Turbulent boundary layer excitation structure vibration response finite element simulation correction method and system

Abstract

This invention belongs to the field of simulation correction technology and discloses a finite element simulation correction method and system for the vibration response of a structure excited by turbulent boundary layer. The method includes: obtaining a turbulent cross-spectral expression as input based on CFD calculations or a classical turbulent cross-spectral model; obtaining analytical results of the vibration displacement, velocity, or acceleration response based on the theoretical model of the vibration response of an elastic plate under turbulent boundary layer excitation using the modal superposition method; obtaining numerical results of the vibration displacement, velocity, or acceleration response based on the spatial discretization of the elastic plate and the numerical model of the plate vibration response under turbulent boundary layer excitation; subtracting the analytical results from the numerical results at the corresponding frequencies to obtain a correction amount for the finite element simulation results of the vibration response of the structure excited by turbulent boundary layer; and subtracting the correction amount from the finite element simulation results of the displacement, velocity, or acceleration response of the turbulent-excited structure to obtain the final correct structural response result.

Description

Technical Field

[0001] This invention belongs to the field of simulation correction technology, and in particular relates to a finite element simulation correction method and system for the vibration response of a structure excited by turbulent boundary layer. Background Technology

[0002] Acoustic stealth is one of the most important performance characteristics of a submarine, making noise control particularly crucial. The main noise sources on a submarine include mechanical noise, propeller noise, and hydrodynamic noise. With increasing speed, the proportion of hydrodynamic noise rapidly increases. Accurate prediction of the submarine's hydrodynamic noise performance is necessary during the design and construction phases. Turbulent-excited structural vibration is one of the main sources of hydrodynamic noise. Because turbulent-excited structural vibration involves fluid-structure interaction and random vibration problems, the solution process is complex and time-consuming; therefore, 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, obtaining accurate results for 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 vibration are often complex, and the signal-to-noise ratio is difficult to control. With the development of finite element method (FEM) software, numerous scholars have researched simulation methods for turbulently excited structural vibration, establishing relatively universal simulation procedures for flow-induced structural vibration. However, the calculation results obtained from currently widely used simulation procedures are generally higher than experimental results.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: the calculation results obtained by the currently widely used simulation process are generally higher than the experimental results. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a finite element simulation correction method and system for the vibration response of turbulent boundary layer-excited structures, enabling rapid and accurate prediction of the vibration response of turbulent-excited structures through finite element simulation and this correction method.

[0006] This invention is implemented as follows: a finite element simulation correction method for the vibration response of a structure excited by turbulent boundary layer, comprising:

[0007] S1. Use fluid simulation software such as Fluent and StarCCM to calculate the turbulent cross spectrum expression of the structural surface, or use classical turbulent cross spectrum models including the Corcos cross spectrum model and the Mellen cross spectrum model as turbulent input;

[0008] S2. Based on stochastic theory and the turbulent cross spectrum described in S1, an analytical model of the vibration response of an elastic plate excited by a turbulent boundary layer is established using the modal superposition method, and analytical results of the plate's vibration displacement, velocity, or acceleration response are obtained.

[0009] S3. Based on the spatial discretization of the plate and the turbulent cross spectrum described in S1, according to the discrete expression form of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the unit is used to replace the pulsating pressure within the unit, and the frequency response function at the center point of the unit is used to replace the frequency response function of the unit, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response.

[0010] S4. Subtract the analytical result obtained in S2 from the numerical result obtained in S3 to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration.

[0011] S5. Based on the pulsating pressure distribution on the structural wall obtained by CFD calculation or the turbulent cross-spectrum model proposed by predecessors, the simulation results of the displacement, velocity or acceleration response of the structure under turbulent excitation are calculated using the finite element simulation process of flow-induced structural vibration. The correction amount in S4 is subtracted from the simulation results to obtain the accurate solution of the structural response.

[0012] Furthermore, S1 specifically includes:

[0013] The cross-power spectrum model of turbulent fluctuating pressure established by Corcos is expressed as follows:

[0014]

[0015] Where Φ p (ω) represents the self-power spectral density. The coefficient α x and α y These represent the longitudinal and transverse coherence losses, respectively; for smooth walls, the value is typically: α x =0.115, α y =0.7. The average convective velocity of the turbulent boundary layer is represented by U. c This indicates that it is related to the free-flow velocity U. ∞ The relationship is: U c =β c U ∞ ,β c =0.65;

[0016] Mellen's turbulent fluctuating pressure cross-power spectrum model is expressed as follows:

[0017]

[0018] Furthermore, S2 specifically includes: For an elastic plate subjected to turbulent excitation, according to stochastic theory, the cross-power spectral density function of the plate displacement response is expressed as:

[0019] S w (u,ξ,ω)=∫∫S pp (ξ',ω)H w (u,u',-ω)×H w (u+ξ,u'+ξ',ω)du'dξ' (3)

[0020] Where u = (x, y) are the coordinates of the observation point, and ξ = (ξ... x ,ξ y Let ω be the spatial distance vector between the two observation points, and S be the angular frequency. pp (ξ',ω) represents the cross-power spectral density of the wall pulsating pressure, H w (u,u',ω) is the complex frequency response function of the plate vibration displacement;

[0021] For a flat plate subjected to turbulent excitation, its governing equations can be written as:

[0022] D p ▽ 4 W(u,ω)-ρhω 2 W(u,ω)=P(u,ω)-P a (u,0+,ω)+P a (u,0-,ω) (4)

[0023] Where D p and m p These represent the bending stiffness and surface density of the flat plate, respectively, and P(u,ω) is the fluctuating pressure of the turbulent boundary layer. a (u,ω) represents the pressure field caused by the vibration of the plate in the flow field;

[0024] Using the modal superposition method, the plate displacement is written as:

[0025]

[0026] Among them W mn (ω) is the modal expansion coefficient, α mn (u) is the shape function, and m and n are the modal numbers;

[0027] The acoustic radiation from the vibration of a flat plate under turbulent excitation is given by the Rayleigh integral:

[0028]

[0029] Assuming that the mutual radiation impedance between the vibration modes of the plate can be ignored, by substituting equations (5) and (6) into equation (4) and utilizing the modal orthogonality, the complex frequency response function of the plate vibration can be obtained.

[0030] Combining the wall pulsating pressure cross power spectral density given by equation (1) or equation (2), and using equation (3) and letting ξ = (0,0), the single-point displacement response self power spectral density of the submerged plate in water can be obtained.

[0031] The relationship between the displacement response, velocity response, and acceleration response of the plate is as follows:

[0032]

[0033] Combining equation (7) and using the average velocity autopower spectrum of the plate response given by the following equation, the average velocity autopower spectrum density of the plate response can be obtained.

[0034]

[0035] Furthermore, S3 specifically includes: spatial discretization based on the structural surface. Assuming the structural surface is divided into N elements, the power spectral density matrix of the plate displacement response in discrete form can be written as:

[0036]

[0037] In the formula S w (ω) is the power spectral density matrix of the displacement response, with diagonal elements S ii (ω) is the self-power spectrum of the displacement response at element i, S ij (ω) represents the displacement cross-power spectral density between elements i and j;

[0038]

[0039] Let H be the frequency response function matrix, and it be a symmetric matrix. ij (ω) represents the displacement response at the i-th element when a unit force of frequency is applied at the j-th element.

[0040]

[0041] Let φ be the power spectral density matrix of the load, with diagonal elements φ ii (ω) represents the self-power spectrum of the force load at element i, φ ij (ω) represents the cross-power spectral density of the force load between elements i and j;

[0042] When dividing the mesh according to the bending wave wavelength of the structure, the correlation between loads can be ignored, and equation (11) can be simplified to a diagonal matrix:

[0043]

[0044] The elements in the matrices in equations (9) to (12) are all expressed using the values ​​of the unit center points. The elements in the frequency response function matrix in equation (10) are obtained by the modal superposition method. The power spectral density matrix of the force load in equation (12) is obtained by the turbulent cross spectrum in step one. By combining equations (9) to (12), the power spectral density matrix of the plate displacement response can be obtained. The average value of the main diagonal elements in equation (9) is the average displacement response power spectrum of the plate. The relationship between the plate velocity, acceleration response and displacement response is still given by equation (7).

[0045] Furthermore, S4 specifically includes: depending on the type of the calculation result, if it is a single-point vibration displacement, velocity or acceleration response, subtract the single-point self-power spectral density obtained by equation (3) from the self-power spectral density of the corresponding element in equation (9); if it is a plate average vibration displacement, velocity or acceleration response, subtract the plate average self-power spectral density obtained by equation (8) from the average value of the main diagonal elements in equation (9).

[0046] Furthermore, S5 specifically includes: dividing the structure and fluid domain into structural meshes and acoustic meshes respectively, assigning corresponding structural material properties and fluid acoustic properties in Abaqus software, changing the structural mesh type from linear element to quadratic element, establishing a fluid-structure interaction finite element model of the structure and fluid domain, and setting the boundary conditions of the response according to the actual situation.

[0047] The time-domain structural wall frequency pulsating pressure load obtained in S1 is subjected to fast Fourier transform to obtain the frequency-domain structural wall frequency pulsating pressure load. The load is then loaded onto the fluid-structure interaction surface of the fluid-structure interaction finite element model using Python code. The established example is run to obtain the structural vibration displacement, velocity, or acceleration response under the frequency-domain pulsating pressure load.

[0048] Based on the correction amount of the finite element simulation results of the flow-induced structural vibration obtained from S4, the correction amount at the corresponding frequency is subtracted from the finite element simulation results to obtain the final frequency domain displacement, velocity, or acceleration response.

[0049] Another objective of this invention is to provide a finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure, which implements the aforementioned finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure, comprising:

[0050] The turbulence cross-spectral representation acquisition module is used to calculate the turbulence cross-spectral representation of the structural surface using fluid simulation software such as Fluent and StarCCM, or to use classical turbulence cross-spectral models, including the Corcos cross-spectral model and the Mellen cross-spectral model, as turbulence input.

[0051] The analytical results acquisition module is used to establish an analytical model of the vibration response of an elastic plate excited by turbulent boundary layer based on stochastic theory and turbulent cross spectrum, using the modal superposition method, and to obtain analytical results of the plate's vibration displacement, velocity, or acceleration response.

[0052] The numerical results acquisition module is used for spatial discretization and turbulent cross-spectrum analysis of the plate. Based on the discrete expression of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the element is used to replace the pulsating pressure within the element, and the frequency response function at the center point of the element is used to replace the frequency response function of the element, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response.

[0053] The correction amount acquisition module is used to subtract the analytical result from the obtained numerical result to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration.

[0054] The accurate solution acquisition module is used to calculate the simulation results of the structural vibration displacement, velocity or acceleration response under turbulent excitation based on the pulsating pressure distribution on the structural wall obtained by CFD calculation or the turbulent cross-spectrum model proposed by predecessors, using the finite element simulation process of flow-induced structural vibration. The simulation results are then subtracted from the correction amount to obtain the accurate solution of the structural response.

[0055] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, causing the processor to perform the steps of the finite element simulation correction method for the vibration response of the turbulent boundary layer-excited structure.

[0056] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure.

[0057] Another objective of this invention is to provide an information data processing terminal for implementing the aforementioned finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure.

[0058] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0059] First, based on the theories of analytical and numerical models, this invention proposes a method for correcting the finite element simulation results of flow-induced structural vibration, which improves the accuracy while retaining the speed of the original simulation process.

[0060] Based on the theories of analytical and numerical models, this invention proposes a method for correcting the finite element simulation results of flow-induced structural vibration, which improves the accuracy while retaining the speed of the original simulation process.

[0061] The technical solution of this invention fills a technical gap in the industry both domestically and internationally: Starting from the theory of analytical and numerical models, this invention proposes a method for correcting the finite element simulation results of flow-induced structural vibration, which improves the accuracy while retaining the speed of the original simulation process.

[0062] Second, this invention makes significant modifications to the finite element simulation method for the vibration response of structures excited by turbulent boundary layers. The following is a description of the existing technical problems it solves and the significant technical advancements it achieves:

[0063] This invention calculates and accurately obtains the turbulent cross-spectral representation of the structural surface using fluid simulation software (such as Fluent, StarCCM, etc.) or classical turbulent cross-spectral models (such as the Corcos cross-spectral model and the Mellen cross-spectral model). This step solves the problems of inaccurate turbulent excitation input and significant differences between the model and the actual situation in existing technologies, providing a solid foundation for the accurate prediction of subsequent structural vibration response.

[0064] Based on stochastic theory and the obtained turbulent cross-spectrum, this invention establishes an analytical model of the vibration response of an elastic plate under turbulent boundary layer excitation using the modal superposition method, and obtains analytical results of the plate's vibration displacement, velocity, or acceleration response. This step transforms the complex turbulent excitation problem into a solvable mathematical model, providing theoretical support for the accurate prediction of structural vibration response.

[0065] This invention establishes a numerical model of the structural response under turbulent excitation through spatial discretization and turbulent cross-spectrum analysis. Using the turbulent pulsating pressure and frequency response functions at the element center points, numerical results of the displacement, velocity, or acceleration response of the vibrating plate are obtained. Subsequently, by comparing the analytical and numerical results, corrections to the finite element simulation results of convective-induced structural vibration are obtained. This step effectively solves the error problems caused by factors such as mesh generation and numerical calculation in finite element simulation, improving the accuracy of the simulation results.

[0066] Finally, based on the fluctuating pressure distribution on the structural wall obtained from CFD calculations or the turbulent cross-spectrum model proposed by predecessors, this invention employs a flow-induced structural vibration finite element simulation process to calculate the simulation results of the structural vibration displacement, velocity, or acceleration response under turbulent excitation. Then, by subtracting the correction amount obtained in the previous steps from these simulation results, the accurate solution of the structural response is obtained. This step not only improves the accuracy of the simulation results but also provides a reliable reference for engineering design and optimization. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is a flowchart of the finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure provided in this embodiment of the invention;

[0069] Figure 2 This is a schematic diagram of the acoustic radiation from the vibration of a turbulently excited flat plate provided in an embodiment of the present invention;

[0070] Figure 3 This is a schematic diagram of the spatial discreteness of the structural surface provided in an embodiment of the present invention;

[0071] Figure 4 This is a flowchart of the finite element simulation of turbulent excitation structure vibration provided in an embodiment of the present invention;

[0072] Figure 5 This is a structural diagram of the finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure provided in an embodiment of the present invention.

[0073] Figure 6 These are comparison diagrams of the finite element simulation structure before and after modification, as well as those from literature experiments and analytical methods, provided in this embodiment of the invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0075] The following are two specific examples illustrating the practical application of the above-mentioned finite element simulation correction method for the vibration response of structures excited by turbulent boundary layers:

[0076] Example 1: Turbulent Cross-Spectrum Representation Calculation and Vibration Response Correction Based on Fluent

[0077] 1. Turbulent cross-spectral representation calculation:

[0078] Fluent, a fluid simulation software, is used to perform fluid dynamics simulations on specific structures, such as flat plates.

[0079] The turbulent cross-spectral representation of the structural surface is calculated using Fluent's turbulence model, assuming that the obtained turbulent cross-spectral data is based on the Corcos cross-spectral model.

[0080] 2. Establishment of analytical model for vibration response:

[0081] Based on stochastic theory and the obtained turbulent cross spectrum, an analytical model of the vibration response of an elastic plate excited by turbulent boundary layer is established using the modal superposition method.

[0082] The analytical results of the plate vibration displacement, velocity, and acceleration response were obtained through calculation.

[0083] 3. Numerical model establishment and simulation result acquisition:

[0084] The flat plate is spatially discretized, and a numerical model is established based on the discrete expression of the structural response under turbulent excitation.

[0085] Numerical results of the plate vibration displacement, velocity, and acceleration response are obtained by using the turbulent pulsating pressure and frequency response function at the unit center point.

[0086] 4. Simulation result correction:

[0087] Subtracting the analytical results from the numerical results yields the correction amount for the finite element simulation results of convection-induced structural vibration.

[0088] 5. Accurate solution acquisition:

[0089] Based on the pulsating pressure distribution on the structural wall obtained by CFD calculation, finite element simulation of flow-induced structural vibration is performed.

[0090] Subtracting the correction amount from the simulation results yields the accurate solution for the structural response.

[0091] Example 2: Correction using Mellen cross-spectral model and experimental data

[0092] 1. Determination of turbulent cross-spectral representation:

[0093] The Mellen cross-spectral model was directly used as the turbulence input to simulate the actual turbulent boundary layer excitation.

[0094] 2. Vibration response analysis and numerical model establishment:

[0095] Similar to Example 1, analytical and numerical models of vibration response were established, and analytical and numerical results were obtained respectively.

[0096] 3. Comparison of experimental data:

[0097] Structural vibration experiments were conducted under the same conditions to obtain experimental data for reference.

[0098] The numerical results are compared with experimental data to evaluate the accuracy of the simulation results.

[0099] 4. Simulation result correction:

[0100] Based on the difference between experimental data and numerical results, the correction amount for the simulation results is calculated.

[0101] 5. Accurate solution acquisition:

[0102] Subtracting the correction amount from the original simulation results yields an accurate solution for the structural response that is closer to the experimental data.

[0103] These two examples demonstrate how to use fluid simulation software and classical turbulent cross-spectral models, combined with techniques such as modal superposition, spatial discretization, and numerical calculation, to perform finite element simulation correction on the structural vibration response under turbulent boundary layer excitation, and obtain a more accurate structural response solution by comparing it with analytical results or experimental data.

[0104] To address the problems existing in the prior art, this invention provides a finite element simulation correction method and system for the vibration response of a turbulent boundary layer-excited structure. The invention will be described in detail below with reference to the accompanying drawings.

[0105] like Figure 1 As shown, the finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure provided in this embodiment of the invention includes:

[0106] Step 1: If the turbulent pulsating pressure input is obtained through simulation, perform LES simulation in fluid simulation software such as Fluent or StarCCM to calculate the turbulent pulsating pressure distribution on the structural wall, and use the software to calculate the spatial expression of the cross-power spectral density of the turbulent pulsating pressure on the structural wall. If the turbulent pulsating pressure input is given by empirical formulas, select a suitable turbulent cross-spectral model, such as the Corcos model or the Mellen model, to obtain the cross-spectral expression of the structural wall.

[0107] The cross-power spectrum model of turbulent fluctuating pressure established by Corcos is expressed as follows:

[0108]

[0109] Where Φ p (ω) represents the self-power spectral density. The coefficient α x and α y These represent the coherence loss in the longitudinal and transverse directions, respectively. For smooth walls, the value is typically: α x =0.115, α y =0.7. The average convective velocity of the turbulent boundary layer is represented by U. c This indicates that it is related to the free-flow velocity U. ∞ The relationship is: U c =β c U ∞ ,β c =0.65.

[0110] Mellen's turbulent fluctuating pressure cross-power spectrum model is expressed as follows:

[0111]

[0112] Step 2: Based on stochastic theory and the turbulent cross-spectral expression described in Step 1, a theoretical model of the vibration response of an elastic plate under turbulent boundary layer pulsating pressure excitation is established using the modal superposition method, and analytical results of the plate's vibration displacement, velocity, or acceleration response are obtained.

[0113] For example Figure 2 The cross-power spectral density function of the displacement response of the elastic plate shown under turbulent excitation, according to stochastic theory, is expressed as:

[0114] S w (u,ξ,ω)=∫∫S pp (ξ',ω)H w (u,u',-ω)×H w (u+ξ,u'+ξ',ω)du'dξ' (3)

[0115] Where u = (x, y) are the coordinates of the observation point, and ξ = (ξ... x ,ξ y Let ω be the spatial distance vector between the two observation points, and ω be the angular frequency. pp (ξ',ω) represents the cross-power spectral density of the wall pulsating pressure. H w (u,u',ω) is the complex frequency response function of the plate vibration displacement.

[0116] For example Figure 2 The governing equations for the turbulently excited flat plate shown can be written as follows:

[0117] D p ▽ 4 W(u,ω)-ρhω 2 W(u,ω)=P(u,ω)-P a (u,0+,ω)+P a (u,0-,ω) (4)

[0118] Where D p and m p Let P(u,ω) be the bending stiffness and surface density of the flat plate, respectively. Let P(u,ω) be the fluctuating pressure of the turbulent boundary layer. a (u,ω) represents the pressure field caused by the vibration of the plate in the flow field.

[0119] Using the modal superposition method, the plate displacement is written as:

[0120]

[0121] Among them W mn (ω) is the modal expansion coefficient, α mn (u) is the shape function, and m and n are the modal numbers.

[0122] The acoustic radiation from the vibration of a flat plate under turbulent excitation is given by the Rayleigh integral:

[0123]

[0124] Assuming that the mutual radiation impedance between the vibration modes of the plate can be ignored, by substituting equations (5) and (6) into equation (4) and utilizing the modal orthogonality, the complex frequency response function of the plate vibration can be obtained.

[0125] Combining the wall pulsating pressure cross power spectral density given by equation (1) or equation (2), and using equation (3) and letting ξ = (0,0), the single-point displacement response self power spectral density of the submerged plate in water can be obtained.

[0126] The relationship between the displacement response, velocity response, and acceleration response of the plate is as follows:

[0127]

[0128] Combining equation (7) and using the average velocity autopower spectrum of the plate response given by the following equation, the average velocity autopower spectrum density of the plate response can be obtained.

[0129]

[0130] Step 3: Based on the spatial discretization of the plate and the turbulent cross spectrum described in Step 1, according to the discrete expression form of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the element is used to replace the pulsating pressure within the element, and the frequency response function at the center point of the element is used to replace the frequency response function of the element, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response.

[0131] Based on the spatial discretization of the structural surface, assuming the structural surface is divided into N elements, such as... Figure 3 The power spectral density matrix of the discrete-form plate displacement response can be written as:

[0132]

[0133] In the formula S w (ω) is the power spectral density matrix of the displacement response, with diagonal elements S ii (ω) is the self-power spectrum of the displacement response at element i, S ij (ω) represents the displacement cross-power spectral density between elements i and j.

[0134]

[0135] Let H be the frequency response function matrix, and it is a symmetric matrix. ij (ω) represents the displacement response at the i-th element when a unit force of frequency is applied at the j-th element.

[0136]

[0137] Let φ be the power spectral density matrix of the load, with diagonal elements φ ii (ω) represents the self-power spectrum of the force load at element i, φ ij (ω) represents the cross-power spectral density of the force load between elements i and j.

[0138] When dividing the mesh according to the bending wave wavelength of the structure, the correlation between loads can be ignored, and equation (11) can be simplified to a diagonal matrix:

[0139]

[0140] The elements in the matrices in equations (9) to (12) are all expressed using the values ​​of the unit center points. The elements in the frequency response function matrix in equation (10) are obtained through modal superposition. The power spectral density matrix of the force load in equation (12) is obtained through the turbulent cross spectrum in step one. By combining equations (9) to (12), the power spectral density matrix of the plate displacement response can be obtained. The average value of the main diagonal elements in equation (9) is the average displacement response power spectrum of the plate. The relationship between the plate velocity, acceleration response and displacement response is still given by equation (7).

[0141] Step 4: Subtract the analytical result obtained in Step 2 from the numerical result obtained in Step 3 to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration.

[0142] Depending on the type of the calculation result, if it is a single-point vibration displacement, velocity or acceleration response, the single-point self-power spectral density obtained by subtracting the self-power spectral density of the corresponding element in equation (9) from that obtained by equation (3); if it is a plate average vibration displacement, velocity or acceleration response, the average value of the main diagonal elements in equation (9) is subtracted from the plate average self-power spectral density obtained by equation (8).

[0143] Step 5: Based on the structural wall pulsating pressure distribution or turbulent cross-spectrum model obtained in Step 1, use the finite element simulation process of flow-induced structural vibration to calculate the simulation results of the structural vibration displacement, velocity, or acceleration response under turbulent excitation. Subtract the correction amount from Step 4 from the simulation results to obtain the accurate solution of the structural response.

[0144] The finite element simulation process for flow-induced structural vibration is shown in Figure 4.

[0145] The structural and fluid domains were meshed into structural and acoustic meshes, respectively. In Abaqus software, the corresponding structural material properties and fluid acoustic properties were assigned to them. The structural mesh type was changed from linear element to quadratic element. A fluid-structure interaction finite element model of the structural and fluid domains was established, and the boundary conditions of the response were set according to the actual situation.

[0146] The time-domain structural wall frequency-fluidized pressure load obtained in step one is subjected to a Fast Fourier Transform to obtain the frequency-domain structural wall frequency-fluidized pressure load, which is then loaded onto the fluid-structure interaction surface of the fluid-structure interaction finite element model using Python code. The established example is then run to obtain the structural vibration displacement, velocity, or acceleration response under the frequency-domain fluctuating pressure load.

[0147] Based on the correction amount obtained from the finite element simulation results of the flow-induced structural vibration in step four, subtract the correction amount at the corresponding frequency from the finite element simulation results to obtain the final frequency domain displacement, velocity, or acceleration response.

[0148] like Figure 5 As shown, the finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure provided in this embodiment of the invention includes:

[0149] The turbulence cross-spectral representation acquisition module is used to calculate the turbulence cross-spectral representation of the structural surface using fluid simulation software such as Fluent and StarCCM, or to use classical turbulence cross-spectral models, including the Corcos cross-spectral model and the Mellen cross-spectral model, as turbulence input.

[0150] The analytical results acquisition module is used to establish an analytical model of the vibration response of an elastic plate excited by turbulent boundary layer based on stochastic theory and turbulent cross spectrum, using the modal superposition method, and to obtain analytical results of the plate's vibration displacement, velocity, or acceleration response.

[0151] The numerical results acquisition module is used for spatial discretization and turbulent cross-spectrum analysis of the plate. Based on the discrete expression of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the element is used to replace the pulsating pressure within the element, and the frequency response function at the center point of the element is used to replace the frequency response function of the element, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response.

[0152] The correction amount acquisition module is used to subtract the analytical result from the obtained numerical result to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration.

[0153] The accurate solution acquisition module is used to calculate the simulation results of the structural vibration displacement, velocity or acceleration response under turbulent excitation based on the pulsating pressure distribution on the structural wall obtained by CFD calculation or the turbulent cross-spectrum model proposed by predecessors, using the finite element simulation process of flow-induced structural vibration. The simulation results are then subtracted from the correction amount to obtain the accurate solution of the structural response.

[0154] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor performs the steps of a finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure.

[0155] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of a finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure.

[0156] An application embodiment of the present invention provides an information data processing terminal, which is used to implement a finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure.

[0157] To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides specific product or related technology application examples of the technical solution claimed.

[0158] Using the modified method described above for finite element analysis of turbulent excitation structural vibration response, a rectangular elastic plate under turbulent excitation in air was calculated and modified using finite element analysis. The results were compared with experimental data from relevant literature. Figure 6 The structure fits well. Plate parameters: length 0.48m, width 0.42m, thickness 3.17mm, density 2700kg / m³, Young's modulus 70GPa, Poisson's ratio 0.3, structural loss factor 0.005. The incoming air velocity is 40m / s, and the kinematic viscosity of the air is 1.5111×10⁻⁵m² / s.

[0159] The embodiments of the present invention have achieved some positive results during the research and development or use process, and have indeed great advantages compared with the prior art. The following content describes them in conjunction with the data, charts and other information of the experimental process.

[0160] The comparison shows that the finite element calculation results before correction are significantly higher than the analytical solution and experimental results at increasing frequencies. By using the correction method, the finite element calculation results are in good agreement with the analytical solution and experimental results. The comparison results effectively verify the correctness of the correction method.

[0161] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0162] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A finite element simulation correction method for the vibration response of a structure excited by turbulent boundary layer, characterized in that, include: S1. Use fluid simulation software such as Fluent or StarCCM to calculate the turbulent cross spectrum expression of the structural surface, or use classical turbulent cross spectrum models, including the Corcos cross spectrum model and the Mellen cross spectrum model, as turbulent input. S2. Based on stochastic theory and the turbulent cross spectrum described in S1, an analytical model of the vibration response of an elastic plate excited by a turbulent boundary layer is established using the modal superposition method, and analytical results of the plate's vibration displacement, velocity, or acceleration response are obtained. S3. Based on the spatial discretization of the plate and the turbulent cross spectrum described in S1, according to the discrete expression form of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the unit is used to replace the pulsating pressure within the unit, and the frequency response function at the center point of the unit is used to replace the frequency response function of the unit, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response. S4. Subtract the analytical result obtained in S2 from the numerical result obtained in S3 to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration. S5. Based on the pulsating pressure distribution on the structural wall obtained by CFD calculation or the turbulent cross-spectrum model proposed by predecessors, the simulation results of the displacement, velocity or acceleration response of the structure under turbulent excitation are calculated using the finite element simulation process of flow-induced structural vibration. The correction amount in S4 is subtracted from the simulation results to obtain the accurate solution of the structural response.

2. The finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure as described in claim 1, characterized in that, S1 specifically includes: The cross-power spectrum model of turbulent fluctuating pressure established by Corcos is expressed as follows: Where Φ p (ω) represents the self-power spectral density, and the coefficient α x and α y These represent the longitudinal and transverse coherence losses, respectively; for a smooth wall, the value is: α x =0.115, α y =0.7, the average convective velocity of the turbulent boundary layer is represented by U. c This indicates that it is related to the free-flow velocity U. ∞ The relationship is: U c =β c U ∞ ,β c =0.65; Mellen's turbulent fluctuating pressure cross-power spectrum model is expressed as follows: ξ=(ξ x ,ξ y ) is the spatial distance vector between two observation points, and ω is the angular frequency.

3. The finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure as described in claim 2, characterized in that, S3 specifically includes: spatial discretization based on the structural surface. Assuming the structural surface is divided into N elements, the power spectral density matrix of the plate displacement response in discrete form is written as: In the formula S w (ω) is the power spectral density matrix of the displacement response, with diagonal elements S ii (ω) is the self-power spectrum of the displacement response at element i, S ij (ω) represents the displacement cross-power spectral density between elements i and j; Let H be the frequency response function matrix, and it be a symmetric matrix. ij (ω) represents the displacement response at the i-th element when a unit force of frequency is applied at the j-th element. Let φ be the power spectral density matrix of the load, with diagonal elements φ ii (ω) represents the self-power spectrum of the force load at element i, φ ij (ω) represents the cross-power spectral density of the force load between elements i and j; When dividing the mesh according to the bending wave wavelength of the structure, the correlation between loads is ignored, and equation (11) simplifies to a diagonal matrix: The elements in the matrices in equations (9) to (12) are all expressed using the values ​​of the unit center points. The elements in the frequency response function matrix in equation (10) are obtained by the modal superposition method. The power spectral density matrix of the force load in equation (12) is obtained by the turbulent cross spectrum in step one. By combining equations (9) to (12), the power spectral density matrix of the plate displacement response is obtained. The average value of the main diagonal elements in equation (9) is the average displacement response power spectrum of the plate.

4. The finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure as described in claim 3, characterized in that, S5 specifically includes: dividing the structure and fluid domain into structural meshes and acoustic meshes respectively, assigning corresponding structural material properties and fluid acoustic properties in Abaqus software, changing the structural mesh type from linear element to quadratic element, establishing a fluid-structure interaction finite element model of the structure and fluid domain, and setting the boundary conditions of the response according to the actual situation. The time-domain structural wall frequency pulsating pressure load obtained in S1 is subjected to fast Fourier transform to obtain the frequency-domain structural wall frequency pulsating pressure load. The load is then loaded onto the fluid-structure interaction surface of the fluid-structure interaction finite element model using Python code. The established example is run to obtain the structural vibration displacement, velocity, or acceleration response under the frequency-domain pulsating pressure load. Based on the correction amount of the finite element simulation results of the flow-induced structural vibration obtained from S4, the correction amount at the corresponding frequency is subtracted from the finite element simulation results to obtain the final frequency domain displacement, velocity, or acceleration response.

5. A finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure, implementing the finite element simulation correction method for the vibration response of a turbulent boundary layer-excited structure as described in any one of claims 1 to 4, characterized in that, include: The turbulence cross-spectral representation acquisition module is used to calculate the turbulence cross-spectral representation of the structural surface using fluid simulation software such as Fluent and StarCCM, or to use classical turbulence cross-spectral models, including the Corcos cross-spectral model and the Mellen cross-spectral model, as turbulence input. The analytical results acquisition module is used to establish an analytical model of the vibration response of an elastic plate excited by turbulent boundary layer based on stochastic theory and turbulent cross spectrum, using the modal superposition method, and to obtain analytical results of the plate's vibration displacement, velocity, or acceleration response. The numerical results acquisition module is used for spatial discretization and turbulent cross-spectrum analysis of the plate. Based on the discrete expression of the structural response under turbulent excitation, i.e., the numerical model, the turbulent pulsating pressure at the center point of the element is used to replace the pulsating pressure within the element, and the frequency response function at the center point of the element is used to replace the frequency response function of the element, so as to obtain the numerical results of the plate vibration displacement, velocity or acceleration response. The correction amount acquisition module is used to subtract the analytical result from the obtained numerical result to obtain the correction amount of the finite element simulation result of the convective-induced structural vibration. The accurate solution acquisition module is used to calculate the simulation results of the structural vibration displacement, velocity or acceleration response under turbulent excitation based on the pulsating pressure distribution on the structural wall obtained by CFD calculation or the turbulent cross-spectrum model proposed by predecessors, using the finite element simulation process of flow-induced structural vibration. The simulation results are then subtracted from the correction amount to obtain the accurate solution of the structural response.

6. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the finite element simulation correction method for turbulent boundary layer-excited structural vibration response as described in any one of claims 1 to 4.

7. A computer-readable storage medium storing a computer program, wherein when executed by a processor, the computer program causes the processor to perform the steps of the finite element simulation correction method for turbulent boundary layer-excited structural vibration response as described in any one of claims 1 to 4.

8. An information data processing terminal, which is used to implement the finite element simulation correction system for the vibration response of a turbulent boundary layer-excited structure as described in claim 5.

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