Method and device for solving fluid-induced structure vibration and acoustic radiation based on modal superposition method

Abstract

The application provides a flow-induced structure vibration and sound radiation solving method and device based on a modal superposition method, which comprises the following steps: establishing a three-dimensional model of a target structure, obtaining a structure overall grid, a structure surface grid, a structure surface geometric model and a fluid domain grid; establishing a fluid-structure coupling model in Abaqus according to the structure overall grid and the fluid domain grid, and calculating a wet modal, determining a modal frequency and a modal vibration mode under the wet modal; calculating an ATV from a structure surface node to a sound pressure field point in Comsol according to the structure surface grid and the structure surface geometric model; obtaining a turbulent fluctuating pressure distribution according to an empirical model or CFD simulation calculation; inputting the results obtained in the above steps as inputs into a flow-induced structure vibration and sound radiation solving program of the modal superposition method, and solving to obtain vibration results of the structure surface and sound radiation results of the sound pressure field point. The application can quickly and accurately calculate the structure vibration and sound radiation under turbulent excitation.

Description

Technical Field

[0001] This invention relates to the field of structural vibration technology, and in particular to a method and apparatus for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method. Background Technology

[0002] With the development of technology and the improvement of anti-submarine technology, improving the stealth performance of submarines has become a huge challenge. Acoustic stealth performance is a crucial component of submarine stealth performance, and the submarine's own radiated noise is one of the important indicators of its acoustic stealth performance. Therefore, the accurate prediction and control of submarine radiated noise is particularly important. As the speed of submarines increases, the proportion of hydrodynamic noise in radiated noise becomes increasingly prominent. Turbulent boundary layer-excited structural vibration radiated noise is one of the main sources of hydrodynamic noise, but it involves fluid-structure interaction and random vibration problems, making the solution process complex and time-consuming. Therefore, the rapid and accurate prediction of turbulent-excited structural vibration is of great significance.

[0003] A review of relevant domestic and international literature reveals that researchers have conducted extensive studies on the prediction of vibration and noise in turbulently excited structures. Some researchers have established analytical models for turbulently excited flat plates and cylindrical shells, and solved for accurate results of structural vibration based on stochastic theory and turbulence models. Other researchers have conducted experimental studies on the vibration and noise of turbulently excited structures; however, experiments on turbulently excited structural vibrations are often complex, and the signal-to-noise ratio is difficult to control. With the development of finite element method (FEM) software, many scholars have studied simulation methods for turbulently excited structural vibrations. However, when using FEM software to calculate the flow-induced response of large structures, it is difficult to simultaneously balance solution efficiency and result accuracy, often requiring complex theories and procedures to correct the calculation results. Summary of the Invention

[0004] This invention provides a method and apparatus for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method, which solves the shortcomings of existing technologies that cannot simultaneously consider the solution efficiency and the accuracy of results when using finite element software to calculate the flow-induced response of large structures, and realizes the rapid and accurate calculation of flow-induced vibration and acoustic radiation of surfaces of arbitrary shapes.

[0005] This invention provides a method for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method, comprising:

[0006] A three-dimensional model of the target structure is established, and the overall structural mesh, structural surface mesh, structural surface geometric model, and fluid domain mesh of the target structure are obtained based on the three-dimensional model.

[0007] A fluid-structure interaction model is established in the finite element software Abaqus based on the overall structural mesh and the fluid domain mesh. The wet modes of the target structure are calculated based on the fluid-structure interaction model, and the modal frequencies and mode shapes of the structural surface nodes under the wet modes are determined.

[0008] Based on the structural surface mesh and the structural surface geometric model, the acoustic transfer vector (ATV) from the structural surface nodes to the acoustic pressure field points is calculated in the finite element software Comsol.

[0009] The turbulent pulsating pressure distribution at the nodes on the structural surface is obtained based on empirical models or CFD simulation calculations.

[0010] The modal frequencies, mode shapes, acoustic transfer vectors (ATVs) from structural surface nodes to acoustic pressure field points, and turbulent pulsating pressure distributions at structural surface nodes under the wet modal conditions are used as inputs and imported into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

[0011] According to the present invention, a method for solving flow-induced structural vibration and acoustic radiation based on modal superposition, after establishing a fluid-structure interaction model in the finite element software Abaqus based on the overall structural mesh and the fluid domain mesh, further includes:

[0012] Apply boundary constraints to the fluid-structure interaction model;

[0013] If the fluid domain is a semi-infinite domain, then set the acoustic infinite element property on the outer surface of the fluid domain or use the non-reflective acoustic impedance property.

[0014] According to the present invention, a method for solving flow-induced structural vibration and acoustic radiation based on modal superposition is provided. The method calculates the acoustic transfer vector (ATV) from the structural surface nodes to the acoustic pressure field points in the finite element software Comsol, based on the structural surface mesh and the structural surface geometric model. The method includes:

[0015] Import the structural surface mesh and the structural surface geometry model into the finite element software Comsol, and select the pressure acoustics-boundary element module;

[0016] A point sound source is set at the point of interest in the sound pressure field, and the sound scattering on the surface of the structure is calculated under the excitation of the point sound source.

[0017] Based on the acoustic scattering from the surface of the structure, the acoustic transfer vector (ATV) from the nodes on the surface of the structure to the sound pressure field points is obtained using reciprocity.

[0018] According to the present invention, a method for solving flow-induced structural vibration and acoustic radiation based on modal superposition is provided, wherein the empirical model is an empirical model of turbulent pulsating pressure self-power spectrum.

[0019] According to the present invention, a method for solving flow-induced structural vibration and acoustic radiation based on modal superposition is provided, wherein the empirical model of turbulent pulsating pressure self-power spectrum is the Goody model.

[0020] The present invention also provides a device for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method, comprising:

[0021] The construction module is used to build a three-dimensional model of the target structure, and to obtain the overall structural mesh, structural surface mesh, structural surface geometric model and fluid domain mesh of the target structure based on the three-dimensional model.

[0022] The first calculation module is used to establish a fluid-structure interaction model in the finite element software Abaqus based on the overall structure mesh and the fluid domain mesh, calculate the wet modes of the target structure based on the fluid-structure interaction model, and determine the modal frequencies and mode shapes of the structural surface nodes under the wet modes.

[0023] The second calculation module is used to calculate the acoustic transfer vector (ATV) from the nodes of the structural surface to the sound pressure field points in the finite element software Comsol, based on the structural surface mesh and the structural surface geometric model.

[0024] The third calculation module is used to obtain the turbulent pulsating pressure distribution at the nodes on the structural surface based on empirical models or CFD simulation calculations.

[0025] The solution module is used to take the modal frequencies, mode shapes, acoustic transfer vectors (ATV) from the structural surface nodes to the acoustic pressure field points, and the turbulent pulsating pressure distribution at the structural surface nodes as inputs, and import them into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

[0026] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the flow-induced structural vibration and acoustic radiation solution method based on the modal superposition method as described above.

[0027] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method as described above.

[0028] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the flow-induced structural vibration and acoustic radiation solution method based on the modal superposition method described above.

[0029] The present invention provides a method and apparatus for solving flow-induced structural vibration and acoustic radiation based on modal superposition. By addressing the structural vibration and acoustic radiation caused by the pulsating pressure of the turbulent boundary layer outside the structure, the method simplifies the flow-induced response solution process from the perspective of the structural response transfer function and utilizes the modal orthogonality characteristics of the structure. At the same time, a flow-induced pulsating pressure load correction factor is introduced, enabling the method to quickly and accurately calculate the flow-induced vibration and acoustic radiation of surfaces with arbitrary shapes. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0031] Figure 1 This is a flowchart illustrating the method for solving flow-induced structural vibration and acoustic radiation based on modal superposition provided by the present invention.

[0032] Figure 2 This is a complete flowchart of the method for solving flow-induced structural vibration and acoustic radiation based on modal superposition provided by the present invention;

[0033] Figure 3 This is a schematic diagram of a cylindrical shell in the flow-induced structural vibration and acoustic radiation solution method based on modal superposition provided by the present invention;

[0034] Figure 4 This is a schematic diagram showing the comparison of vibration velocities at the midpoint 1 of a cylindrical shell in the flow-induced structural vibration and acoustic radiation solution method based on modal superposition provided by this invention.

[0035] Figure 5 This is a schematic diagram showing the comparison of vibration velocities at the midpoint 2 of a cylindrical shell in the flow-induced structural vibration and acoustic radiation solution method based on modal superposition provided by this invention.

[0036] Figure 6 This is a schematic diagram showing the comparison of sound pressure field points in the flow-induced structural vibration and sound radiation solution method based on modal superposition provided by this invention;

[0037] Figure 7 This is a schematic diagram of the device for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method provided by the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0039] The following is combined with Figure 1 The present invention describes a method for solving flow-induced structural vibration and acoustic radiation based on modal superposition, comprising:

[0040] Step 101: Establish a three-dimensional model of the target structure, and obtain the overall structural mesh, surface mesh, surface geometric model, and fluid domain mesh of the target structure based on the three-dimensional model;

[0041] A three-dimensional shell model of the target structure can be established. Based on the minimum bending wavelength of the structure, the shell element mesh is generated according to the minimum meshing requirement of 6 elements within one wavelength. A fluid domain of appropriate size is established based on the shape of the structure, and a volume mesh is generated.

[0042] Export the geometric model of the structural surface, the overall structural mesh, and the fluid domain mesh. Additionally, export the mesh file of the structural surface.

[0043] Step 102: Establish a fluid-structure interaction model in the finite element software Abaqus based on the overall structural mesh and the fluid domain mesh; calculate the wet modes of the target structure based on the fluid-structure interaction model; and determine the modal frequencies and mode shapes of the structural surface nodes under the wet modes.

[0044] Import the overall structural mesh and fluid domain mesh exported in step 101 into the finite element software Abaqus, and use Tie connections to establish the fluid-structure interaction relationship between the structure and the fluid domain.

[0045] Establish a natural frequency analysis step, set the natural frequency solution range, and select a mode shape that is normalized with respect to the mass matrix to extract the modal frequencies and the mode shapes of the structural surface nodes.

[0046] Step 103: Based on the structural surface mesh and the structural surface geometric model, calculate the acoustic transfer vector (ATV) from the structural surface nodes to the sound pressure field points in the finite element software Comsol.

[0047] Step 104: Obtain the turbulent pulsating pressure distribution at the nodes on the structural surface based on empirical models or CFD (Computational Fluid Dynamics) simulations.

[0048] Step 105: The modal frequencies, mode shapes, acoustic transfer vectors (ATV) from structural surface nodes to acoustic pressure field points, and turbulent pulsating pressure distributions at structural surface nodes under the wet modal conditions are taken as inputs and imported into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

[0049] Using the modal superposition method and the inputs obtained in steps 101 to 104, the vibration response and acoustic radiation of the structural surface are solved. The specific process is as follows: Figure 2 As shown.

[0050] This embodiment simplifies the flow-induced response solution process by taking into account the structural vibration and acoustic radiation caused by the turbulent boundary layer pulsating pressure outside the structure, starting from the perspective of the structural response transfer function and utilizing the modal orthogonality characteristics of the structure. At the same time, a flow-induced pulsating pressure load correction factor is introduced, enabling the method to quickly and accurately calculate the flow-induced vibration and acoustic radiation of surfaces with arbitrary shapes.

[0051] Based on the above embodiments, this embodiment, after establishing a fluid-structure interaction model in the finite element software Abaqus according to the overall structural mesh and the fluid domain mesh, further includes:

[0052] Apply boundary constraints to the fluid-structure interaction model according to actual needs;

[0053] If the fluid domain is a semi-infinite domain, then set the acoustic infinite property or use the non-reflecting acoustic impedance property on the outer surface of the fluid domain.

[0054] Based on the above embodiments, this embodiment calculates the acoustic transfer vector (ATV) from the structural surface nodes to the sound pressure field points in the finite element software Comsol, according to the structural surface mesh and the structural surface geometric model, including:

[0055] Import the structural surface mesh and the structural surface geometry model into the finite element software Comsol, and select the pressure acoustics-boundary element module;

[0056] A point sound source is set at the point of interest in the sound pressure field, and the sound scattering on the surface of the structure is calculated under the excitation of the point sound source.

[0057] Based on the acoustic scattering from the surface of the structure, the acoustic transfer vector (ATV) from the nodes on the surface of the structure to the sound pressure field points is obtained using reciprocity.

[0058] Based on the above embodiments, the empirical model described in this embodiment is the empirical model of turbulent pulsating pressure self-power spectrum.

[0059] Based on the above embodiments, the empirical model of turbulent pulsating pressure self-power spectrum in this embodiment is the Goody model.

[0060] The following is the relevant theory of the solution method for flow-induced structural vibration and acoustic radiation based on the modal superposition method provided in this embodiment.

[0061] For an N-degree-of-freedom system, its equation of motion is:

[0062] (1)

[0063] in, (2)

[0064] This is called the impedance matrix of the system, and its dimension is N×N.

[0065] make (3)

[0066] This is called the admittance matrix of the system, also known as the frequency response function.

[0067] Assume the principal mode matrix of the N-degree-of-freedom system is And make it affect the system's quality matrix. Normalization, that is:

[0068] (4)

[0069] Using the system's principal modes of vibration and their orthogonality, equation (3) is transformed as follows:

[0070] (5)

[0071] in, is the modal damping ratio.

[0072] (6)

[0073] It is called the modal admittance matrix.

[0074] According to stochastic theory, in discrete form, the power spectrum matrix of the structural vibration displacement response excited by turbulent pulsating pressure can be written as:

[0075] (7)

[0076] in, The displacement response power spectrum at element i. The cross-power spectrum of the displacement response between element i and element j. The power spectral density matrix of the turbulent pulsating pressure load is given by the following formula:

[0077] (8)

[0078] in, Let i be the self-power spectral density of the load at element i. Let be the cross-power spectral density of the load between element i and element j.

[0079] The complex frequency response function matrix is ​​given by the formula:

[0080] (9)

[0081] in, The meaning is to apply an angular frequency of at element j. The displacement response at element i under a unit harmonic force, and has .

[0082] Substituting formula (5) into formula (7) yields:

[0083] (10)

[0084] According to formula (10), the natural frequencies of the N-degree-of-freedom system are obtained. Principal mode matrix Modal damping ratio and load matrix Then, the displacement response power spectrum matrix of the N-degree-of-freedom system can be solved.

[0085] The power spectral density matrix of the structural velocity response is then:

[0086] (11)

[0087] The power spectral density matrix of the structural velocity response is actually expressed as:

[0088] (12)

[0089] in, Let be the vibration velocity of the i-th sample segment.

[0090] If the normal vibration velocity and the acoustic propagation vector (ATV) of the structural surface are known, then the sound pressure at the field point can be expressed as:

[0091] (13)

[0092] The power spectral density matrix of the sound pressure at the field point is then expressed as:

[0093] (14)

[0094] Substituting equations (12) and (13) into equation (14), we obtain the power spectral density matrix of the sound pressure at the field point:

[0095] (15)

[0096] Combining formulas (10), (11), and (15), the power spectral density matrix of the sound pressure at the field point is further expressed as:

[0097] (16)

[0098] in This is the modal sound transfer vector.

[0099] The specific steps of the modal superposition method include: obtaining the modal frequency and modal damping ratio, and then obtaining the modal frequency response function matrix through formula (6); obtaining the turbulent turbulent pressure excitation force matrix through formula (8) after obtaining the pulsating pressure at the nodal surface of the structure; substituting the modal frequency response function matrix, mode shape, and turbulent turbulent pressure excitation force matrix into formula (10) to obtain the displacement power spectral density matrix of the nodal surface of the structure; and after obtaining the acoustic transfer vector ATV, substituting the modal frequency response function matrix, mode shape, turbulent turbulent pressure excitation force matrix, and acoustic transfer vector ATV into formula (16) to obtain the acoustic pressure self-power spectral density matrix of the sound pressure field point.

[0100] For example, calculate the vibration response and sound radiation at the sound pressure point of a cylindrical shell with simply supported ends and no end plates, when subjected to turbulent pulsating pressure excitation in the presence of external water. A schematic diagram of the cylindrical shell is shown below. Figure 3 The parameters of the cylindrical shell are shown in Table 1.

[0101] Table 1 Parameter Table

[0102]

[0103] The turbulent pulsating pressure on the cylindrical shell is assumed to be 1 Pa at each node, and the cross-power spectrum of the pulsating pressure is modeled using the Corcos cross-power spectrum. The calculation frequency band for vibration and acoustic radiation is 100 to 500 Hz, with a calculation step size of 5 Hz.

[0104] Two nodes are selected on the cylindrical shell, and the vibration velocity results obtained by this method are compared with those obtained by the analytical method. Figure 4 and Figure 5 As shown. A comparison of the sound pressure level results at the sound pressure field points with the analytical method results is shown below. Figure 6 As shown.

[0105] The following describes the device for solving the vibration and acoustic radiation of flow-induced structures based on the modal superposition method provided by the present invention. The device for solving the vibration and acoustic radiation of flow-induced structures based on the modal superposition method described below can be referred to in correspondence with the method for solving the vibration and acoustic radiation of flow-induced structures based on the modal superposition method described above.

[0106] like Figure 7 As shown, the device includes a construction module 701, a first calculation module 702, a second calculation module 703, a third calculation module 704, and a solution module 705, wherein:

[0107] The construction module 701 is used to build a three-dimensional model of the target structure, and to obtain the overall structural mesh, structural surface mesh, structural surface geometric model and fluid domain mesh of the target structure based on the three-dimensional model.

[0108] The first calculation module 702 is used to establish a fluid-structure interaction model in the finite element software Abaqus based on the overall structure mesh and the fluid domain mesh, calculate the wet modes of the target structure based on the fluid-structure interaction model, and determine the modal frequencies and mode shapes of the structural surface nodes under the wet modes.

[0109] The second calculation module 703 is used to calculate the acoustic transfer vector (ATV) from the nodes of the structural surface to the sound pressure field points in the finite element software Comsol, based on the structural surface mesh and the structural surface geometric model.

[0110] The third calculation module 704 is used to obtain the turbulent pulsating pressure distribution at the nodes on the structural surface based on empirical models or CFD simulation calculations.

[0111] The solution module 705 is used to take the modal frequencies, mode shapes, acoustic transfer vectors (ATV) from the structural surface nodes to the acoustic pressure field points, and the turbulent pulsating pressure distribution at the structural surface nodes as inputs, and import them into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

[0112] This embodiment simplifies the flow-induced response solution process by taking into account the structural vibration and acoustic radiation caused by the turbulent boundary layer pulsating pressure outside the structure, starting from the perspective of the structural response transfer function and utilizing the modal orthogonality characteristics of the structure. At the same time, a flow-induced pulsating pressure load correction factor is introduced, enabling the method to quickly and accurately calculate the flow-induced vibration and acoustic radiation of surfaces with arbitrary shapes.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for solving flow-induced structural vibration and acoustic radiation based on modal superposition, characterized in that, include: A three-dimensional model of the target structure is established, and the overall structural mesh, structural surface mesh, structural surface geometric model, and fluid domain mesh of the target structure are obtained based on the three-dimensional model. A fluid-structure interaction model is established in the finite element software Abaqus based on the overall structural mesh and the fluid domain mesh. The wet modes of the target structure are calculated based on the fluid-structure interaction model, and the modal frequencies and mode shapes of the structural surface nodes under the wet modes are determined. Based on the structural surface mesh and the structural surface geometric model, the acoustic transfer vector (ATV) from the structural surface nodes to the acoustic pressure field points is calculated in the finite element software Comsol. The turbulent pulsating pressure distribution at the nodes on the structural surface is obtained based on empirical models or CFD simulation calculations. The modal frequencies, mode shapes, acoustic transfer vectors (ATVs) from structural surface nodes to acoustic pressure field points, and turbulent pulsating pressure distributions at structural surface nodes under the wet modal conditions are used as inputs and imported into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

2. The method for solving flow-induced structural vibration and acoustic radiation based on modal superposition as described in claim 1, characterized in that, After establishing a fluid-structure interaction model in the finite element software Abaqus based on the overall structural mesh and the fluid domain mesh, the process also includes: Apply boundary constraints to the fluid-structure interaction model; If the fluid domain is a semi-infinite domain, then set the acoustic infinite element property on the outer surface of the fluid domain or use the non-reflective acoustic impedance property.

3. The method for solving flow-induced structural vibration and acoustic radiation based on modal superposition as described in claim 1, characterized in that, Based on the structural surface mesh and the structural surface geometric model, the acoustic transfer vector (ATV) from the structural surface nodes to the acoustic pressure field points is calculated in the finite element software Comsol, including: Import the structural surface mesh and the structural surface geometry model into the finite element software Comsol, and select the pressure acoustics-boundary element module; A point sound source is set at the point of interest in the sound pressure field, and the sound scattering on the surface of the structure is calculated under the excitation of the point sound source. Based on the acoustic scattering from the surface of the structure, the acoustic transfer vector (ATV) from the nodes on the surface of the structure to the sound pressure field points is obtained using reciprocity.

4. The method for solving flow-induced structural vibration and acoustic radiation based on modal superposition as described in claim 1, characterized in that, The empirical model is the empirical model of turbulent pulsating pressure self-power spectrum.

5. The method for solving flow-induced structural vibration and acoustic radiation based on modal superposition as described in claim 4, characterized in that, The empirical model for the self-power spectrum of turbulent pulsating pressure is the Goody model.

6. A device for solving flow-induced structural vibration and acoustic radiation based on the modal superposition method, characterized in that, include: The construction module is used to build a three-dimensional model of the target structure, and to obtain the overall structural mesh, structural surface mesh, structural surface geometric model and fluid domain mesh of the target structure based on the three-dimensional model. The first calculation module is used to establish a fluid-structure interaction model in the finite element software Abaqus based on the overall structure mesh and the fluid domain mesh, calculate the wet modes of the target structure based on the fluid-structure interaction model, and determine the modal frequencies and mode shapes of the structural surface nodes under the wet modes. The second calculation module is used to calculate the acoustic transfer vector (ATV) from the nodes of the structural surface to the sound pressure field points in the finite element software Comsol, based on the structural surface mesh and the structural surface geometric model. The third calculation module is used to obtain the turbulent pulsating pressure distribution at the nodes on the structural surface based on empirical models or CFD simulation calculations. The solution module is used to take the modal frequencies, mode shapes, acoustic transfer vectors (ATV) from the structural surface nodes to the acoustic pressure field points, and the turbulent pulsating pressure distribution at the structural surface nodes as inputs, and import them into the flow-induced structural vibration and acoustic radiation solution program of the modal superposition method to obtain the vibration results of the structural surface and the acoustic radiation results of the acoustic pressure field points.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method for solving the flow-induced structural vibration and acoustic radiation based on the modal superposition method as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for solving the flow-induced structural vibration and acoustic radiation based on the modal superposition method as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for solving the flow-induced structural vibration and acoustic radiation based on the modal superposition method as described in any one of claims 1 to 5.

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