CN111259328B - Method for detecting nonlinear characteristics of spacecraft structure driven by free vibration displacement response - Google Patents

Method for detecting nonlinear characteristics of spacecraft structure driven by free vibration displacement response Download PDF

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CN111259328B
CN111259328B CN202010047096.2A CN202010047096A CN111259328B CN 111259328 B CN111259328 B CN 111259328B CN 202010047096 A CN202010047096 A CN 202010047096A CN 111259328 B CN111259328 B CN 111259328B
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费庆国
曹芝腑
姜东�
靳慧
杭晓晨
朱锐
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Abstract

The invention provides a method for detecting the nonlinear characteristics of a free vibration displacement response driven spacecraft structure, which comprises the following steps: (1) applying different initial displacements on a spacecraft structure to be detected and containing a hinge, and extracting the actual measurement displacement dynamic response of the structure in a free vibration state; (2) performing dynamic modal decomposition on the structure free vibration displacement response under the first initial displacement to obtain a dynamic modal matrix of the structure and a characteristic value corresponding to the dynamic modal matrix; (3) decomposing the obtained dynamic modal matrix and the corresponding characteristic value thereof, reconstructing the displacement dynamic response under the initial displacement condition of the second amplification, performing difference analysis on the displacement dynamic response and the actually measured displacement dynamic response under the initial condition of the second amplification, and detecting the existence of structural nonlinearity. The problem of detecting whether the nonlinear characteristics exist in the spacecraft structure with the hinge is solved by directly utilizing the displacement response of the structure in the free vibration state, so that whether the nonlinear characteristics exist in the spacecraft structure can be effectively judged.

Description

Method for detecting nonlinear characteristics of spacecraft structure driven by free vibration displacement response
Technical Field
The invention belongs to the field of nonlinear structure identification, and particularly relates to a nonlinear detection method based on free vibration displacement response data driving.
Background
With the development of the spacecraft structure towards large size, the forms of the spacecraft structure are more and more diversified, and the expressed dynamic characteristics are more complex. How to judge whether the structure has nonlinear characteristics from the dynamic response of the spacecraft structure is one of the key problems influencing the establishment of an accurate analysis model of the spacecraft structure. The main reason is that the existence of nonlinearity makes the analysis method of the spacecraft structure more complex, so that the dynamic behavior of the spacecraft has the characteristic of being difficult to predict. And the detection of the existence of nonlinearity in the spacecraft structure is beneficial to qualitative judgment and qualitative analysis of the dynamic behavior of the spacecraft. How to detect whether nonlinear characteristics exist in a spacecraft structure becomes an actual engineering problem to be solved urgently.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for detecting nonlinear characteristics of a spacecraft structure driven by free vibration displacement response, which can effectively detect whether nonlinear characteristics exist in the spacecraft structure and has practical engineering significance.
In order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a method for detecting the nonlinear characteristics of a free vibration displacement response driven spacecraft structure comprises the following steps:
(1) applying different two times of initial displacement on a spacecraft structure containing a hinge to be detected, and extracting the actual measurement displacement dynamic response of the structure in a free vibration state;
(2) performing dynamic modal decomposition on the structure free vibration displacement response under the first initial displacement to obtain a dynamic modal matrix of the structure and a characteristic value corresponding to the dynamic modal matrix;
(3) and by utilizing the dynamic modal matrix obtained by decomposition and the corresponding characteristic value thereof, reconstructing the displacement dynamic response under the initial displacement condition of the second amplification, and performing difference analysis on the reconstructed displacement dynamic response and the actually measured displacement dynamic response under the initial condition of the second amplification, thereby detecting whether structural nonlinearity exists or not.
Further, in the step (1), different initial displacements are applied to the structure of the spacecraft to be detected, which contains the hinge, and the measured displacement dynamic response of the structure in the free vibration state is extracted, and the method specifically comprises the following steps:
(1.1) applying initial displacement conditions u of different magnitudes for a spacecraft structure comprising a hinge1And cu1Wherein u is1Taking c as an amplification factor as an initial displacement vector, and taking 10-50 generally;
(1.2) measuring the free vibration actual measurement displacement dynamic response X of the structure to be detected under the initial displacement condition (1.1) by using a displacement meter1And X2Wherein X is1Is an initial displacement u1Downward displacement response, X2Is an initial displacement cu1Downward displacement response.
Further, in the step (2), dynamic modal decomposition is performed on the structure free vibration displacement response under the first initial displacement to obtain a dynamic modal matrix of the structure and a corresponding characteristic value thereof, and the specific steps include the following steps:
(2.1) Using the initial Displacement u1The following structure free vibration displacement response is constructed as the following displacement vector X'1And X ″)1：
Figure BDA0002369814820000021
Figure BDA0002369814820000022
Wherein the content of the first and second substances,
Figure BDA0002369814820000023
denotes the displacement of the nth measuring point at the mth time, t, at the ith measurementmRepresenting the mth moment, M is the total number of the measurement time points;
(2.2) for the displacement vector X1' singular value decomposition:
X′1＝UΣVT (12)
u, sigma and V are respectively a left singular vector matrix, a singular value matrix and a right singular vector matrix;
(2.3) decomposition of the results using singular values and the displacement vector X ″)1Solving a dynamic matrix:
A＝X″1VΣ-1UT (13)
wherein, A is a dynamic matrix obtained by a data driving method, and an eigenvector matrix and an eigenvalue matrix of the dynamic matrix are solved by MATLAB:
AΨ＝ΨΛ (14)
wherein Ψ and Λ are a eigenvector matrix and an eigenvalue matrix respectively;
(2.4) constructing a dynamic mode matrix and a corresponding eigenvalue matrix by using the results of (2.1) to (2.3):
Φ＝X″1VΣ-1Ψ (15)
Figure BDA0002369814820000024
wherein phi represents a dynamic mode matrix, omega represents a dynamic mode characteristic value matrix, and delta t represents a measurement time step.
Further, in the step (3), by using the dynamic modal matrix obtained by decomposition and the corresponding eigenvalue thereof, reconstructing the displacement motion response under the initial displacement condition of the second amplification, and performing difference analysis on the reconstructed displacement motion response and the displacement motion response under the initial condition of the second amplification actually measured, thereby detecting whether structural nonlinearity exists, and the specific steps include the following steps:
(3.1) utilizing the dynamic modal matrix obtained in the step (2) and the corresponding characteristic value matrix thereof to amplify the initial displacement condition cu1Reconstructing the estimated displacement response:
Figure BDA0002369814820000031
wherein the content of the first and second substances,
Figure BDA0002369814820000032
an estimated displacement motion response representing the scaled-up initial displacement condition reconstruction;
(3.2) response to estimated motion of the displacement
Figure BDA0002369814820000033
And the measured displacement dynamic response X2Performing differential analysis:
Figure BDA0002369814820000034
wherein epsilon is a difference index, if epsilon is larger than a preset threshold value, the structure is a nonlinear structure, and if the value is larger, the nonlinear characteristic of the structure is more obvious.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention provides a method for detecting nonlinear characteristics of a free vibration displacement response-driven spacecraft structure, which can effectively judge whether nonlinear characteristics exist in the spacecraft structure with a hinge or not by directly extracting the free vibration displacement response of the spacecraft structure with the hinge under different initial displacement conditions and utilizing the difference analysis of reconstructed displacement and actually measured displacement, and has practical engineering significance for the detection and judgment of the nonlinear characteristics.
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FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 shows an initial displacement u according to an embodiment of the present invention1Displacement X of lower mass blocks1；
FIG. 3 is an initial displacement cu in an embodiment of the present invention1Displacement X of lower mass blocks2；
FIG. 4 illustrates an embodiment of the present invention utilizing an initial displacement cu1Displacement of reconstructed masses
Figure BDA0002369814820000035
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
This embodiment adopts a five-degree-of-freedom nonlinear spring-damper-mass system to illustrate the process of the method of the present invention, and fig. 1 is a flow chart of the method. The mass of the mass block is respectively as follows: m is1＝20kg，m2＝10kg，m3＝15kg，m4＝10kg，m55 kg; linear spring rate k1＝20N/m，k2＝10N/m，k3＝40N/m，k4＝50N/m，k5100N/m; the nonlinear spring rate is shown in table 1:
TABLE 1 nonlinear spring rate coefficient parameter values
Figure BDA0002369814820000046
The method adopts proportional damping, namely the proportional damping coefficients are 0.01 and 0.01 respectively, and the method comprises the following steps:
(1) applying initial displacements of different magnitude orders on the structure to be detected, and extracting the actual measurement displacement dynamic response of the structure in a free vibration state:
(11) applying initial displacement conditions u with different magnitude orders aiming at a structure to be detected1And cu1Wherein u is1＝[0.01；0.05；0；0；0]m is an initial displacement vector, c is an amplification factor, which is usually 10-50, and in this embodiment, c is 20;
(12) measuring the free vibration actual measurement displacement dynamic response X of the structure to be detected under the (11) initial displacement condition by using a displacement meter1And X2Wherein X is1Is an initial displacement u1The lower displacement response being constituted by the displacement response of five masses, i.e.
Figure BDA0002369814820000041
As shown in fig. 2; x2Is an initial displacement cu1The lower displacement response, likewise consisting of five mass displacement responses, i.e.
Figure BDA0002369814820000042
As shown in fig. 3, M is the number of times of measurement, in this example, M is 100001, and the time interval is 0.001 s.
(2) Performing dynamic modal decomposition on the structure free vibration displacement response under the condition of small-magnitude initial displacement to obtain a dynamic modal matrix of the structure and a corresponding characteristic value:
(21) the following displacement X 'is constructed by utilizing the structure free vibration displacement response under the condition of small-magnitude initial displacement'1And X ″)1：
Figure BDA0002369814820000043
Figure BDA0002369814820000044
Wherein
Figure BDA0002369814820000045
Denotes the displacement of the nth measuring point at the mth time, t, at the ith measurementmRepresents the m-th time;
(22) for displacement vector X1' singular value decomposition:
X′1＝UΣVT (21)
u, sigma and V are respectively a left singular vector matrix, a singular value matrix and a right singular vector matrix;
(23) using singular value decomposition results and displacement vector X ″)1Solving a dynamic matrix:
A＝X″1VΣ-1UT (22)
wherein A is a dynamic matrix obtained by using a data driving method, and an eigenvector matrix and an eigenvalue matrix of the dynamic matrix are solved by using MATLAB:
AΨ＝ΨΛ (23)
psi and lambda are respectively a feature vector matrix and a feature value matrix;
(24) and (3) constructing a dynamic mode matrix and a corresponding characteristic value matrix by using the results of (2.1) to (2.3):
Φ＝X″1VΣ-1Ψ (24)
Figure BDA0002369814820000051
where Φ represents a dynamic mode matrix, Ω represents a dynamic mode eigenvalue matrix, and Δ t represents a measurement time step.
(3) By utilizing the dynamic modal matrix obtained by decomposition and the corresponding characteristic value thereof, the existence of structural nonlinearity is detected by reconstructing the displacement dynamic response under the condition of a large-scale initial displacement and performing difference analysis on the displacement dynamic response and the actually measured displacement dynamic response under the large-scale initial condition:
(31) utilizing the dynamic modal matrix obtained in the step (2) and the corresponding characteristic value matrix thereof to pass through a large-scale initial displacement condition cu1Reconstructing the estimated displacement response:
Figure BDA0002369814820000052
wherein
Figure BDA0002369814820000053
Represents the reconstructed estimated displacement response under a large number of levels of initial displacement, as shown in fig. 4;
(32) response to estimated motion
Figure BDA0002369814820000054
And the measured displacement dynamic response X2Performing differential analysis:
Figure BDA0002369814820000055
wherein epsiloniI is 1,2, …,5, which is a dissimilarity index, if the value is greater than a threshold, the structure is a nonlinear structure, and if the value is farther from a preset threshold, the nonlinear characteristic of the structure is more obvious. In this example, the difference index ∈ ═ 0.4848; 0.8071, respectively; 0.7208, respectively; 0.8335, respectively; 0.8813]The preset threshold is 0.1, and the relationship between each value in epsilon and the threshold is compared, so that the structure has nonlinearity.

Claims (4)

1. A method for detecting the nonlinear characteristics of a free vibration displacement response driven spacecraft structure is characterized by comprising the following steps:
(1) applying different two times of initial displacement on a spacecraft structure containing a hinge to be detected, and extracting the actual measurement displacement dynamic response of the structure in a free vibration state;
(2) performing dynamic modal decomposition on the structure free vibration displacement response under the first initial displacement to obtain a dynamic modal matrix of the structure and a characteristic value corresponding to the dynamic modal matrix;
(3) and by utilizing the dynamic modal matrix obtained by decomposition and the corresponding characteristic value thereof, reconstructing the displacement dynamic response under the initial displacement condition of the second amplification, and performing difference analysis on the reconstructed displacement dynamic response and the actually measured displacement dynamic response under the initial condition of the second amplification, thereby detecting whether structural nonlinearity exists or not.
2. The method for detecting the nonlinear characteristic of the free vibration displacement response-driven spacecraft structure as claimed in claim 1, wherein in the step (1), different initial displacements are applied to the spacecraft structure containing the hinge to be detected, and the measured displacement dynamic response of the structure in the free vibration state is extracted, and the specific steps comprise the following steps:
(1.1) applying initial displacement conditions u of different magnitudes for a spacecraft structure comprising a hinge1And cu1Wherein u is1Is the initial displacement vector, c is the amplification factor;
(1.2) measuring the free vibration actual measurement displacement dynamic response X of the structure to be detected under the initial displacement condition (1.1) by using a displacement meter1And X2Wherein X is1Is an initial displacement u1Downward displacement response, X2Is an initial displacement cu1Downward displacement response.
3. The method for detecting the nonlinear characteristic of the spacecraft structure driven by the free vibration displacement response as recited in claim 2, wherein in the step (2), the dynamic modal decomposition is performed on the structure free vibration displacement response under the first initial displacement to obtain a dynamic modal matrix of the structure and a corresponding characteristic value thereof, and the specific steps include the following steps:
(2.1) Using the initial Displacement u1The following structure free vibration displacement response is constructed as the following displacement vector X'1And X ″)1：
Figure FDA0002822579870000011
Figure FDA0002822579870000012
Wherein the content of the first and second substances,
Figure FDA0002822579870000013
denotes the displacement of the nth measuring point at the mth time, t, at the ith measurementmRepresenting the mth moment, M is the total number of the measurement time points;
(2.2) to displacement vector X'1Singular value decomposition is carried out:
X′1＝UΣVT (3)
u, sigma and V are respectively a left singular vector matrix, a singular value matrix and a right singular vector matrix;
(2.3) decomposition of the results using singular values and the displacement vector X ″)1Solving a dynamic matrix:
A＝X″1VΣ-1UT (4)
wherein, A is a dynamic matrix obtained by a data driving method, and an eigenvector matrix and an eigenvalue matrix of the dynamic matrix are solved by MATLAB:
AΨ＝ΨΛ (5)
wherein Ψ and Λ are a eigenvector matrix and an eigenvalue matrix respectively;
(2.4) constructing a dynamic mode matrix and a corresponding eigenvalue matrix by using the results of (2.1) to (2.3):
Φ＝X″1VΣ-1Ψ (6)
Figure FDA0002822579870000021
wherein phi represents a dynamic mode matrix, omega represents a dynamic mode characteristic value matrix, and delta t represents a measurement time step.
4. The method for detecting the nonlinear characteristic of the spacecraft structure driven by the free vibration displacement response according to claim 3, wherein in the step (3), the dynamic modal matrix obtained by decomposition and the corresponding characteristic value thereof are used for reconstructing the displacement motion response under the initial displacement condition of the second amplification and performing the difference analysis on the displacement motion response under the initial condition of the second amplification and the measured displacement motion response under the initial condition of the second amplification, so as to detect whether the structural nonlinearity exists, and the method specifically comprises the following steps:
(3.1) utilizing the dynamic modal matrix obtained in the step (2) and the corresponding characteristic value matrix thereof to amplify the initial displacement condition cu1Reconstructing the estimated displacement response:
Figure FDA0002822579870000022
wherein the content of the first and second substances,
Figure FDA0002822579870000023
an estimated displacement motion response representing the scaled-up initial displacement condition reconstruction;
(3.2) response to estimated motion of the displacement
Figure FDA0002822579870000024
And the measured displacement dynamic response X2Performing differential analysis:
Figure FDA0002822579870000025
wherein epsilon is a difference index, and if epsilon is larger than a preset threshold value, the structure is a nonlinear structure.
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