawings.
The method for identifying the nonlinear damping based on the data driving under the pulse excitation of the embodiment is used for identifying damping parameters of a nonlinear vibration system with multiple degrees of freedom, wherein the nonlinear vibration system with multiple degrees of freedom comprises at least one linear structure (such as a mother structure) and a nonlinear structure (such as a local accessory) connected with the linear structure, and the embodiment is exemplified by a two-degree-of-freedom nonlinear vibration system as shown in fig. 1. In fig. 1, M represents the mass of a linear structure, M represents the mass of a nonlinear structure, the linear coupling between the two is weak, k1 and k2 represent linear stiffness terms of the linear structure and the nonlinear structure, respectively, c1 represents a linear damping term of the linear structure,And a damping term representing the nonlinear structure, y (t) represents the displacement of the linear structure, and x (t) represents the displacement of the nonlinear structure.
The identification method comprises the following steps:
(1) Generating a pulse signal, acting on a two-degree-of-freedom nonlinear vibration system, obtaining an actual measurement transient response, obtaining a characteristic displacement and a characteristic speed by using the actual measurement transient response, extracting an instantaneous frequency, and obtaining a damping-speed curve according to the characteristic displacement and the instantaneous frequency, wherein the method comprises the following substeps:
11 Firstly, a pulse signal is generated by adopting a force hammer structure and acts on a two-degree-of-freedom nonlinear vibration system, the transient acceleration response is measured by utilizing an acceleration sensor, and the characteristic displacement delta c is defined according to response data:
Wherein x (T) and y (T) are displacements of the nonlinear structure and the linear structure respectively, delta (T) =x (T) -y (T) is a relative displacement between the nonlinear structure and the linear structure, delta T is a period of the lowest frequency involved in measurement response, and delta t=0.1 s; delta c (T) is the maximum value of delta (T) in delta T time;
12 Time-frequency analysis is carried out on the relative displacement delta (t), instantaneous frequency is extracted according to a time-frequency analysis chart obtained by wavelet transformation, and damping zeta c (t) related to time t is obtained according to the characteristic displacement and the instantaneous frequency:
Where δ c is the characteristic displacement, ω c is the instantaneous frequency, For the first derivative of the characteristic displacement delta c with respect to time,/>Is the first derivative of the instantaneous frequency omega c with respect to time; and directly measuring or calculating according to the displacement to obtain the speed of the nonlinear structure, and establishing a damping-speed curve by combining the formula (2).
(2) Providing a corresponding dynamic model according to the obtained damping-speed curve, defining damping according to the dynamic model, fitting with the damping-speed curve, and determining unknown damping parameters of the system based on a mode search algorithm, wherein the method comprises the following sub-steps:
21 A dynamic equation of a two-degree-of-freedom nonlinear vibration system structure characterized by a nonlinear structure is:
m represents the mass of the nonlinear structure, x represents the displacement of the nonlinear structure, y represents the displacement of the linear structure, delta=x-y represents the relative displacement between the nonlinear structure and the linear structure, A linear stiffness term and a damping term of the nonlinear structure respectively;
Wherein the damping term Is formed by nonlinear damping/>And linear damping c;
Taking coulomb damping as an example, Formula (3) is written as:
And m=0.05, k 2 =300, c=0.3; μ=0.25;
22 Record delta = 0.85 delta c and From the kinetic equation, damping ζ (v c) is obtained with respect to the characteristic velocity:
Wherein δ c is the characteristic displacement and v c is the characteristic velocity;
23 And (3) finally determining unknown damping parameters C and C of the system based on a mode searching algorithm by fitting the formula (5) with the damping-speed curve.
As shown in fig. 2, the measured damping-speed curve is compared with the fitted damping-speed curve.
Claims (2)
1. The method for identifying the nonlinear damping based on the data driving under the pulse excitation is used for identifying a multi-degree-of-freedom nonlinear vibration system, wherein the multi-degree-of-freedom nonlinear vibration system comprises a linear structure and a nonlinear structure, and the nonlinear structure comprises a damping item and a linear stiffness item which are connected in parallel, and is characterized by comprising the following steps:
(1) A pulse signal is acted on the multi-degree-of-freedom nonlinear vibration system, actual measurement transient response after the pulse signal is acted is obtained, characteristic displacement and characteristic speed are obtained by utilizing the actual measurement transient response, instantaneous frequency is extracted, and a damping-speed curve is obtained according to the characteristic displacement and the instantaneous frequency;
(2) Establishing a corresponding dynamic model according to the damping-speed curve, defining damping according to the dynamic model, fitting with the damping-speed curve, and finally determining unknown damping parameters of a nonlinear structure;
the step (1) specifically comprises the following sub-steps:
11 A pulse signal is applied to a two-degree-of-freedom nonlinear vibration system to obtain actual measurement transient response after action, and characteristic displacement delta c is defined according to response data:
Wherein T represents time, x (T), y (T) are displacements of the nonlinear structure and the linear structure respectively, δ (T) =x (T) -y (T) is a relative displacement between the nonlinear structure and the linear structure, Δt is a period of the lowest frequency involved in measurement response, and δ c (T) is a maximum value of |δ (T) | in Δt time;
12 Time-frequency analysis is carried out on the relative displacement delta (t), instantaneous frequency is extracted according to a time-frequency analysis chart obtained by wavelet transformation, and damping zeta c (t) related to time t is obtained according to the characteristic displacement and the instantaneous frequency:
Where δ c is the characteristic displacement, ω c is the instantaneous frequency, For the first derivative of the characteristic displacement delta c with respect to time,/>Is the first derivative of the instantaneous frequency omega c with respect to time;
in combination with the speed of the nonlinear structure, a damping-speed curve is established.
2. The method for identifying nonlinear damping based on data driving under pulse excitation according to claim 1, wherein said step (2) specifically comprises the following sub-steps:
21 Establishing a kinetic equation characterizing a two-degree-of-freedom nonlinear vibration system in a nonlinear structure:
wherein m and x are the mass of the nonlinear structure and the displacement of the nonlinear structure respectively, and delta is the relative displacement between the nonlinear structure and the linear structure; k 2, A linear stiffness term and a damping term of the nonlinear structure respectively;
And damping term Represents a nonlinear damping term/>And linear damping term c;
22 Record(s) δ＝0.85δc、/>From the kinetic equation (3), a damping function relation is derived for the characteristic velocity:
Wherein δ c is the characteristic displacement and v c is the characteristic velocity;
23 Fitting equation (4) to the damping-speed curve, and finally determining the unknown damping parameters C and C of the system based on a mode search algorithm.
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| CN107609221A (en) * | 2017-08-15 | 2018-01-19 | 东南大学 | It is a kind of that hinged structure nonlinear parameter recognition methods is contained based on genetic algorithm |
| CN110083920A (en) * | 2019-04-23 | 2019-08-02 | 西南交通大学 | The analysis method of non-proportional damping structural random response under a kind of geological process |
| CN112632694A (en) * | 2020-12-02 | 2021-04-09 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
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| CN107609221A (en) * | 2017-08-15 | 2018-01-19 | 东南大学 | It is a kind of that hinged structure nonlinear parameter recognition methods is contained based on genetic algorithm |
| CN110083920A (en) * | 2019-04-23 | 2019-08-02 | 西南交通大学 | The analysis method of non-proportional damping structural random response under a kind of geological process |
| CN112632694A (en) * | 2020-12-02 | 2021-04-09 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
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