A method and system for calculating energy-averaged finite element method for structural random vibration analysis

Abstract

This invention belongs to the field of structural vibration analysis technology and discloses an energy-averaged finite element method and system for structural random vibration analysis, including: S1, using fluid simulation software Fluent and StarCCM to perform fluid dynamics simulation to obtain the long-term turbulent pulsating pressure distribution of the structural wall in the time domain; S2, dividing the pulsating pressure obtained in S1 into segments with some overlap between segments, and performing Fourier transforms on each segment to obtain multiple sets of wall turbulent pulsating pressures in the frequency domain; S3, establishing a fluid-structure interaction dynamic model of the structure and fluid domain, applying the wall turbulent pulsating pressure loads obtained in S2 in the frequency domain, and performing steady-state dynamic harmonic response analysis on each segment; S4, based on the vibration response results of the multiple sets of harmonic response analyses in S3, taking the energy average of these results to obtain the result of random vibration analysis.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration analysis technology, and particularly relates to an energy-averaged finite element method and system for structural random vibration analysis. Background Technology

[0002] Turbulent boundary layer-excited structural vibrations and noise are among the main noise sources for submarines during high-speed underwater navigation, making the prediction of vibration and noise in turbulently excited structures crucial. Thanks to the development of finite element software, finite element simulation is now widely used for the analysis and calculation of turbulent boundary layer pulsating pressure and structural vibration noise. Domestic and international scholars have conducted extensive research on finite element simulation calculations of turbulently excited structural vibrations and have proposed a relatively universal finite element simulation process for turbulently excited structural vibrations.

[0003] Analysis of widely used finite element simulation analysis procedures and results reveals some shortcomings in existing procedures. Since turbulence in reality is a stochastic process, the analysis of turbulent-excited structural vibration should be a stochastic vibration analysis. In the currently used finite element analysis procedures for flow-induced structural vibration, the turbulent pulsating pressure load comes from a set of time-domain pulsating pressures. The corresponding fluid-structure interaction analysis is a harmonic response analysis under a single turbulent pulsating pressure condition, not a stochastic vibration analysis. The harmonic response analysis is only one sample in the stochastic vibration analysis, and the results obtained differ from actual stochastic vibration results.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: In the current finite element analysis process for flow-induced structural vibration, the turbulent pulsating pressure load comes from a set of time-domain pulsating pressures. The corresponding fluid-structure interaction analysis is a harmonic response analysis under a single turbulent pulsating pressure condition, not a random vibration analysis. The harmonic response analysis is only a sample in the random vibration analysis, and the results obtained differ from the actual random vibration results. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides an energy-averaged finite element method and system for structural random vibration analysis. By averaging energy, the results of random vibration analysis can be obtained through harmonic response analysis using finite element simulation.

[0006] This invention is implemented as follows: an energy-averaged finite element method for analyzing the random vibration of structures, comprising:

[0007] S1. Fluid dynamics simulation was performed using fluid simulation software such as Fluent and StarCCM to obtain the long-term turbulent pulsating pressure distribution on the structural wall in the time domain.

[0008] S2. The time-domain pulsating pressure obtained in S1 is segmented, with some overlap between each segment, and Fourier transform is performed on each segment to obtain multiple sets of frequency-domain wall turbulent pulsating pressures.

[0009] S3. Establish fluid-structure interaction dynamic models of the structure and fluid domain, apply the wall turbulent pulsating pressure loads in the frequency domain obtained in S2, and perform steady-state dynamic harmonic response analysis respectively;

[0010] S4. Based on the vibration response results of the multi-harmonic response analysis in S3, take the average energy of these results to obtain the results of the random vibration analysis.

[0011] Furthermore, S1 specifically includes: dividing the fluid domain into fluid meshes, importing the mesh model into fluid simulation software such as Fluent or StarCCM, and establishing a fluid dynamics simulation model. Transient flow field calculations are performed based on the LES model, with the calculation time step determined according to the highest frequency of the steady-state dynamic analysis, yielding the turbulent fluctuation pressure distribution on the structural wall over a period of time. The turbulent fluctuation pressure curve in the time domain is observed; only the portion exhibiting periodic fluctuations, i.e., after entering steady state, can be considered as the effective load for the fluid-structure interaction calculation of the structure.

[0012] Furthermore, S2 specifically includes: performing a Fast Fourier Transform (FFT) on each group of time-domain turbulent fluctuating pressures in Matlab to obtain the frequency-domain turbulent fluctuating pressures; the frequency-domain turbulent fluctuating pressures should be expressed in the form of real part + imaginary part. The obtained frequency-domain turbulent fluctuating pressures of the structural wall are exported as .dat files according to each frequency point. Each .dat file represents the fluctuating pressure distribution at each node of the structural wall at that frequency point. It should be noted that when exporting the .dat files, the real and imaginary parts should be stored in two separate .dat files; that is, the fluctuating pressure distribution at each frequency point should consist of one real part .dat file and one imaginary part .dat file.

[0013] Furthermore, S3 specifically includes: reasonably simplifying the 3D structural model to reduce computational load; extracting mid-surfaces at appropriate locations to establish a shell model; and constructing a fluid domain. The structure and fluid domain are meshed separately using structural and acoustic meshes, with the meshing principle being 1 / 6 of the bending wave wavelength and 1 / 6 of the acoustic wave wavelength, respectively. The meshed structural and acoustic models are imported into Abaqus, and assigned structural material properties and fluid acoustic properties, respectively. The structural mesh type is changed from linear elements to quadratic elements to improve the accuracy of structural response calculations. Tie interactions are established between the structural and acoustic meshes to form fluid-structure interaction. Appropriate boundary conditions are set for the structural model based on actual conditions. The fluid-structure interaction finite element model is then complete.

[0014] After establishing the fluid-structure interaction finite element model, the structural wall frequency pulsating pressure loads obtained in step two were applied in groups using Python code. Each group of pulsating pressure loads formed a calculation case. The pulsating pressure was applied by mesh node interpolation. The structural fluid-structure interaction steady-state dynamic analysis was performed under multiple cases to obtain multiple harmonic response analysis results.

[0015] Furthermore, S4 specifically includes: assuming the structure surface has N elements, when performing steady-state dynamic analysis in Abaqus, it is actually performing harmonic response analysis, that is:

[0016] W(ω)=H(ω)F(ω) (1)

[0017] In the formula, W(ω) is the displacement response vector of the element, W(ω)={W1(ω)W2(ω)…W N (ω)} T H(ω) is the frequency response function matrix.

[0018] F(ω)={F1(ω)F2(ω)…F N (ω)} T (2)

[0019] This represents the force load vector of the element;

[0020] In discrete form, the power spectral density matrix for analyzing the random response of structural vibration is:

[0021]

[0022] The load Φ(ω) is a matrix, and its relationship with F(ω) is as follows:

[0023]

[0024] Comparing equations (1), (3), and (4), it can be concluded that the random vibration analysis under a single working condition can be obtained from harmonic response analysis, i.e.

[0025]

[0026] However, when performing random vibration analysis of a turbulently excited structure, according to turbulence models such as the Corcos model, the greater the distance between two points on the structural surface, the weaker the correlation between the pulsating pressure loads at those two points. When the mesh is divided according to 1 / 6 of the wavelength of the structural bending wave, the correlation between the loads of each element is very weak, close to 0, meaning that off-diagonal elements should be ignored. Therefore, we have...

[0027]

[0028] In the formula This is the load matrix after ignoring cross-correlation. We can see... The form is a diagonal matrix that cannot be decomposed into a load vector multiplied by its conjugate transpose; that is, given any vector F(ω), there does not exist.

[0029] At this point, harmonic response analyses under multiple operating conditions are needed to approximate the results of the random response analysis. Assuming a total of M independent harmonic response analyses were performed, for the i-th harmonic response analysis:

[0030] W i (ω)=H(ω)F i (ω) (7)

[0031] In the formula

[0032]

[0033] In the formula, Each element is an independent random variable, randomly distributed between 0 and 2π, and its meaning is the phase angle of the pulsating pressure load of each unit; for each harmonic response analysis, the vector formed by the pulsating pressure phase angle is also different;

[0034]

[0035] in The main diagonal element is F i 2 (ω), the non-main diagonal elements are because and If all are uniformly randomly distributed between 0 and 2π, then we have:

[0036]

[0037] Then, by performing multiple harmonic response analyses and using equation (5) to express the random response analysis, we can obtain...

[0038]

[0039] in To disregard the random vibration response without considering the cross-correlation between loads, The result is the harmonic response calculated under the i-th random phase load excitation. As can be seen from Equation (11), the energy average of multiple harmonic response analysis results is used to finally obtain the result of random vibration analysis.

[0040] Another object of the present invention is to provide an energy-averaged finite element method for calculating the energy of random vibrations of a structure, which implements the energy-averaged finite element method for calculating random vibrations of the structure, comprising:

[0041] The module for obtaining time-domain turbulent pulsating pressure distribution is used to perform fluid dynamics simulations using fluid simulation software such as Fluent and StarCCM to obtain the long-term turbulent pulsating pressure distribution of the structural wall in the time domain.

[0042] The frequency domain wall turbulence pulsating pressure acquisition module is used to segment the obtained time domain pulsating pressure, with some overlap between each segment, and perform Fourier transform on each segment to obtain multiple sets of frequency domain wall turbulence pulsating pressure.

[0043] The steady-state dynamic harmonic response analysis module is used to establish fluid-structure interaction dynamic models in the structural and fluid domains, apply the obtained frequency domain wall turbulent pulsating pressure loads, and perform steady-state dynamic harmonic response analysis respectively.

[0044] The random vibration analysis module is used to obtain the results of random vibration analysis by taking the average energy of the vibration response results based on the analysis of multiple harmonic responses.

[0045] 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, which, when executed by the processor, causes the processor to perform the steps of the energy-averaged finite element calculation method for the structural random vibration analysis.

[0046] 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 energy-averaged finite element method for analyzing the random vibration of a structure.

[0047] Another objective of this invention is to provide an information data processing terminal for implementing the energy-averaged finite element method for structural random vibration analysis.

[0048] 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:

[0049] First, this invention obtains the results of random vibration analysis by averaging the energy through multiple finite element simulations and using harmonic response analysis, making it feasible to perform random vibration analysis of large structures under turbulent excitation using finite element software.

[0050] This invention approximates the equivalent random vibration analysis by averaging the energy results of multiple finite element harmonic response analyses, making it feasible to perform random vibration analysis on large structures using finite elements, and avoiding the complexity of providing the spectral matrix required for traditional finite element random vibration analysis.

[0051] The technical solution of this invention fills a technical gap in the industry both domestically and internationally: This invention uses the energy averaging results of multiple finite element harmonic response analyses to approximate equivalent random vibration analysis, making it feasible to perform random vibration analysis on large structures using finite element methods.

[0052] Second, this invention utilizes fluid simulation software (such as Fluent and StarCCM) to perform fluid dynamics simulations, enabling accurate simulation and acquisition of the turbulent pulsating pressure distribution on the structural wall over a long time domain. This step overcomes the limitations of traditional methods that cannot directly measure or simulate the turbulent pulsating pressure on the structural wall under complex fluid environments, providing more reliable and accurate input data for random vibration analysis.

[0053] This invention employs a piecewise approach and Fourier transform to convert time-domain fluctuating pressure into multiple sets of wall turbulent fluctuating pressure in the frequency domain. This method not only reduces the complexity of data processing but also enables subsequent dynamic analysis to be performed in the frequency domain, thereby improving analytical efficiency and accuracy. Through analysis in multiple frequency domains, this invention can more comprehensively consider the influence of the frequency domain characteristics of turbulent fluctuating pressure on structural vibration response.

[0054] This invention establishes a fluid-structure interaction (FSI) dynamic model encompassing both the structural and fluid domains, and applies turbulent, fluctuating pressure loads on the wall in the frequency domain to perform steady-state dynamic harmonic response analysis. This FSI analysis method fully considers the interaction between the fluid and the structure, making the analysis results closer to reality. Through multiple harmonic response analyses, this invention can obtain the vibration response characteristics of the structure at different frequencies, providing an important basis for structural design and optimization.

[0055] This invention obtains the results of random vibration analysis by averaging the energy of vibration response from multiple harmonic response analyses. This method comprehensively considers the energy distribution of structural vibration responses at different frequencies, avoiding the biases that may result from single-frequency analysis. Through energy averaging, this invention achieves more accurate and reliable random vibration analysis results, providing strong support for the safety and reliability assessment of structures. Attached Figure Description

[0056] 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.

[0057] Figure 1 This is a flowchart of the energy-averaged finite element method for structural random vibration analysis provided in this embodiment of the invention;

[0058] Figure 2 This is a schematic diagram of the turbulent pulsating pressure curve provided in an embodiment of the present invention;

[0059] Figure 3 This is a schematic diagram of time-domain pulsating pressure segmentation provided in an embodiment of the present invention;

[0060] Figure 4 This is a structural diagram of energy-averaged finite element calculation for structural random vibration analysis provided in an embodiment of the present invention;

[0061] Figure 5 This is a schematic diagram of a simply supported plate subjected to six random forces, provided in an embodiment of the present invention.

[0062] Figure 6 This is a graph showing the results of random response analysis and harmonic response analysis provided in an embodiment of the present invention. Detailed Implementation

[0063] 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.

[0064] The following are two specific examples illustrating the practical application of the energy-averaged finite element method for structural random vibration analysis:

[0065] ### Example 1: Random Vibration Analysis of Bridge Structure

[0066] 1. Fluid dynamics simulation:

[0067] Fluent, a fluid simulation software, was used to simulate the fluid environment surrounding the bridge structure.

[0068] By conducting long-term simulations (such as 200 seconds), the turbulent pulsating pressure distribution data of the bridge wall in the time domain were obtained.

[0069] 2. Pulsating pressure handling:

[0070] The time-domain pulsating pressure data is segmented by time, with each segment being 50 seconds long and adjacent segments having a 10-second overlap.

[0071] Perform a Fourier transform on each data segment to obtain multiple sets of wall turbulent fluctuation pressures in the frequency domain.

[0072] 3. Fluid-structure interaction dynamics model:

[0073] A fluid-structure interaction dynamic model of the bridge structure and the fluid domain was established in finite element analysis software.

[0074] The wall turbulent pulsating pressure in the frequency domain is applied as a load to the model.

[0075] 4. Steady-state dynamic harmonic response analysis:

[0076] Steady-state dynamic harmonic response analysis was performed on the load in each frequency domain to obtain the vibration response of the bridge structure at different frequencies.

[0077] 5. Energy Averaging and Result Output:

[0078] Energy averaging is performed on all vibration response results in the frequency domain.

[0079] The final random vibration analysis results are output, including response parameters such as displacement, velocity, and acceleration.

[0080] ###Example 2: Wind-Induced Random Vibration Analysis of High-Rise Buildings

[0081] 1. Fluid dynamics simulation:

[0082] The StarCCM software was used to simulate the wind field around a high-rise building.

[0083] By setting parameters such as wind speed and wind direction, and simulating wind field changes over a long period of time (e.g., 300 seconds), the temporal turbulent pressure distribution on the building wall is obtained.

[0084] 2. Pulsating pressure handling:

[0085] Divide the time-domain pulsating pressure data into segments based on time length (e.g., 60 seconds) and set appropriate crossover times (e.g., 15 seconds).

[0086] Perform a Fourier transform on each data segment to obtain multiple sets of wind-induced turbulent fluctuation pressures in the frequency domain.

[0087] 3. Fluid-structure interaction dynamics model:

[0088] A fluid-structure interaction model of a high-rise building and a wind field was established in finite element software.

[0089] The wind-induced turbulent fluctuation pressure in the frequency domain is applied as a load to the model.

[0090] 4. Steady-state dynamic harmonic response analysis:

[0091] Steady-state dynamic harmonic response analysis was performed on the load in each frequency domain to obtain the vibration response of the high-rise building at different frequencies.

[0092] 5. Energy Averaging and Result Output:

[0093] Energy averaging is performed on all vibration response results in the frequency domain.

[0094] The random vibration analysis results of high-rise buildings are obtained, providing data support for structural design.

[0095] These two examples demonstrate the application of the energy-averaged finite element method in random vibration analysis of bridge structures and high-rise buildings, respectively. Through steps such as fluid dynamics simulation, pulsating pressure processing, fluid-structure interaction dynamics model establishment, steady-state dynamic harmonic response analysis, and energy averaging, the vibration response of the structure at different frequencies is obtained, and the random vibration analysis results are finally output.

[0096] To address the problems existing in the prior art, this invention provides an energy-averaged finite element method and system for structural random vibration analysis. The invention will be described in detail below with reference to the accompanying drawings.

[0097] like Figure 1 As shown, the energy-averaged finite element method for structural stochastic vibration analysis provided in this embodiment of the invention includes:

[0098] Step 1: Mesh the fluid domain and import the mesh model into fluid simulation software such as Fluent or StarCCM to establish a fluid dynamics simulation model. Perform transient flow field calculations based on the LES model. The calculation time step is determined according to the highest frequency of the steady-state dynamic analysis to obtain the turbulent fluctuation pressure distribution on the structural wall over a period of time. Observe the turbulent fluctuation pressure curve in the time domain. Only the portion showing periodic fluctuations, i.e., after entering steady state, can be used as the effective load for the fluid-structure interaction calculation of the structure. Figure 2 The total time for the pulsating pressure curve to reach steady state should be as long as possible, preferably more than 5 seconds.

[0099] Step 2: Divide the turbulent fluctuating pressure in the time domain obtained in Step 1 into segments. The duration of each segment is determined based on the frequency step size used in the steady-state dynamics analysis. There needs to be a certain overlap between the time segments, such as 50% overlap. Figure 3 As shown, a number of segments of 10 or more is optimal, yielding multiple sets of time-domain turbulent fluctuation pressures.

[0100] In Matlab, a Fast Fourier Transform (FFT) is performed on each group of time-domain turbulent fluctuating pressures to obtain the frequency-domain turbulent fluctuating pressures. The frequency-domain turbulent fluctuating pressures should be expressed in the form of real part + imaginary part. The obtained frequency-domain turbulent fluctuating pressures of the structural wall are exported as .dat files according to each frequency point. Each .dat file represents the fluctuating pressure distribution at each node of the structural wall at that frequency point. It should be noted that when exporting the .dat files, the real and imaginary parts should be stored in two separate .dat files; that is, the fluctuating pressure distribution at each frequency point should consist of one real part .dat file and one imaginary part .dat file.

[0101] Step 3: Establish the fluid-structure interaction finite element model of the structure and fluid domain. The 3D structural model is simplified to reduce computational load. A shell model is created by extracting mid-surfaces at appropriate locations, and the fluid domain is constructed. Structural and acoustic meshes are created for the structure and fluid domain respectively, with the meshing principle being 1 / 6 of the wavelength of the structural bending wave and 1 / 6 of the wavelength of the acoustic wave. The resulting structural and acoustic mesh models are imported into Abaqus, and structural material properties and fluid acoustic properties are assigned respectively. The structural mesh type is changed from linear elements to quadratic elements to improve the accuracy of structural response calculations. Tie interactions are established between the structural and acoustic meshes to form fluid-structure interaction. Appropriate boundary conditions are set for the structural model based on actual conditions. The fluid-structure interaction finite element model is now complete.

[0102] After establishing the fluid-structure interaction finite element model, Python code was used to apply the frequency-fluidic pressure loads on the structural wall obtained in step two in groups, with each group of fluctuating pressure loads forming a separate computational case. The fluctuating pressure was applied using mesh node interpolation. Steady-state dynamic analysis of the structure under multiple cases was performed, yielding multiple harmonic response analysis results.

[0103] Step 4: Perform energy averaging on the multiple harmonic response analysis results obtained in Step 3 to obtain the corresponding random vibration analysis calculation results.

[0104] It is mainly based on the following theory:

[0105] Assume the structure surface has N elements. When performing steady-state dynamic analysis in Abaqus, it is actually performing harmonic response analysis, i.e.:

[0106] W(ω)=H(ω)F(ω) (1)

[0107] In the formula, W(ω) is the displacement response vector of the element, W(ω)={W1(ω)W2(ω)…W N (ω)} T H(ω) is the frequency response function matrix.

[0108] F(ω)={F1(ω)F2(ω)…F N (ω)} T (2)

[0109] This is the force load vector of the element.

[0110] In discrete form, the power spectral density matrix for analyzing the random response of structural vibration is:

[0111]

[0112] The load Φ(ω) is a matrix, and its relationship with F(ω) is as follows:

[0113]

[0114] Comparing equations (1), (3), and (4), it can be concluded that the random vibration analysis under a single working condition can be obtained from harmonic response analysis, i.e.

[0115]

[0116] However, when performing random vibration analysis of a turbulently excited structure, according to turbulence models such as the Corcos model, the greater the distance between two points on the structural surface, the weaker the correlation between the pulsating pressure loads at those two points. When the mesh is generated based on 1 / 6 of the bending wave wavelength, the correlation between the loads of each element is very weak, close to 0, meaning that off-diagonal elements should be ignored. Therefore, we have...

[0117]

[0118] In the formula This is the load matrix after ignoring cross-correlation. We can see... The form is a diagonal matrix that cannot be decomposed into a load vector multiplied by its conjugate transpose. That is, given any vector F(ω), there does not exist...

[0119] At this point, harmonic response analyses under multiple operating conditions are needed to approximate the results of the random response analysis. Assuming a total of M independent harmonic response analyses were performed, for the i-th harmonic response analysis:

[0120] W i (ω)=H(ω)F i (ω) (7)

[0121] In the formula

[0122]

[0123] In the formula, Each element is an independent random variable, randomly distributed between 0 and 2π, and represents the phase angle of the pulsating pressure load for each element. For each harmonic response analysis, the vector formed by the pulsating pressure phase angles is also different.

[0124]

[0125] in The main diagonal element is F i 2 (ω), the non-main diagonal elements are because and If all are uniformly randomly distributed between 0 and 2π, then we have:

[0126]

[0127] Then, by performing multiple harmonic response analyses and using equation (5) to express the random response analysis, we can obtain...

[0128]

[0129] in To disregard the random vibration response without considering the cross-correlation between loads, The result is the harmonic response calculated under the i-th random phase load excitation. As can be seen from Equation (11), the result of random vibration analysis is finally obtained by averaging the energy of multiple harmonic response analysis results.

[0130] like Figure 4 As shown, the energy-averaged finite element method (FEA) system for structural stochastic vibration analysis provided in this embodiment of the invention includes:

[0131] The module for obtaining time-domain turbulent pulsating pressure distribution is used to perform fluid dynamics simulations using fluid simulation software such as Fluent and StarCCM to obtain the long-term turbulent pulsating pressure distribution of the structural wall in the time domain.

[0132] The frequency domain wall turbulence pulsating pressure acquisition module is used to segment the obtained time domain pulsating pressure, with some overlap between each segment, and perform Fourier transform on each segment to obtain multiple sets of frequency domain wall turbulence pulsating pressure.

[0133] The steady-state dynamic harmonic response analysis module is used to establish fluid-structure interaction dynamic models in the structural and fluid domains, apply the obtained frequency domain wall turbulent pulsating pressure loads, and perform steady-state dynamic harmonic response analysis respectively.

[0134] The random vibration analysis module is used to obtain the results of random vibration analysis by taking the average energy of the vibration response results based on the analysis of multiple harmonic responses.

[0135] Numerical Example Verification

[0136] The method is validated using the random response analysis and corresponding harmonic response analysis results of a simply supported plate. (Aluminum plate, density 2700 kg / m³) 3 Young's modulus 70e9Pa, Poisson's ratio 0.33, loss factor 0.01), length L x 0.8m, width L y 0.6m in diameter and 3mm in thickness. It is subjected to six random excitation forces, each with an amplitude of 1N and a power spectral density of 1N. 2 / Hz, such as Figure 5 .

[0137] Figure 6The results are from random response analysis and harmonic response analysis. It can be seen that by averaging the results of multiple harmonic response calculations with random load phases, the analysis results after one random vibration can be simulated, and the more calculations performed, the closer the results become.

[0138] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the energy-averaged finite element method for structural random vibration analysis.

[0139] 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 an energy-averaged finite element method for analyzing random vibrations of a structure.

[0140] An application embodiment of the present invention provides an information data processing terminal, which is used to realize an energy-averaged finite element calculation system for structural random vibration analysis.

[0141] The method is validated using the random response analysis and corresponding harmonic response analysis results of a simply supported plate. (Aluminum plate, density 2700 kg / m³) 3 Young's modulus 70e9Pa, Poisson's ratio 0.33, loss factor 0.01), length L x 0.8m, width L y 0.6m in diameter and 3mm in thickness. It is subjected to six random excitation forces, each with an amplitude of 1N and a power spectral density of 1N. 2 / Hz, such as Figure 5 .

[0142] Figure 6 The results are from random response analysis and harmonic response analysis. It can be seen that by averaging the results of multiple harmonic response calculations with random load phases, the analysis results after one random vibration can be simulated, and the more calculations performed, the closer the results become.

[0143] 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.

[0144] 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 method for calculating the energy-averaged finite element method for analyzing stochastic vibrations of structures, characterized in that, include: S1. Fluid dynamics simulation was performed using Fluent and StarCCM software to obtain the long-term turbulent pulsating pressure distribution on the structural wall in the time domain. S2. The time-domain pulsating pressure obtained in S1 is segmented, with some overlap between each segment, and Fourier transform is performed on each segment to obtain multiple sets of frequency-domain wall turbulent pulsating pressures. S3. Establish fluid-structure interaction dynamic models of the structure and fluid domain, apply the wall turbulent pulsating pressure loads in the frequency domain obtained in S2, and perform steady-state dynamic harmonic response analysis respectively; S4. Based on the vibration response results of the multi-harmonic response analysis in S3, take the average energy of these results to obtain the results of the random vibration analysis; S3 specifically includes: reasonably simplifying the three-dimensional structural model to reduce the amount of computation, extracting the mid-surface at appropriate locations to establish a shell model, and simultaneously constructing a fluid domain; The structural and fluid domains were meshed using structural and acoustic meshes respectively, with the meshing principle being 1 / 6 of the wavelength of the structural bending wave and 1 / 6 of the wavelength of the acoustic wave. The meshed structural and acoustic models were imported into Abaqus, and structural material properties and fluid acoustic properties were assigned to them respectively. The structural mesh type was changed from linear element to quadratic element to improve the accuracy of structural response calculation. Tie interactions were established between the structural and acoustic meshes to form fluid-structure interaction. Appropriate boundary conditions were set for the structural model according to the actual situation, and the fluid-structure interaction finite element model was completed. After establishing the fluid-structure interaction finite element model, the structural wall frequency pulsating pressure loads obtained in step two were applied in groups using Python code. Each group of pulsating pressure loads formed a calculation case. The pulsating pressure was applied by mesh node interpolation. The structural fluid-structure interaction steady-state dynamic analysis was performed under multiple cases to obtain multiple harmonic response analysis results.

2. The energy-averaged finite element method for structural random vibration analysis as described in claim 1, characterized in that, S1 specifically includes: dividing the fluid domain into fluid meshes, importing the mesh model into Fluent or StarCCM fluid simulation software, establishing a fluid dynamics simulation model, performing transient flow field calculations based on the LES model, determining the calculation time step according to the highest frequency of steady-state dynamic analysis, obtaining the turbulent fluctuation pressure distribution on the structural wall over a period of time, observing the turbulent fluctuation pressure curve in the time domain, and only the part after the periodic fluctuations appear, i.e., after entering steady state, can be used as the effective load for structural fluid-structure interaction calculations.

3. The energy-averaged finite element method for structural random vibration analysis as described in claim 1, characterized in that, S2 specifically includes: performing a Fast Fourier Transform (FFT) on each group of time-domain turbulent fluctuating pressures in Matlab to obtain the frequency-domain turbulent fluctuating pressures; the frequency-domain turbulent fluctuating pressures should be expressed in the form of real part + imaginary part; exporting the obtained frequency-domain turbulent fluctuating pressures of the structural wall as .dat files according to each frequency point, with each .dat file representing the fluctuating pressure distribution at each node of the structural wall at that frequency point; it should be noted that when exporting the .dat files, the real and imaginary parts should be stored in two separate .dat files, that is, the fluctuating pressure distribution at each frequency point should consist of a real part .dat file and an imaginary part .dat file.

4. The energy-averaged finite element method for analyzing stochastic vibrations of structures as described in claim 1, characterized in that, S4 specifically includes: assuming the structure surface has N elements, when performing steady-state dynamic analysis in Abaqus, it is actually performing harmonic response analysis, that is: W(ω)=H(ω)F(ω) (1) In the formula, W(ω) is the displacement response vector of the element, W(ω)={W1(ω)W2(ω)…W N (ω)} T H(ω) is the frequency response function matrix. F(ω)={F1(ω) F2(ω) … F N (oh)} T (2) This represents the force load vector of the element; In discrete form, the power spectral density matrix for analyzing the random response of structural vibration is: The load Φ(ω) is a matrix, and its relationship with F(ω) is as follows: Comparing equations (1), (3), and (4), it can be concluded that the random vibration analysis under a single working condition can be obtained from harmonic response analysis, i.e. However, when performing random vibration analysis of a turbulently excited structure, according to the Corcos turbulence model, the greater the distance between two points on the structural surface, the weaker the correlation between the pulsating pressure loads at those two points. When the mesh is divided according to 1 / 6 of the bending wave wavelength, the correlation between the loads of each element is very weak, close to 0, meaning that off-diagonal elements should be ignored. Therefore, we have... In the formula To ignore the load matrix after cross-correlation, we can see The form is a diagonal matrix that cannot be decomposed into a load vector multiplied by its conjugate transpose; that is, given any vector F(ω), there does not exist. At this point, harmonic response analysis under multiple operating conditions is needed to approximate the results of the random response analysis. Assuming a total of M independent harmonic response analyses were performed, for the i-th harmonic response analysis: W i (ω)=H(ω)F i (oh) (7) In the formula In the formula, Each element is an independent random variable, randomly distributed between 0 and 2π, and its meaning is the phase angle of the pulsating pressure load of each unit; for each harmonic response analysis, the vector formed by the pulsating pressure phase angle is also different; in The main diagonal element is F i 2 (ω), the non-main diagonal elements are because and If all are uniformly randomly distributed between 0 and 2π, then we have: Then, by performing multiple harmonic response analyses and using equation (5) to express the random response analysis, we can obtain... in To disregard the random vibration response without considering the cross-correlation between loads, The result is the harmonic response calculated under the i-th random phase load excitation. As can be seen from Equation (11), the energy average of multiple harmonic response analysis results is used to finally obtain the result of random vibration analysis.

5. A system for calculating the energy-averaged finite element method for structural random vibration analysis, which implements the energy-averaged finite element method for calculating structural random vibration analysis as described in any one of claims 1 to 4, characterized in that, include: The module for obtaining time-domain turbulent pulsating pressure distribution is used to perform fluid dynamics simulations using fluid simulation software such as Fluent and StarCCM to obtain the long-term turbulent pulsating pressure distribution of the structural wall in the time domain. The frequency domain wall turbulence pulsating pressure acquisition module is used to segment the obtained time domain pulsating pressure, with some overlap between each segment, and perform Fourier transform on each segment to obtain multiple sets of frequency domain wall turbulence pulsating pressure. The steady-state dynamic harmonic response analysis module is used to establish fluid-structure interaction dynamic models in the structural and fluid domains, apply the obtained frequency domain wall turbulent pulsating pressure loads, and perform steady-state dynamic harmonic response analysis respectively. The random vibration analysis module is used to obtain the results of random vibration analysis by taking the average energy of the vibration response results based on the analysis of multiple harmonic responses.

6. A computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the energy-averaged finite element method for structural random vibration analysis as described in any one of claims 1 to 4.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the energy-averaged finite element method for structural random vibration analysis as described in any one of claims 1 to 4.

8. An information data processing terminal, which is used to implement the energy-averaged finite element calculation system for structural random vibration analysis as described in claim 5.

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