A multi-point excitation time-domain load identification method

Abstract

The application discloses a kind of multi-point excited time domain load identification method, using modal superposition method to carry out the transient dynamics response analysis of engineering equipment structure, respectively on each excitation load degree of freedom, obtain the time history response of all expected response degrees of freedom;In frequency domain, construct the transmission relationship between the external excitation load degree of freedom and the expected response degree of freedom, respectively Fourier transform is carried out to all the applied external excitation load and the obtained dynamics response, then construct transfer function at each frequency point;According to the expected dynamics response, construct appropriate external excitation load, Fourier transform is carried out to all the expected dynamics response, according to the constructed transfer function, calculate the external excitation load at each frequency point in frequency domain;Finally, using inverse Fourier transform converts the external excitation load in frequency domain to time domain;The application can solve the ill-posed problem of time domain load identification, and also can provide important support for dynamics control under different dynamic load environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of load identification in time history analysis, and particularly relates to a multi-point excitation time domain load identification method. BACKGROUND

[0002] In the development process of engineering equipment structure, the external excitation load of the structure needs to be identified according to the response data measured in the test, and the vibration environment adaptability of the structure is evaluated in combination with numerical simulation.

[0003] Load identification is a process of determining the vibration load according to the vibration response, and the existing time domain load identification method is mainly aimed at simple structures and is difficult to be applied to complex engineering equipment structures. On the one hand, it is difficult to obtain the characteristic parameters of the overall structure, and on the other hand, the robustness of the dynamic load identification algorithm is poor. Since the structure transfer function matrix is a condition number large ill-conditioned matrix, direct numerical integration method for load identification is often not convergent, which is an ill-posed problem.

[0004] Therefore, it is necessary to develop a multi-point excitation time domain load identification algorithm suitable for engineering equipment structure dynamics analysis to solve the above problems. SUMMARY

[0005] The purpose of the present application is to design a multi-point excitation time domain load identification method to solve the above problems.

[0006] The present application achieves the above-mentioned purpose through the following technical solutions:

[0007] A multi-point excitation time domain load identification method, comprising the following steps:

[0008] S1: establishing a finite element analysis model of a complex engineering equipment structure;

[0009] S2: carrying out modal analysis to obtain the modal frequency and modal shape of the structure;

[0010] S3: constructing a transfer function between the external excitation load degrees of freedom and the expected response degrees of freedom;

[0011] S4: constructing the external excitation load in the frequency domain;

[0012] S5: calculating the time sequence of the external excitation load;

[0013] S6: verifying the constructed time domain excitation load.

[0014] Specifically, step S3 comprises:

[0015] S31: applying an excitation load f1 at the external excitation load node, carrying out transient dynamics analysis, and extracting the acceleration response of all expected response degrees of freedom: x 11x 21 x l1 ;

[0016] S32: Apply the excitation load f2 at the external excitation load node, carry out transient dynamics analysis, and extract the acceleration response of all desired response degrees of freedom: x 12 x 22 x l2 ;

[0017] S33: Repeat the above steps until the excitation load f k is applied at the last external excitation load node, carry out transient dynamics analysis, and extract the acceleration response of all desired response degrees of freedom: x 1k x 2k x lk ;

[0018] S34: Fourier transform all excitation loads to obtain

[0019] S35: Fourier transform all acceleration responses to obtain:

[0020] S36: Calculate the transfer function G between the external excitation load degrees of freedom and the desired response degrees of freedom at each discrete frequency point.

[0021]

[0022] Specifically, step S4 includes:

[0023] S41: Fourier transform all desired dynamic responses to obtain

[0024] S42: Identify the external excitation load at each discrete frequency point using the transfer function G calculated in S36.

[0025]

[0026] The present application has the following advantages:

[0027] By combining Fourier transform and inverse Fourier transform, the external excitation load in the time domain is identified using the dynamic transfer characteristics in the frequency domain, avoiding the cumulative effect of the time integration process.

[0028] By directly establishing the transfer relationship between the external excitation load degrees of freedom and the desired response degrees of freedom through the position vector, the ill-conditioned singularity of the transfer matrix is greatly reduced, ensuring the stability of the load identification process.

[0029] The modal superposition method is used to construct the transfer function, and the calculation cost of dynamic analysis is reduced, and the load identification algorithm is applied to complex engineering equipment structures. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 The step flow chart of the embodiment of the present application is provided.

[0031] Figure 2 The structural schematic diagram of the rubber vibration isolation system is provided.

[0032] Figure 3 The schematic diagram of the expected acceleration response of the moving part is provided.

[0033] Figure 4 The schematic diagram of the finite element model of the rubber vibration isolation system is provided.

[0034] Figure 5 The schematic diagram of the overturning mode of the rubber vibration isolation system is provided.

[0035] Figure 6 The schematic diagram of the stretching mode of the rubber vibration isolation system is provided.

[0036] Figure 7 The schematic diagram of the constructed time-history external excitation load is provided.

[0037] Figure 8 The schematic diagram of the comparison between the simulated acceleration response and the expected value is provided. DETAILED DESCRIPTION

[0038] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0039] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0040] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0041] In the description of the present application, it should be understood that the terms "upper", "lower", "inner", "outer", "left", "right", and the like indicate the orientation or positional relationship shown in the drawings, or the orientation or positional relationship commonly understood by those skilled in the art, or the orientation or positional relationship commonly understood by those skilled in the art, only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0042] In addition, the terms "first", "second", and the like are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0043] In the description of the present application, it should be noted that, unless otherwise specified and limited, the terms "provided", "connected" and the like should be understood broadly, for example, "connected" can be fixedly connected, or detachably connected, or integrally connected; can be mechanically connected, or electrically connected; can be directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0044] The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0045] For the engineering equipment structure in the field of aerospace and military industry, the influence of material, geometry, boundary nonlinearity is ignored, and a n-degree-of-freedom structure dynamics differential equation can be expressed as

[0046]

[0047] In the formula, are the mass, damping, and stiffness matrices of the system, respectively. , respectively, represent the displacement, velocity, and acceleration response vectors of the structure. represents the external excitation load vector, which only acts on part of the degrees of freedom of the structure, and can be expressed as

[0048]

[0049] wherein, represents the i th The position vector of the external excitation load is a sparse vector, i.e. the corresponding position of the i th degree of freedom is "1", and the rest is "0". k is the dimension of the external excitation load. is the time history data of the i th external excitation load, and N is the data length, generally taking the power of 2, such as 1024.

[0050] Extract part of the dynamic response from the whole structure as the desired control target.

[0051]

[0052] where, denotes the i th Position vector of the desired response, also a sparse vector.

[0053] According to the principle of discrete Fourier transform, the external excitation load and the dynamic response can be expressed as

[0054]

[0055]

[0056] where, j is the imaginary unit.

[0057] Substitute the above equation into equation (1), at m th Discrete frequency points, the external excitation load and the dynamic response satisfy

[0058]

[0059] where, ω is the discrete angular frequency,

[0060] Substitute equations (2-3) into equation (5) to obtain

[0061]

[0062] From equation (6), the transfer function between the external excitation load and the desired response is

[0063] G = L exp · (k-ω 2 ·m+ω·c·j) -1 ·L ext (7)

[0064] where, l is the dimension of the desired dynamic response. Generally, l≥k, otherwise, there will be an under-constrained problem, resulting in infinite solutions of the identified external excitation load.

[0065] The middle part of the right side of equation (7) is the inverse of the dynamic stiffness matrix of the structure, which is very costly to calculate directly for complex engineering structures, and the modal superposition method is generally used for calculation.

[0066]

[0067] where, Modal vector. ξi ω i are the modal frequencies and modal dampings, respectively. th ω

[0068] The transfer function in equation (8) is a matrix with large condition number, which is ill-conditioned. In contrast, equation (7) directly establishes the transfer relationship between the external excitation load and the expected response by using the position vector, which greatly reduces the ill-conditioned singularity of the transfer matrix and ensures the stability of the load identification process.

[0069] When the dimension of the expected dynamic response is equal to the dimension of the external excitation load, i.e., l=k, the external excitation load at each discrete frequency point can be directly solved using equation (6).

[0070]

[0071] However, when the dimension of the expected dynamic response is greater than the dimension of the external excitation load, i.e., l>k, the least squares method needs to be used to fit the external excitation load at each discrete frequency point.

[0072]

[0073] The time history of the external excitation load can be obtained according to the inverse discrete Fourier transform.

[0074]

[0075] where Δt is the discrete time step.

[0076] Embodiment:

[0077] As shown in FIG. 1, the vibration isolation system composed of a moving part (an analog of an electronic device), a fixed boundary, and a rubber isolator, a proper external excitation load is applied to the moving part, and the acceleration response of the moving part in three directions (x-y-z) reaches the effect as shown in FIG. 2, and the example is demonstrated. Figure 2 Figure 3 As shown in FIG. 3, the embodiment includes the following steps:

[0078] As shown in FIG. 4, the embodiment includes the following steps: Figure 1 S1: For the rubber vibration isolation system, a finite element model as shown in FIG. 5 is established by using a finite element software, including establishing a geometric model, meshing, assigning material properties, applying boundary conditions, etc.

[0079] Figure 2 S2: Modal analysis is carried out to obtain the modal frequencies and modal shapes of the structure, as shown in FIGS. 6 and 7. Figure 4

[0080] Figure 5 Figure 6

[0081] ​​​​​​S3: Construct the transfer function between the external excitation load DOF and the desired dynamic response DOF.

[0082] S31: Apply x-direction excitation load f x at the external excitation load node, carry out transient dynamic analysis, extract the acceleration response of all desired response corresponding nodes: x1, y1, z1. The time history data of the external excitation load is not mandatory, but for the sake of simplicity, the response data of Figure 3 is directly applied as the external excitation load here (the frequency domain data of S34 and S41 can be shared later).

[0083] S32: Apply y-direction excitation load f y at the external excitation load node, carry out transient dynamic analysis, extract the acceleration response of all desired response corresponding nodes: x2, y2, z2.

[0084] S33: Apply z-direction excitation load f z at the external excitation load node, carry out transient dynamic analysis, extract the acceleration response of all desired response corresponding nodes: x3, y3, z3.

[0085] S34: Fourier transform all excitation loads to obtain

[0086] S35: Fourier transform all acceleration responses to obtain

[0087] S36: Calculate the transfer function G between the external excitation node and the desired response corresponding node at each discrete frequency point.

[0088]

[0089] S4: Construct the external excitation load in the frequency domain.

[0090] S41: Fourier transform all desired acceleration responses to obtain

[0091] S42: The dimension of the desired dynamic response is equal to the dimension of the external excitation load, i.e. l=k=3, directly identify the external excitation load of each discrete frequency point by formula (9)

[0092]

[0093] S5: Calculate the time sequence of the external excitation load, as shown in Figure 7 .

[0094]

[0095]

[0096]

[0097] S6: verifying the constructed time-domain excitation load. The time history data calculated by formula (14) is applied to the external excitation load node, the acceleration response of the expected response freedom degree is extracted, and is compared with Figure 3 , as shown in Figure 8 .

[0098] As can be seen from Figure 8 , the acceleration response obtained by simulation is in good agreement with the expected value, and the effect of load identification is achieved.

[0099] The above only describes the preferred embodiments of the present application, and it should be noted that for ordinary skilled persons in the art, without departing from the technical principles of the present application, several improvements and refinements can be made, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for identifying time-domain loads with multi-point excitation, characterized in that, Includes the following steps: S1: Establish a finite element analysis model for complex engineering equipment structures; S2: Conduct modal analysis to obtain the modal frequencies and mode shapes of the structure; S1 and S2 include: for engineering equipment structures in the aerospace and military fields, neglecting the effects of material, geometry, and boundary nonlinearity, a differential equation for the dynamics of an n-degree-of-freedom structure can be expressed as: In the formula, These are the mass, damping, and stiffness matrices of the system, respectively. These represent the displacement, velocity, and acceleration response vectors of the structure, respectively. The external excitation load vector, acting only on a portion of the structure's degrees of freedom, can be represented as: in, Indicate i th The position vector of the external excitation load is a sparse vector, that is, in i th The degree of freedom is "1" for the corresponding position and "0" for the rest; k is the dimension of the external excitation load; For i th Time history data of external excitation load, where N is the data length; Extracting a portion of the dynamic response from the overall structure as the desired control objective: in, Indicate i th The position vector of the expected response is also a sparse vector; According to the principle of discrete Fourier transform, the external excitation load and dynamic response can be expressed as: Where j is the imaginary unit; Substituting the above equation into equation (1), in m th Discrete frequency points, external excitation load and dynamic response satisfy In the formula, ω is the discrete angular frequency. Substituting equation (2-3) into equation (5) yields... S3: Construct the transfer function between the external excitation load degree of freedom and the desired response degree of freedom; from equation (6), the transfer function between the external excitation load degree of freedom and the desired response degree of freedom is: G=L exp ·(k-ω 2 ·m+ω·c·j) -1 ·L ext (7) In the formula, l is the dimension of the desired dynamic response; The modal superposition method is used for calculation: In the formula, Modal vector; ξ i ω i i th Modal frequency and modal damping; Step S3 includes: S31: Apply excitation load f1 to the external excitation load node, perform transient dynamic analysis, and extract the acceleration response of all desired response degrees of freedom: x 11 x 21 , ..., x l1 ; S32: Apply excitation load f2 to the external excitation load node, perform transient dynamic analysis, and extract the acceleration response of all desired response degrees of freedom: x 12 x 22 , ..., x l2 ; S33: Repeat the above steps until the excitation load f is applied at the last external excitation load node. k Conduct transient dynamic analysis to extract the acceleration response for all desired degrees of freedom: x 1k x 2k , ..., x lk ; S34: Perform a Fourier transform on all excitation loads to obtain... S35: Perform a Fourier transform on all acceleration responses to obtain: S36: Calculate the transfer function G between the external excitation load degree of freedom and the desired response degree of freedom at each discrete frequency point; S4: Construct an external excitation load in the frequency domain; Step S4 includes: S41: Perform a Fourier transform on all desired dynamic responses to obtain... S42: Identify the external excitation load at each discrete frequency point using the dynamic transfer function G calculated in S36. S5: Time sequence for calculating external excitation load; S6: Verify the constructed time-domain excitation load.

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