A frequency response calculation method, device and electronic equipment

Abstract

The present application relates to a kind of frequency response calculation method, device and electronic equipment, it is related to engineering technical field, it is intended to reduce the amount of calculation, improve the calculation efficiency of frequency response, comprising: in the process of frequency scanning to the detected structure, for each frequency point scanned, based on frequency point, modal solution parameter, degree of freedom information and the physical attribute of detected structure, construct the frequency response equation with damping, wherein, frequency point is used to reflect the excitation frequency applied to the detected structure, degree of freedom information is used to indicate at least one response dimension in frequency response analysis Concerned with;The frequency response equation with damping is reduced order, and first frequency response equation is obtained;In the case that there is damping in the physical attribute of detected structure, based on complex symmetric matrix, first frequency response equation is twice reduced order, and second frequency response equation is obtained;Based on second frequency response equation, the frequency response result corresponding to frequency point is obtained.

Description

Technical Field

[0001] This invention relates to the field of engineering technology, and more specifically to a method, apparatus, and electronic device for calculating frequency response. Background Technology

[0002] Frequency response analysis of structural systems is a core method for evaluating their dynamic performance and is crucial in industries such as automotive and aerospace. With the increasing complexity of modern products, finite element models typically have millions of degrees of freedom, requiring accurate high-frequency responses at hundreds of frequency points, which poses a significant challenge to computational capabilities.

[0003] Current frequency response analysis methods include direct methods and modal frequency response methods. Direct frequency response analysis requires solving a large-scale complex linear system of equations at each frequency point. Modal frequency response methods first use the Lanczos algorithm to solve the undamped generalized eigenvalue problem to obtain the modal matrix for order reduction, and then solve the coupled frequency response equations in the modal space. The solution still requires direct methods (such as LU decomposition) or iterative methods. For undamped systems, due to their modal orthogonality, the reduced-order equations are completely decoupled and can be solved efficiently. However, practical engineering structures commonly exhibit non-proportional or proportional damping composed of modal damping or structural damping.

[0004] Therefore, the current frequency response analysis methods used for damped engineering structures suffer from large computational loads and high computational costs. Summary of the Invention

[0005] This invention provides a method, apparatus, and electronic device for calculating frequency response, aiming to reduce the computational load and improve the computational efficiency of frequency response.

[0006] In a first aspect, the present invention provides a method for calculating frequency response, comprising: during frequency scanning of a structure under test, for each scanned frequency point, constructing a damped frequency response equation based on the frequency point, modal solution parameters, degree-of-freedom information, and physical properties of the structure under test, wherein the frequency point reflects the excitation frequency applied to the structure under test, and the degree-of-freedom information indicates at least one response dimension of interest in the frequency response analysis. The damped frequency response equation is then reduced in order to obtain a first frequency response equation. If damping exists in the physical properties of the structure under test, a second order reduction is performed on the first frequency response equation based on a complex symmetric matrix to obtain a second frequency response equation, wherein the complex symmetric matrix is ​​constructed based on the damped frequency response equation and the damping information of the structure under test. Based on the second frequency response equation, the frequency response result corresponding to the frequency point is obtained.

[0007] Based on the aforementioned technical means, this invention constructs a damped frequency response equation for each frequency point during frequency scanning of the tested structure, combining modal solution parameters, degree-of-freedom information, and the physical properties of the tested structure. This equation accurately reflects the dynamic response characteristics of the structure under actual working conditions. Furthermore, the damped frequency response equation is reduced in order to obtain a first frequency response equation, effectively reducing the solution scale. When damping exists in the physical properties of the tested structure, the first frequency response equation is further reduced in order to obtain a second frequency response equation, thereby further compressing the computational load while preserving the damping effect. Finally, the frequency response result corresponding to the frequency point is obtained based on the second frequency response equation. Therefore, this invention can significantly reduce the computational load and effectively improve the computational efficiency of frequency response calculations for large and complex structures containing damping characteristics.

[0008] Furthermore, the damped frequency response equation is reduced in order using the Automated Multi-Level Substructuring (AMLS) algorithm to obtain the first frequency response equation.

[0009] Based on the aforementioned technical means, AMLS can be used to reduce the order of the damped frequency response equation by performing multi-level substructure partitioning and condensation. This can significantly reduce the degree of freedom of the equation, thereby efficiently projecting the original high-dimensional frequency response equation to a low-dimensional modal space. Furthermore, it only focuses on a portion of the substructure, reducing the computational load. At the same time, since the AMLS algorithm itself has the parallel computing capability to handle ultra-large-scale problems, the solution time can be further shortened, making the frequency response analysis of the damped frequency response equation at multiple frequency points fast and feasible.

[0010] Furthermore, based on the AMLS method, the undamped generalized eigenvalue equation of the detected structure is constructed and solved to obtain the undamped generalized eigenvalue solution; based on the modal solution parameters, some eigenvectors in the undamped generalized eigenvalue solution are selected to construct a dimension-reduced subspace; the frequency response equation with damping is projected into the dimension-reduced subspace to obtain the first frequency response equation.

[0011] Based on the above technical means, by solving the undamped generalized eigenvalue equation of the tested structure, an undamped generalized eigenvalue solution that can accurately reflect the inherent characteristics of the structure can be obtained. On this basis, some eigenvectors are selected to construct a dimension-reduced subspace, which can approximate the overall vibration behavior of the structure with a small number of key modes. Furthermore, the original damped frequency response equation is projected onto the dimension-reduced subspace, so that the high-dimensional complex equation is effectively compressed into a low-dimensional modal space for description.

[0012] Furthermore, the complex symmetric matrix is ​​solved to obtain the complex modal eigenvectors; a complex eigenvector space is constructed based on the complex modal eigenvectors; the first frequency response equation is projected onto the complex eigenvector space to perform a second order reduction, resulting in the second frequency response equation.

[0013] Based on the above technical means, by solving the complex symmetric matrix based on damping information, a complex modal eigenvector that can accurately reflect the damping characteristics of the system is obtained; a complex eigenvector space is constructed using the complex modal eigenvector, which contains the coupling and modulation effect of damping on the vibration modes; the first frequency response equation is projected onto this complex eigenvector space for a second order reduction, thereby further compressing the equation scale while fully preserving the damping characteristics of the tested structure.

[0014] Furthermore, the inverse of the second frequency response equation is obtained, and then the modal solution of the second frequency response equation is obtained based on the inverse of the second frequency response equation; the frequency response result corresponding to the frequency point is obtained based on the modal solution of the second frequency response equation.

[0015] Based on the above technical means, by inverting the second frequency response equation obtained after second-order reduction, and then obtaining the modal solution of the equation based on its inverse matrix, the solution process is carried out in a highly compressed low-dimensional space, which significantly reduces the computational complexity of the inversion operation. On this basis, the frequency response result corresponding to the frequency point is obtained based on the modal solution of the second frequency response equation, thus completing the complete solution from the reduced-order space to the final physical response.

[0016] Furthermore, the modal solution parameters include the output modal order, modal cutoff frequency, and substructure control parameters set during the modal solution process. The substructure control parameters are used to set the dimensions of the substructure.

[0017] Based on the aforementioned technical means, the output modal order determines the number of modes extracted from the generalized eigenvalue problem and is associated with the dimension of the subsequent dimensionality reduction subspace. By reasonably configuring the output modal order, the scale of the reduction can be effectively controlled while ensuring computational accuracy. The parameters controlling the substructure modal solution are adjusted when using methods such as AMLS for modal extraction, including substructure partitioning, hierarchy depth, and internal truncation frequency, to ensure that the modal solution process can maintain high efficiency and numerical stability in large and complex structures.

[0018] Furthermore, in the absence of damping in the physical properties of the tested structure, the first frequency response equation is solved directly to obtain the frequency response result corresponding to the frequency point.

[0019] Based on the above technical means, since the first frequency response equation has undergone initial order reduction, its equation size is significantly reduced compared to the original frequency response equation, making the computational burden extremely low when solving the small-scale equation after order reduction by the direct method. At the same time, the equation structure is simpler in the case of no damping, and accurate frequency response results can be obtained efficiently with a very simple calculation process under the premise that the structural damping is negligible. This provides a lightweight solution approach for the rapid vibration analysis of large-scale undamped or weakly damped structures.

[0020] Secondly, the present invention provides a frequency response calculation device, comprising a construction module and a calculation module; the construction module is used to construct a damped frequency response equation for each scanned frequency point during frequency scanning of the structure under test, based on the frequency point, modal solution parameters, degree of freedom information, and physical properties of the structure under test; the calculation module is used to reduce the order of the damped frequency response equation to obtain a first frequency response equation; when damping exists in the physical properties of the structure under test, a second order reduction is performed on the first frequency response equation based on a complex symmetric matrix to obtain a second frequency response equation, wherein the complex symmetric matrix is ​​constructed based on the damped frequency response equation and the damping information of the structure under test; and the frequency response result corresponding to the frequency point is obtained based on the second frequency response equation.

[0021] Furthermore, the computation module is also used to reduce the order of the damped frequency response equation using the Automatic Multi-Level Substructure Algorithm (AMLS) to obtain the first frequency response equation.

[0022] Furthermore, the computation module is also used to construct and solve the undamped generalized eigenvalue equation of the detected structure based on the AMLS method to obtain the undamped generalized eigenvalue solution; based on the modal solution parameters, select some eigenvectors in the undamped generalized eigenvalue solution to construct a dimension-reduced subspace; and project the damped frequency response equation into the dimension-reduced subspace to obtain the first frequency response equation.

[0023] Furthermore, the computation module is also used to solve the complex symmetric matrix to obtain the complex modal eigenvectors; construct a complex eigenvector space based on the complex modal eigenvectors; and project the first frequency response equation onto the complex eigenvector space to perform a second order reduction to obtain the second frequency response equation.

[0024] Furthermore, the calculation module is also used to invert the second frequency response equation, and then obtain the modal solution of the second frequency response equation based on the inverse of the second frequency response equation; and obtain the frequency response result corresponding to the frequency point based on the modal solution of the second frequency response equation.

[0025] Furthermore, the modal solution parameters include the output modal order, modal cutoff frequency, and substructure control parameters set during the modal solution process. The substructure control parameters are used to set the dimensions of the substructure.

[0026] Furthermore, the calculation module is also used to directly solve the first frequency response equation when there is no damping in the physical properties of the detected structure, and obtain the frequency response result corresponding to the frequency point.

[0027] Thirdly, the present invention provides an electronic device comprising: a processor and a memory; the memory storing processor-executable instructions. When the processor is configured to execute the instructions, the electronic device implements the method of the first aspect described above.

[0028] Fourthly, the present invention provides a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the method of the first aspect described above.

[0029] Fifthly, the present invention provides a computer program product comprising computer program instructions that, when executed by a processor, implement the method of the first aspect described above.

[0030] It should be noted that the technical effects of any of the implementation methods in aspects two through five can be found in the technical effects of the corresponding implementation methods in aspect one, and will not be repeated here.

[0031] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0032] Figure 1 A schematic diagram of the architecture of a frequency response computing system provided by the present invention; Figure 2 A flowchart illustrating a method for calculating frequency response provided by the present invention; Figure 3 A flowchart illustrating another method for calculating frequency response provided by the present invention; Figure 4 A flowchart illustrating another method for calculating frequency response provided by the present invention; Figure 5 A schematic diagram illustrating the composition of a frequency response computing device provided by the present invention; Figure 6 This is a schematic diagram of the structure of an electronic device provided by the present invention. Detailed Implementation

[0033] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0034] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0035] The following is a detailed description of a frequency response calculation method, apparatus, and electronic device provided by the present invention, with reference to the accompanying drawings.

[0036] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0037] The terms "first" and "second," etc., used in the specification and drawings of this invention are used to distinguish different objects or to distinguish different treatments of the same object, rather than to describe a specific order of objects.

[0038] Furthermore, the terms "comprising" and "having," and any variations thereof, used in the description of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to such processes, methods, products, or apparatus.

[0039] It should be noted that in the embodiments of the present invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0040] To facilitate a clear description of the technical solutions of the embodiments of the present invention, the terms "first" and "second" are used in the embodiments of the present invention to distinguish the same or similar items with essentially the same function and effect. Those skilled in the art can understand that the terms "first" and "second" are not intended to limit the quantity or execution order.

[0041] In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0042] The embodiments provided by the present invention will now be described in detail with reference to the accompanying drawings.

[0043] The frequency response calculation method provided by this invention can be applied to, for example... Figure 1 The frequency response calculation system shown. For example... Figure 1 As shown, the frequency response calculation system 10 of the present invention includes: a computing device 11.

[0044] In some embodiments, the computing device 11 can acquire data such as frequency points, modal solution parameters, degree of freedom information, and physical properties of the structure under test, so that the computing device 11 can construct a damped frequency response equation based on the acquired data.

[0045] In some embodiments, the computing device 11 can also project the constructed frequency response equation with damping onto the vector space to reduce its order and solve it, thereby compressing the amount of computation and reducing the computational cost.

[0046] In some embodiments, the computing device 11 can be a server, such as a single server or a server cluster consisting of multiple servers. In some embodiments, the server cluster can also be a distributed cluster.

[0047] In some embodiments, the computing device 11 can be a terminal device, such as a mobile phone, tablet computer, desktop computer, laptop computer, handheld computer, notebook computer, ultra-mobile personal computer (UMPC), netbook, cellular phone, personal digital assistant (PDA), augmented reality (AR) / virtual reality (VR) device, etc. The embodiments of the present invention do not impose special limitations on the specific form of the terminal device.

[0048] Optionally, the computing device 11 can also store the acquired frequency points, modal solution parameters, degree of freedom information, and physical property data of the detected structure to facilitate data retrieval, processing, and analysis.

[0049] In some embodiments, the frequency response computing system 10 may further include a display device 12.

[0050] A communication connection is established between the display device 12 and the computing device 11. For example, the connection method can be wireless, such as Bluetooth or Wi-Fi; or it can be wired, such as fiber optic, etc., without limitation. For example, the display device 12 and the computing device 11 can be connected to the Internet via a router, thereby enabling the communication connection between them.

[0051] In some embodiments, the display device 12 is used to display the calculation results of the frequency response analysis. For example, the display device 12 presents the calculation results of the frequency response analysis to the user by displaying them on a screen.

[0052] In some embodiments, the computing device 11 and the display device 12 may be as follows: Figure 1 As shown, there are two separate devices, or the computing device 11 and the display device 12 can be integrated into the same device.

[0053] It should be noted that the system architecture described in the embodiments of the present invention is for the purpose of more clearly illustrating the technical solutions of the embodiments of the present invention, and does not constitute a limitation on the technical solutions provided by the embodiments of the present invention. As those skilled in the art will know, with the evolution of system architecture, the technical solutions provided by the embodiments of the present invention are also applicable to similar technical problems.

[0054] The frequency response calculation method proposed in this invention can be widely applied in industrial fields such as automobiles and aerospace, with the goal of calculating the frequency response at each excitation frequency point. This type of computational solution addresses modal frequency response problems, focusing on large structural systems with widely distributed structural damping and viscous damping. For example, in a full-scale automotive finite element model, viscous dampers are used in the suspension to control the movement of the springs supporting the vehicle. Taking the automotive engine mount system as an example, sinusoidal / cosine sweep loads simulating engine vibration excitation can be applied at 90 mount points, and vibration transmission path analysis can be performed using the steering wheel as the target response point.

[0055] The frequency response calculation method provided in this embodiment of the invention can be applied to computing devices in a frequency response calculation system, such as... Figure 2 As shown, the method for calculating the frequency response includes the following steps S201~S204: S201. During the frequency scanning of the structure under test, for each frequency point scanned, a damped frequency response equation is constructed based on the frequency point, modal solution parameters, degree of freedom information, and physical properties of the structure under test.

[0056] Among them, the frequency point is used to reflect the excitation frequency applied to the structure under test, and the degree of freedom information is used to indicate at least one response dimension of interest in the frequency response analysis.

[0057] In some embodiments, frequency scanning refers to the process of applying a series of continuously varying harmonic excitations to the structure under test in order to obtain the dynamic response characteristics of the structure at different excitation frequencies. Frequency scanning covers the entire frequency band from the start frequency to the end frequency.

[0058] For example, frequency scanning may include a start frequency, an end frequency, and all discrete frequency values ​​determined by the frequency step size. Frequency scanning may also include various scanning methods such as logarithmic frequency scanning or linear frequency scanning.

[0059] In some embodiments, the frequency point is a discrete excitation frequency value set during the frequency scanning process. Each frequency point corresponds to an independent frequency response calculation condition, and the set of all frequency points constitutes the sampling of the target frequency band.

[0060] In some embodiments, modal solution parameters are control parameters configured when performing modal analysis on the structure under test. They are used to guide the specific calculation process of extracting mode shapes and natural frequencies from the generalized eigenvalue problem. The modal solution parameters directly determine the composition of the subsequent reduced-order subspace.

[0061] In some embodiments, the modal solution parameters include the output modal order, modal cutoff frequency, and substructure control parameters set during the modal solution process. The substructure control parameters are used to set the dimensions of the substructure.

[0062] For example, the output mode order is used to specify the number of eigenvalue solutions extracted from the generalized eigenvalue problem. The size of the output mode order directly determines the dimension of the reduced subspace. Setting the output mode order too high will increase the computational burden, while setting it too low may lead to mode truncation error.

[0063] For example, the substructure control parameters are used to set the substructure partitioning method and substructure hierarchy depth when using the automatic multi-level substructure algorithm for modal solving.

[0064] For example, the modal cutoff frequency refers to a frequency threshold set in modal analysis or modal superposition-based analysis to determine which modes to retain and which to discard.

[0065] In some embodiments, the degree of freedom information is a data identifier used in frequency response analysis to indicate the location and direction of the response of interest on the structure being tested. The degree of freedom information typically corresponds to the motion components of a specific node in a finite element model in a specific coordinate axis direction, and is used to specify the location of the measurement point for which the output result is required.

[0066] For example, the degree of freedom information may include the node number and measurement direction of key measuring points on the structure being tested. The degree of freedom information may also include the coordinates of the reference point position and the response output dimension used to evaluate the vibration level of the structure. The degree of freedom information may include multiple response points to form the basis of vibration transmission path analysis.

[0067] In some embodiments, damping refers to the mechanism and measure of energy dissipation during vibration of the tested structure, and may include structural damping and viscous damping. The presence of damping causes the energy of the vibrating system to dissipate gradually, which is represented by the imaginary term in the dynamic stiffness matrix in the frequency domain.

[0068] For example, damping can include viscous damping and structural damping. Viscous damping describes an energy dissipation mechanism that is proportional to velocity. In a large automotive finite element model, viscous damping describes devices such as shock absorbers and engine mounts. The viscous damper generates a force at both ends of the device, which opposes the relative velocity between the two ends of the device, and the magnitude of the force is proportional to the relative velocity. Structural damping describes energy dissipation caused by internal friction of the material that is proportional to displacement but independent of frequency.

[0069] For example, both structural damping and viscous damping can constitute proportional damping or non-proportional damping, the key being whether the damping is uniformly distributed in space. If the damping distribution is uniform, or the damping matrix can be expressed as a linear combination of the mass matrix and the stiffness matrix, then it is proportional damping, with modal decoupling; if the damping is locally concentrated or unevenly distributed, then it is non-proportional damping, with modal coupling.

[0070] In some embodiments, the damped frequency response equation is a frequency domain dynamic equation describing the structure under test under harmonic excitation considering the energy dissipation mechanism. The coefficient matrix of the damped frequency response equation includes mass, stiffness, and various damping terms. The solution scale of the damped frequency response equation is the same as the finite element degree of freedom of the structure under test.

[0071] For example, the constructed damped frequency response equation can be shown below.

[0072]

[0073] in, , representing the finite element mass matrix of the structure being tested. This represents the stiffness matrix of the structure being tested. Represents the number of degrees of freedom in a finite element method. Scalar It is the global structural damping coefficient, i= . This represents the viscous damping matrix in the finite element method. This is the modal structural damping matrix, representing the local deviation of a specific element relative to the global structural damping level. In the frequency response, structural damping generates imaginary terms in the complex stiffness matrix that are independent of the excitation frequency. For the excitation force matrix... Frequency response At each excitation frequency The value is obtained by solving a set of complex linear equations in the frequency response equation with damping, where... This represents the number of load conditions.

[0074] In some embodiments, a damped frequency response equation is constructed based on the frequency point, modal solution parameters, degree of freedom information, and physical properties of the structure under test, so that the equation can accurately reflect the dynamic response characteristics of the structure under actual working conditions.

[0075] S202. The frequency response equation with damping is reduced in order to obtain the first frequency response equation.

[0076] In some embodiments, order reduction refers to the process of projecting the original high-dimensional damped frequency response equation to a low-dimensional subspace through mathematical transformation. The purpose of order reduction is to reduce the scale of the equation solution while preserving the main physical properties of the structure.

[0077] For example, the order reduction process may include a modal projection-based reduction method, or a subspace-based moment matching reduction method. The automatic multi-level substructure algorithm may be used as the reduction tool. In some embodiments, AMLS is used to reduce the order of the damped frequency response equation to obtain a first frequency response equation.

[0078] In some embodiments, AMLS refers to an eigenvalue solving and model order reduction method for ultra-large-scale finite element models. It recursively divides the overall structure into multi-level substructures, performs local condensation and modal synthesis on each substructure, and finally obtains the approximate global modes of the overall structure. AMLS can significantly reduce the solution scale and computation time of eigenvalue problems.

[0079] In some embodiments, after solving the undamped generalized eigenvalue problem using the AMLS algorithm, the damped frequency response equation is projected to reduce its order. Compared to directly using the Lanczos algorithm to solve the generalized eigenvalue problem for modal order reduction in traditional frequency response analysis, this avoids iterative projection and solution of the system matrix at each frequency point, allowing focus only on some substructures and degrees of freedom. Especially when the model has millions of degrees of freedom and hundreds of frequency points, the overall computational load is significantly reduced, improving computational efficiency.

[0080] In some embodiments, step S202 can be implemented as the following steps a1 to a3.

[0081] a1. Based on the AMLS method, construct and solve the undamped generalized eigenvalue equation of the detected structure to obtain the undamped generalized eigenvalue solution.

[0082] In some embodiments, the undamped generalized eigenvalue equation is a mathematical equation describing the free vibration characteristics of the structure under test. The form of the undamped generalized eigenvalue equation is that the stiffness matrix multiplied by the modal matrix is ​​equal to the mass matrix multiplied by the modal matrix multiplied by the eigenvalue diagonal matrix. The solution of the undamped generalized eigenvalue equation gives the natural frequencies and corresponding vibration mode shapes of the structure under test.

[0083] In some embodiments, the undamped generalized eigenvalue solution refers to the set of eigenvalue pairs obtained by solving the undamped generalized eigenvalue equation. The undamped generalized eigenvalue solution includes eigenvalues ​​and corresponding eigenvectors. The eigenvalues ​​reflect the square of the natural frequency of the detected structure, and the eigenvectors reflect the mode shapes of the detected structure.

[0084] In some embodiments, the stiffness matrix and mass matrix can be obtained as input by reading the finite element model data of the structure under test. The stiffness matrix and mass matrix can be passed to the AMLS solver by calling the AMLS method's solver program. The AMLS solver can then perform recursive substructure partitioning, local modal solving, and global condensation feature solving to obtain the undamped generalized feature solution. Finally, the eigenvalue matrix and modal matrix can be obtained by reading the output file of the AMLS solver.

[0085] An example of the undamped generalized eigenvalue problem is as follows.

[0086]

[0087] in, This represents the stiffness matrix of the structure being tested. This represents the finite element mass matrix of the structure being tested. This represents the eigenvalue matrix used to solve the undamped generalized eigenvalue problem. Represents the mode matrix, This indicates the number of modes obtained below the cutoff frequency, where the cutoff frequency represents the set upper frequency limit.

[0088] a2. Based on the modal solution parameters, select some eigenvectors from the undamped generalized eigenvalue solution to construct a dimension-reduced subspace.

[0089] In some embodiments, a subset of eigenvectors refers to a number of eigenvectors selected from all eigenvectors contained in the undamped generalized eigensol according to a specific rule, and the subset of eigenvectors constitutes the projection basis for subsequent order reduction processing.

[0090] In some embodiments, the reduced-dimensional subspace is a low-dimensional linear space spanned by selected eigenvectors. The dimension of the reduced-dimensional subspace is equal to the number of selected eigenvectors. The reduced-dimensional subspace is used to project the damped frequency response equation onto the low-dimensional space for solution.

[0091] In some embodiments, the number of feature vectors to be selected can be obtained by reading the output mode order in the mode solving parameters.

[0092] For example, the values ​​of all eigenvectors can be obtained by analyzing the mode matrix Φ in the undamped generalized eigensol. Then, based on the output mode order, the first few columns of the mode matrix Φ are truncated to obtain a subset of eigenvectors, which are then updated to Φ. By arranging the selected subset of eigenvectors into a matrix form, the basis matrix of the dimension-reduced subspace is constructed.

[0093] a3. Project the damped frequency response equation onto a reduced-dimensional subspace to obtain the first frequency response equation.

[0094] In some embodiments, projection refers to the process of mapping equations or vectors in a high-dimensional space to a low-dimensional subspace through mathematical transformation. The projection operation is usually implemented by multiplying the transpose of the subspace basis matrix with the original matrix.

[0095] For example, let The damped frequency response equation is obtained by left multiplying... Thus, the first frequency response equation is obtained. The first frequency response equation can be shown below.

[0096]

[0097] in, , Let represent the excitation force matrix. Due to modal orthogonality and mass normalization, the mass matrix is ​​diagonalized to . The stiffness matrix is ​​diagonalized to , Eigenvalue matrix for solving the undamped generalized eigenvalue problem Having the same physical quantities, the finite element viscous damping matrix is ​​diagonalized to The modal structure damping matrix is ​​diagonalized to , This represents the number of modes obtained below the cutoff frequency.

[0098] In some embodiments, by solving the undamped generalized eigenvalue equation of the detected structure, an undamped generalized eigenvalue solution that can accurately reflect the inherent characteristics of the structure is obtained; on this basis, a portion of the eigenvectors are selected to construct a dimension-reduced subspace, which can approximate the overall vibration behavior of the structure with a small number of key modes; furthermore, the original damped frequency response equation is projected onto the dimension-reduced subspace, so that the high-dimensional complex equation is effectively compressed into a low-dimensional modal space for description.

[0099] S203. When damping exists in the physical properties of the tested structure, the first frequency response equation is reduced to a second order based on the complex symmetric matrix to obtain the second frequency response equation.

[0100] The complex symmetric matrix is ​​based on the frequency response equation with damping and the damping information of the structure being tested.

[0101] In some embodiments, the presence of damping in the physical properties of the tested structure indicates that the structure has an energy dissipation mechanism. Frequency response analysis aims to accurately describe this physical process in a mathematical model, meaning that a damping matrix or damping coefficient needs to be introduced during the construction of the frequency response equation. This results in the coefficient matrix of the frequency response equation containing imaginary terms related to damping. The damping matrix or damping coefficient characterizes the strength, type, and distribution of damping; the imaginary unit represents phase lag: viscous damping causes the response to lag the excitation by 90°, while structural damping introduces a fixed phase difference independent of frequency. The real and imaginary parts of the complex number together determine the amplitude and phase angle of the vibration.

[0102] For example, when a sinusoidal displacement is applied to a purely viscous damping element (such as a shock absorber), the resulting damping force is not synchronized with the displacement, but with the velocity. In simple harmonic motion, the velocity waveform leads the displacement waveform by 90° (displacement lags velocity by 90°). Therefore, the damping force is 90° out of phase with respect to the displacement.

[0103] In some embodiments, the presence of damping in the physical properties of the tested structure can be determined by reading the physical property parameters of the tested structure and judging whether there are non-zero terms in the viscous damping matrix, the global structural damping coefficient, and the local structural damping matrix.

[0104] In some embodiments, the first frequency response equation can be reduced to a second frequency response equation by a second order based on a complex symmetric matrix; the complex symmetric matrix is ​​constructed based on the frequency response equation with damping and the damping information of the detected structure.

[0105] In some embodiments, a complex symmetric matrix is ​​a square matrix whose transpose is equal to itself and whose elements are complex numbers. A complex symmetric matrix is ​​usually composed of a stiffness matrix, a mass matrix and a damping matrix. The symmetry of the complex symmetric matrix comes from the inherent symmetry of the stiffness matrix and mass matrix and the symmetric construction of the damping matrix in finite element discretization.

[0106] For example, define a complex symmetric and frequency-independent matrix. It can be as shown below.

[0107]

[0108] in, Represents a complex symmetric matrix. This represents the diagonalized stiffness matrix. This represents the diagonalized modal structure damping matrix. This represents the global structural damping coefficient. Represents the imaginary unit. This represents the number of modes obtained below the cutoff frequency.

[0109] In some embodiments, the damping information of the detected structure refers to all parameters and matrices describing the energy dissipation mechanism of the detected structure. The damping information of the detected structure includes the viscous damping matrix, the global structural damping coefficient, and the local structural damping matrix, which constitute the main source of the imaginary terms in the frequency response equation.

[0110] In some embodiments, step S203 can be implemented as the following steps b1 to b3.

[0111] b1. Solve for the complex symmetric matrix to obtain the complex modal eigenvectors.

[0112] For example, the problem of finding the eigenvalues ​​of a complex symmetric matrix can be described as follows.

[0113]

[0114] in, Represents a complex eigenvalue matrix. Let represent the complex eigenvector matrix corresponding to the eigenvalues, where This represents the number of modes obtained below the cutoff frequency.

[0115] b2. Construct a complex feature vector space based on complex modal feature vectors.

[0116] For example, This is the constructed complex eigenvector space. Normalized to satisfy:

[0117] in, Represents the identity matrix.

[0118] b3. Project the first frequency response equation onto the complex eigenvector space to perform a second order reduction, and obtain the second frequency response equation.

[0119] For example, the first frequency response equation can be rewritten according to a complex symmetric matrix as follows.

[0120]

[0121] For example, in the automotive industry, the viscous damping matrix is ​​very sparse, which results in a typically very low rank. The modal viscous damping matrix is ​​decomposed into... Among them, the condensed viscous damping matrix Only includes finite element viscous damping matrices The non-zero rows and columns. Include The middle corresponds to Rows of non-zero elements. In automotive structures, typically... It can have dozens of degrees of freedom.

[0122] Next, for the matrix Perform singular value decomposition, and the singular value decomposition yields .

[0123] in, Includes singular values, and It is an orthogonal matrix. yes rank, and , The alternative representation of the rewritten first frequency response equation can be shown below.

[0124]

[0125] in and , , This represents the excitation force matrix.

[0126] Then, let and use The alternative representation of the first frequency response equation after rewriting the left-multiplication equation is:

[0127] in, This represents the complex eigenvector matrix corresponding to the eigenvalues. Indicates the excitation frequency. This represents the mass matrix after diagonalization. Represents the imaginary unit. , This represents the excitation force matrix. Then, based on the normalized... The above equation can be rewritten as:

[0128] Next, let's denote the diagonal matrix. for: Then the above equation can be expressed as the second frequency response equation:

[0129] in , , .

[0130] In some embodiments, the complex symmetric matrix fully preserves the damping characteristics of the detected structure and its coupling relationship in the frequency response equation. As the basis for the second-order reduction transformation, it can ensure the effective transmission of damping information while further compressing the equation size. Through the second-order reduction process, the first frequency response equation is projected from the modal space to a lower-dimensional subspace modulated by the damping information, so that the final second frequency response equation inherits the damping characteristics of the original structure and has a more compact mathematical form, thus reducing the computational load.

[0131] S204. Based on the second frequency response equation, the frequency response results corresponding to the frequency points are obtained.

[0132] In some embodiments, the coefficient matrix of the second frequency response equation Contains diagonal matrix Add a low-rank matrix , and If sparse matrices are directly decomposed, it is necessary to... The computational cost of this operation is high. The Sherman-Morrison-Woodbury (SMW) formula is used to perform the operation on the coefficient matrix. Perform efficient inverse calculation.

[0133] In some embodiments, the SMW formula is an identity in linear algebra used to calculate the inverse of a matrix, specifically addressing the problem of finding the inverse when the matrix can be expressed as a basic matrix plus a low-rank correction term. The SMW formula provides an equivalent transformation method that converts the inversion of a higher-order matrix into the inversion of a lower-order matrix, which can significantly reduce the computational cost of solving linear equation systems with special structures.

[0134] For example, using the SMW formula, the inverse of the coefficient matrix in the second frequency response equation is:

[0135] in , , and Then, solve. available:

[0136] Finally, the modal solution is obtained through inverse transformation. :

[0137] For example, by The frequency response can then be calculated.

[0138] In some embodiments, apart from the gyroscopic effect, most structural systems have a symmetric viscous damping matrix. .for In this situation, The eigenvalue decomposition of a matrix is ​​expressed as In this case, the modal solution becomes:

[0139] in, , , , Represents the excitation force matrix. This represents the complex eigenvector matrix corresponding to the eigenvalues.

[0140] In some embodiments, by inverting the second frequency response equation obtained after second-order reduction, and then obtaining the modal solution of the equation based on its inverse matrix, the solution process is carried out in a highly compressed low-dimensional space, significantly reducing the computational complexity of the inversion operation. Based on this, the frequency response result corresponding to the frequency point is obtained based on the modal solution of the second frequency response equation, completing the complete solution from the reduced-order space to the final physical response. In some embodiments, the frequency response calculation method provided by the present invention further includes directly solving the first frequency response equation to obtain the frequency response result corresponding to the frequency point when there is no damping in the physical properties of the detected structure.

[0141] In some embodiments, direct solution refers to numerically solving the system of equations using direct methods. Direct solution is typically based on matrix factorization techniques, such as LU decomposition or Cholesky decomposition. Direct solution can obtain the exact solution to the system of equations in a finite number of computational steps without involving an iterative convergence process.

[0142] For example, the ZGETRF function in the LAPACK library can be called to perform LU decomposition on the coefficient matrix of the first frequency response equation, obtaining the decomposed lower triangular matrix L and upper triangular matrix U. Then, the ZGETRS function is called to use the decomposed L and U to perform back-substitution on the right-hand side of the first frequency response equation, obtaining the modal coordinate response vector q(ω). The computing device reads the modal matrix Φ from the previous steps and calculates the frequency response result X(ω) in degrees of freedom by multiplying Φ by q(ω).

[0143] In some embodiments, since the first frequency response equation has undergone initial order reduction, its equation size is significantly reduced compared to the original frequency response equation, making the computational burden extremely low when solving the small-scale equation after order reduction by the direct method. At the same time, the equation structure is simpler in the case of no damping, and accurate frequency response results can be obtained efficiently with a very simple calculation process under the premise that the structural damping is negligible, providing a lightweight solution approach for rapid vibration analysis of large-scale undamped or weakly damped structures.

[0144] In some embodiments, the frequency response calculation method provided by the present invention can solve the undamped generalized eigenvalue problem using the AMLS algorithm, then project the damped frequency response equation to obtain the first frequency response equation, focusing only on some substructures and degrees of freedom; next, construct complex eigenvectors, and project the first frequency response equation focusing only on some substructures and degrees of freedom into the complex eigenvector space to obtain the second frequency response equation. The second frequency response equation has a low-rank modified structure, which enables fast inversion using the SMW formula, greatly improving the solution efficiency and avoiding the high costs associated with traditional methods that either directly solve in physical space (computational complexity increases with the cube of the degrees of freedom) or directly solve the coupled modal equations after projecting and reducing the order of the generalized eigenvalue problem using Lanczos (computational complexity increases with the cube of the number of modes).

[0145] For example, Table 1 shows the number of operations in each step of the frequency response calculation method. The frequency response calculation method requires... The complex symmetric eigenvalue problem is solved in one operation, and this calculation only needs to be performed once. At each frequency point, when have When there is a right-hand item, need This operation is performed once. If the force is independent of the frequency, then step 7 in the table only needs to be calculated once before the frequency scan. For the calculation... Steps 8 and 9 in the table require This operation, the inverse transformation in step 19 of the table requires... Therefore, the calculation of frequency response is concentrated in solving the eigenvalue problem, which requires one operation. The calculations, and the load conditions at each frequency point. The cost of decomposing the finite element viscous damping matrix and the matrix multiplications associated with the low-rank matrix is ​​negligible.

[0146] Table 1. Computational operations and computational complexity for each step.

[0147] For example, such as Figure 3 As shown, after the frequency response calculation process begins, step S1 is executed first to construct a damped frequency response equation based on the frequency point, modal solution parameters, degree of freedom information, and the physical properties of the detected structure. Next, step S2 is executed to obtain the first frequency response equation. The damped frequency response equation is reduced in order by calculating the undamped generalized eigenvalue problem. Then, step S3 is executed to determine if damping exists. If not, step S4 is executed to begin frequency sweeping. Next, step S5 is executed to directly solve the first frequency response equation to obtain the frequency response result corresponding to the frequency point. Then, step S6 is executed to determine if frequency sweeping is complete. If not, the process returns to step S4; if complete, step S7 is executed to complete the frequency response calculation, and then the process ends. If step S3 determines that damping exists, step S8 is executed for preprocessing, transforming the first frequency response equation based on the complex characteristic equation. Next, step S9 is executed to begin frequency sweeping. Then, step S10 is executed to solve the eigenvalues ​​of the complex symmetric matrix to construct the projection space. Next, step S11 is executed to obtain the second frequency response equation. The first frequency response equation is projected onto the projection space constructed by the eigenvectors of the complex symmetric matrix to obtain the second frequency response equation. Then, step S12 is executed to invert the second frequency response equation and determine the frequency response result corresponding to the frequency point based on the inversion result. Then, step S13 is executed to determine whether the frequency sweep is complete. If not, the process returns to step S9; if complete, step S14 is executed to complete the frequency response calculation method, achieving rapid frequency response calculation for the detected structure under damping conditions, and then the process ends.

[0148] For example, such as Figure 4 As shown, after the frequency response calculation process begins, modal solution information is first input to determine the specific dimensions of the subsequent calculations. Then, the frequency point is input to determine the applied excitation frequency. Next, the degrees of freedom are input to determine the computational dimensions of interest in the frequency response analysis. The automatic multi-level substructure algorithm is then used to reduce the order of the constructed damped frequency response equation, obtaining the first frequency response equation. Next, the characteristic equations of the substructure containing the degrees of freedom of interest are calculated, transforming the calculations in physical space to modal space, thus reducing the computational load. Finally, a rapid solution to the frequency response problem is achieved, and the process ends.

[0149] The foregoing primarily describes the solutions provided by the embodiments of the present invention from a methodological perspective. To achieve the aforementioned functions, the frequency response computing device includes hardware structures and / or software modules corresponding to the execution of each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments disclosed herein, the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0150] like Figure 5 As shown, the frequency response calculation device 1000 includes: a construction module 1001 and a calculation module 1002; the construction module is used to construct a damped frequency response equation for each scanned frequency point during the frequency scanning process of the structure under test, based on the frequency point, modal solution parameters, degree of freedom information, and physical properties of the structure under test; the calculation module is used to reduce the order of the damped frequency response equation to obtain a first frequency response equation; when damping exists in the physical properties of the structure under test, a second order reduction is performed on the first frequency response equation based on a complex symmetric matrix to obtain a second frequency response equation, the complex symmetric matrix being constructed based on the damped frequency response equation and the damping information of the structure under test; based on the second frequency response equation, the frequency response result corresponding to the frequency point is obtained.

[0151] Furthermore, the calculation module 1002 is also used to reduce the order of the damped frequency response equation by employing the Automatic Multi-Level Substructure Algorithm (AMLS) to obtain the first frequency response equation.

[0152] Furthermore, the calculation module 1002 is also used to construct and solve the undamped generalized eigenvalue equation of the detected structure based on the AMLS method to obtain the undamped generalized eigenvalue solution; based on the modal solution parameters, select some eigenvectors in the undamped generalized eigenvalue solution to construct a dimension-reduced subspace; and project the damped frequency response equation into the dimension-reduced subspace to obtain the first frequency response equation.

[0153] Furthermore, the calculation module 1002 is also used to solve the complex symmetric matrix to obtain the complex modal eigenvectors; construct a complex eigenvector space based on the complex modal eigenvectors; and project the first frequency response equation onto the complex eigenvector space to perform a second order reduction to obtain the second frequency response equation.

[0154] Furthermore, the calculation module 1002 is also used to invert the second frequency response equation, and then obtain the modal solution of the second frequency response equation based on the inverse of the second frequency response equation; and obtain the frequency response result corresponding to the frequency point based on the modal solution of the second frequency response equation.

[0155] Furthermore, the modal solution parameters include the output modal order, modal cutoff frequency, and substructure control parameters set during the modal solution process. The substructure control parameters are used to set the dimensions of the substructure.

[0156] Furthermore, the calculation module 1002 is also used to directly solve the first frequency response equation when there is no damping in the physical properties of the detected structure, and obtain the frequency response result corresponding to the frequency point.

[0157] like Figure 6 As shown, the electronic device 1100 includes, but is not limited to, a processor 1101 and a memory 1102.

[0158] The memory 1102 described above is used to store the executable instructions of the processor 1101. It is understood that the processor 1101 is configured to execute instructions to perform the frequency response calculation in the above embodiment.

[0159] It should be noted that those skilled in the art will understand that Figure 6 The electronic device structure shown does not constitute a limitation on electronic device 1100; electronic device 1100 may include, but is not limited to, other electronic devices. Figure 6 This may indicate more or fewer components, or combinations of certain components, or different component arrangements.

[0160] Processor 1101 is the control center of electronic device 1100. It connects various parts of the electronic device via various interfaces and lines. By running or executing software programs and / or modules stored in memory 1102, and by calling data stored in memory 1102, it performs various functions and processes data of electronic device 1100, thereby providing overall monitoring of electronic device 1100. Processor 1101 may include one or more processing units. Optionally, processor 1101 may integrate an application processor and a modem processor. The application processor mainly handles the operating system, user interface, and applications, while the modem processor mainly handles wireless communication. It is understood that the modem processor may not be integrated into processor 1101.

[0161] The memory 1102 can be used to store software programs and various data. The memory 1102 may primarily include a program storage area and a data storage area. The program storage area may store the operating system, application programs required by at least one functional module (such as a determination unit, processing unit, etc.), etc. Furthermore, the memory 1102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0162] In an exemplary embodiment, a computer-readable storage medium including instructions is also provided, such as a memory 1102 including instructions, which can be executed by a processor 1101 of an electronic device 1100 to implement the frequency response calculation method in the above embodiments.

[0163] In actual implementation, Figure 5 The functions of both the construction module 1001 and the calculation module 1002 can be provided by... Figure 6 The processor 1101 calls the computer program stored in the memory 1102 to implement the process. The specific execution process can be found in the method section of the previous embodiment, and will not be repeated here.

[0164] Optionally, the computer-readable storage medium may be a non-transitory computer-readable storage medium, such as a read-only memory (ROM), random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device.

[0165] In an exemplary embodiment, the present invention also provides a computer program product including one or more instructions, which can be executed by the processor 1101 of the electronic device 1100 to complete the frequency response calculation method in the above embodiment.

[0166] It should be noted that when one or more instructions in the computer-readable storage medium or computer program product are executed by the processor of an electronic device, they implement the various processes of the above method embodiments and achieve the same technical effect as the above method. To avoid repetition, they will not be described again here.

[0167] Through the above description of the embodiments, those skilled in the art can clearly understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0168] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0169] The units described as separate components may or may not be physically separate. A component shown as a unit can be one or more physical units; that is, it can be located in one place or distributed in multiple different locations. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0170] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0171] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a readable storage medium. Based on this understanding, the technical solution of the embodiments of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, ROM, RAM, magnetic disks, or optical disks.

[0172] The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention.

Claims

1. A method for calculating frequency response, characterized in that, The method includes: During the frequency scanning of the structure under test, for each frequency point scanned, a damped frequency response equation is constructed based on the frequency point, modal solution parameters, degree of freedom information, and physical properties of the structure under test. The frequency point is used to reflect the excitation frequency applied to the structure under test, and the degree of freedom information is used to indicate at least one response dimension of interest in the frequency response analysis. The frequency response equation with damping is reduced in order to obtain the first frequency response equation; When damping exists in the physical properties of the detected structure, the first frequency response equation is reduced to a second order based on a complex symmetric matrix to obtain the second frequency response equation. The complex symmetric matrix is ​​constructed based on the damped frequency response equation and the damping information of the detected structure. Based on the second frequency response equation, the frequency response result corresponding to the frequency point is obtained.

2. The method for calculating frequency response according to claim 1, characterized in that, The process of reducing the order of the damped frequency response equation to obtain the first frequency response equation includes: The damped frequency response equation is reduced in order using the Automatic Multi-Level Substructure Algorithm (AMLS) to obtain the first frequency response equation.

3. The method for calculating frequency response according to claim 2, characterized in that, The frequency response equation with damping is reduced in order using the Automatic Multi-Level Substructure Algorithm (AMLS) to obtain the first frequency response equation, which includes: Based on the AMLS, the undamped generalized eigenvalue equation of the detected structure is constructed and solved to obtain the undamped generalized eigenvalue solution. Based on the modal solution parameters, select some eigenvectors from the undamped generalized eigensol to construct a dimension-reduced subspace; Projecting the damped frequency response equation into the reduced-dimensional subspace yields the first frequency response equation.

4. The method for calculating frequency response according to claim 1, characterized in that, The second frequency response equation is obtained by performing a second-order reduction process on the first frequency response equation based on a complex symmetric matrix, including: Solving the complex symmetric matrix yields the complex modal eigenvectors; Construct a complex feature vector space based on the complex modal feature vectors; The first frequency response equation is projected onto the complex eigenvector space to perform a second order reduction, resulting in the second frequency response equation.

5. The method for calculating frequency response according to claim 1, characterized in that, The step of obtaining the frequency response result corresponding to the frequency point based on the second frequency response equation includes: The inverse of the second frequency response equation is obtained, and then the modal solution of the second frequency response equation is obtained based on the inverse of the second frequency response equation; The frequency response result corresponding to the frequency point is obtained based on the modal solution of the second frequency response equation.

6. The method for calculating frequency response according to claim 1, characterized in that, The modal solution parameters include the output modal order, modal cutoff frequency, and substructure control parameters set during the modal solution process. The substructure control parameters are used to set the dimensions of the substructure.

7. The method for calculating frequency response according to claim 1, characterized in that, The method further includes: If the damping is absent in the physical properties of the tested structure, the first frequency response equation is solved directly to obtain the frequency response result corresponding to the frequency point.

8. A frequency response computing device, characterized in that, The frequency response computing device includes a construction module and a computing module; The construction module is used to construct a damped frequency response equation for each frequency point scanned during the frequency scanning process of the structure under test, based on the frequency point, modal solution parameters, degree of freedom information and the physical properties of the structure under test. The calculation module is used to reduce the order of the damped frequency response equation to obtain the first frequency response equation. When damping exists in the physical properties of the detected structure, the first frequency response equation is reduced to a second order based on a complex symmetric matrix to obtain a second frequency response equation. The complex symmetric matrix is ​​constructed based on the damped frequency response equation and the damping information of the detected structure. Based on the second frequency response equation, the frequency response result corresponding to the frequency point is obtained.

9. An electronic device, characterized in that, include: Processor and memory; The memory stores instructions that the processor can execute; When the processor is configured to execute the instructions, it causes the electronics to implement the frequency response calculation method as described in any one of claims 1-7.

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