Steel-concrete composite beam acoustic vibration calculation method based on FEM-BEM-SEA

Abstract

The invention discloses a steel-concrete composite beam sound and vibration calculation method based on FEM-BEM-SEA, and belongs to the technical field of rail transit bridge vibration and noise reduction. The method comprises the following steps: determining the upper limit cut-off frequency of boundary element calculation; determining a lower limit starting frequency of statistical energy analysis; determining a boundary frequency based on the upper limit cut-off frequency and the lower limit start frequency; constructing a bridge finite element model of a bridge structure, and calculating vibration response in a full-frequency-band range when the train passes through the bridge; inputting the vibration response into the bridge boundary element model, and calculating an acoustic response within a range below the boundary frequency when the train passes through the bridge; establishing a bridge statistical energy analysis model of the bridge structure, and calculating acoustic response in a range above the boundary frequency; and jointly using the vibration response and the acoustic response as an acoustic vibration calculation result of the steel-concrete composite beam. According to the method, the problem that high-precision calculation and low calculation workload cannot be met at the same time during sound and vibration calculation of an existing bridge structure is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration reduction and noise reduction of rail transit bridges, and specifically relates to a vibration-acoustic calculation method for a steel-concrete composite beam based on FEM-BEM-SEA. Background Art

[0002] With the full deployment of the high-speed railway network and the rapid development of high-speed railway bridges, people's transportation has been greatly facilitated. However, the problem of bridge structure vibration and noise caused by trains passing over bridges has become increasingly prominent and has received more and more attention.

[0003] However, the complexity and diversity of bridge structures are undoubtedly a huge challenge for researchers who are accustomed to using a single calculation method. At present, most rail transit bridges have broadband characteristics, which involves the calculation of low-frequency and medium-high frequency noise. Therefore, how to select a calculation method that can both meet the calculation accuracy and reduce the calculation workload is an urgent problem to be solved by technicians in this field. Summary of the invention

[0004] The invention provides a steel-concrete composite beam acoustic vibration calculation method based on FEM-BEM-SEA, which solves the problem that high-precision calculation and low calculation workload cannot be satisfied simultaneously in the existing bridge structure acoustic vibration calculation.

[0005] In order to solve the above technical problems, the technical solution of the present invention is: a method for calculating the acoustic vibration of a steel-concrete composite beam based on FEM-BEM-SEA, comprising the following steps:

[0006] S1. Based on the finite element method and boundary element method, the mesh size of the finite element model and the boundary element model is selected, and the upper cutoff frequency of the boundary element calculation is determined;

[0007] S2. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems, and the total statistical energy analysis matrix and the modal number of each subsystem are calculated, and the lower limit starting frequency of the statistical energy analysis is determined according to the modal number;

[0008] S3, determining the demarcation frequency based on the upper limit cut-off frequency and the lower limit starting frequency;

[0009] S4. Based on the mesh size of the finite element model, the bridge-related parameters are input into the finite element model to obtain a bridge finite element model of the bridge structure, and the vibration response of the train passing the bridge in the full frequency range is calculated by the bridge finite element model;

[0010] S5. constructing a bridge boundary element model of the bridge structure based on the mesh size of the boundary element model, and inputting the vibration response into the bridge boundary element model to calculate the acoustic response within a range below the boundary frequency when the train passes over the bridge;

[0011] S6. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established, and statistical energy analysis is performed through the bridge statistical energy analysis model to calculate the acoustic response within a range above the demarcation frequency;

[0012] S7. The acoustic response within the range below the demarcation frequency, the acoustic response within the range above the demarcation frequency, and the vibration response within the full frequency range are taken together as the acoustic-vibration calculation results of the steel-concrete composite beam.

[0013] Furthermore, the specific steps of step S1 are:

[0014] S11. Based on the finite element method, construct the structural multi-degree-of-freedom motion differential equations of the finite element model;

[0015] S12, calculating the maximum element size of the finite element model and the boundary element model;

[0016] S13, based on prediction accuracy and computational efficiency, selecting the upper cutoff frequency of the boundary element model;

[0017] S14. Based on the maximum unit size and the upper cutoff frequency, select the mesh size of the finite element model and the boundary element model.

[0018] Furthermore, the expression of the structural multi-degree-of-freedom motion differential equation in step S11 is:

[0019]

[0020] Where M, C and K represent the mass, damping and stiffness matrices of the structure respectively. and x represent acceleration, velocity and displacement vectors respectively, and F represents the external load vector.

[0021] Furthermore, the calculation formula of the maximum unit size in step S12 is:

[0022]

[0023] Where Δd represents the maximum element size of the finite element model, Δd' represents the maximum element size of the boundary element model, and λ min represents the minimum vibration wavelength, C v represents the speed of vibration waves propagating in the structure, f u represents the upper cutoff frequency, ρ, E and μ represent the density, elastic modulus and Poisson's ratio of the material respectively, C s Represents the speed of sound at which vibration waves propagate in a structure.

[0024] Furthermore, the specific steps of step S2 are:

[0025] S21. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems;

[0026] S22, construct the power flow balance equation of each subsystem;

[0027] S23, based on the power flow balance equation, all subsystems are coupled to obtain the total statistical energy analysis matrix;

[0028] S24, calculating the modal number of each subsystem;

[0029] S25. Based on the modal number, determine the lower limit starting frequency of statistical energy analysis.

[0030] Furthermore, the expression of the power flow balance equation in step S22 is:

[0031]

[0032] Among them, Φ m represents the input power of the mth subsystem, represents the center frequency of the analysis band, ξ m represents the damping loss factor of the mth subsystem, E m and E n denote the vibration energy of the mth subsystem and the nth subsystem, ξ mn represents the coupling loss factor between the mth subsystem and the nth subsystem, and N represents the number of subsystems;

[0033] The expression of the total statistical energy analysis matrix in step S23 is:

[0034]

[0035] Among them, Φ represents the column vector of input power, ξ represents the loss factor matrix of the entire system, and E represents the column vector of vibration energy;

[0036] The calculation formula of the modal number in step S24 is:

[0037]

[0038] Among them, N m represents the mode number of the mth subsystem, δ m represents the modal density of the mth subsystem, Indicates the analysis bandwidth.

[0039] Furthermore, the bridge-related parameters include component size, material density and unit type; and a vehicle-track-bridge system coupling model needs to be constructed when the train passes the bridge.

[0040] Furthermore, the specific steps of step S5 are:

[0041] S51, select the acoustic equation of the boundary element model, and combine the Green function and the Neumann boundary condition to obtain the conventional Helmholtz integral equation of the boundary element model;

[0042] S52, based on the grid size of the boundary element model, setting the field point grid and the sound reflection surface of the boundary element model to obtain a bridge boundary element model of the bridge structure;

[0043] S53, using the vibration response as the acoustic mesh of the bridge boundary element model;

[0044] S54. Based on the bridge boundary element model, calculate the acoustic response within the range below the boundary frequency when the train passes the bridge.

[0045] Furthermore, the expression of the acoustic equation in step S51 is:

[0046]

[0047] Among them, s(·) represents the space The steady-state sound pressure at the position, κ represents the spatial angular wave number, represents the Laplace operator, r, θ and Together they represent spatial position coordinates;

[0048] The expression of the conventional Helmholtz integral equation in step S51 is:

[0049]

[0050] Among them, G f (·) represents the free field space Green function, m represents the surface normal vector, P a and P b represent the field points of the observation position and the sound source position respectively, S - , S and S + Respectively represent the interior space, surface and exterior space of the structure;

[0051] The expression of the acoustic response in step S54 is:

[0052]

[0053] Among them, s(P a ) represents the steady-state sound pressure at the observation location, P b1 and P b2 They represent the field points on the inside and outside of the sound source surface respectively.

[0054] Furthermore, the specific steps of step S6 are:

[0055] S61. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established;

[0056] S62. Calculate the sound radiation efficiency of the bridge structure by using a bridge statistical energy analysis model;

[0057] S63. Calculate the radiated sound power of the bridge structure;

[0058] S64. Calculate the acoustic response above the cut-off frequency by using the acoustic radiation efficiency and radiated acoustic power;

[0059] The expression of the sound radiation efficiency is:

[0060]

[0061] Where σ represents the sound radiation efficiency, f represents the frequency, and f 1,1 、f e and f c All represent intermediate variables, a and b represent the length and width of the plate respectively, S' represents the surface area of ​​the plate, D represents the bending stiffness of the plate, c represents the speed of sound, ρ represents the density of the plate, h represents the thickness of the plate, and α represents the intermediate parameter;

[0062] The expression of the radiated sound power is:

[0063]

[0064] Among them, W rad,i represents the radiated sound power of plate i, ρ0 represents the air density, σ i is the acoustic radiation efficiency of plate i, S i represents the surface area of ​​plate i, represents the mean square velocity of plate i;

[0065] The expression of the acoustic response is:

[0066]

[0067] in, represents the sound pressure at the observation point, and d represents the distance from the observation point p to the bridge.

[0068] The beneficial effects of the present invention are as follows: (1) a method for calculating the acoustic vibration response of a railway steel-concrete composite beam bridge based on a hybrid finite element (FEM)-boundary element (BEM)-statistical energy analysis (SEA) is proposed. By analyzing the boundary frequency, the finite element-boundary element calculation method is used to predict low-frequency noise, and the statistical energy analysis method is used to predict medium and high-frequency noise. This combined analysis method effectively combines the advantages of each method and achieves a balance between calculation efficiency and accuracy.

[0069] (2) The present invention can provide technical support for calculating and predicting broadband vehicle-induced structural vibration noise in the bridge field. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 The figure is a flow chart of the acoustic-vibration calculation method of the steel-concrete composite beam based on FEM-BEM-SEA of the present invention.

[0071] Figure 2 It is a schematic diagram of the full bridge dimensions of the steel-concrete composite beam bridge of the present invention.

[0072] Figure 3 This is a graph showing the relationship between the modal number of the bridge subsystem of the present invention and the frequency.

[0073] Figure 4 This is the vehicle-track-bridge system coupling model of the present invention.

[0074] Figure 5 It is a frequency spectrum of the dynamic wheel-rail force and the force transmitted to the bridge and a relationship diagram of the corresponding force transmission rate changing with frequency according to the present invention.

[0075] Figure 6 It is a finite element-boundary element numerical simulation analysis model for the steel-concrete composite beam bridge of the present invention.

[0076] Figure 7 This is a statistical energy analysis model diagram of the steel-concrete composite beam bridge of the present invention.

[0077] Figure 8 This is a detailed layout diagram of the noise measurement points and acceleration measurement points of the present invention.

[0078] Fig. 9 It is a comparison chart of the on-site measurement and simulation prediction results of the vibration acceleration measurement point V-1 and the sound pressure measurement point S-1 in the embodiment of the present invention. DETAILED DESCRIPTION

[0079] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

[0080] Example 1

[0081] like Figure 1 As shown, the present invention provides a method for calculating the acoustic vibration of a steel-concrete composite beam based on FEM-BEM-SEA, comprising the following steps:

[0082] S1. Based on the finite element method and boundary element method, the mesh size of the finite element model and the boundary element model is selected, and the upper cutoff frequency of the boundary element calculation is determined;

[0083] S2. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems, and the total statistical energy analysis matrix and the modal number of each subsystem are calculated, and the lower limit starting frequency of the statistical energy analysis is determined according to the modal number;

[0084] S3, determining the demarcation frequency based on the upper limit cut-off frequency and the lower limit starting frequency;

[0085] S4. Based on the mesh size of the finite element model, the bridge-related parameters are input into the finite element model to obtain a bridge finite element model of the bridge structure, and the vibration response of the train passing the bridge in the full frequency range is calculated by the bridge finite element model;

[0086] S5. constructing a bridge boundary element model of the bridge structure based on the mesh size of the boundary element model, and inputting the vibration response into the bridge boundary element model to calculate the acoustic response within a range below the boundary frequency when the train passes over the bridge;

[0087] S6. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established, and statistical energy analysis is performed through the bridge statistical energy analysis model to calculate the acoustic response within a range above the demarcation frequency;

[0088] S7. The acoustic response within the range below the demarcation frequency, the acoustic response within the range above the demarcation frequency, and the vibration response within the full frequency range are taken together as the acoustic-vibration calculation results of the steel-concrete composite beam.

[0089] In this embodiment 1, the upper cutoff frequency of the boundary element BEM and the lower start frequency of the statistical energy analysis SEA are only used to determine the demarcation frequency. The full frequency range is determined by the specific engineering situation and has nothing to do with the upper and lower frequency limits. For example, the full frequency range of a bridge noise is 0-2000Hz (determined according to the actual engineering calculation requirements), and the demarcation frequency is 200Hz (determined according to the upper cutoff frequency of the BEM and the lower start frequency of the SEA). In this case, the BEM is used to solve the acoustic response in the range of 0-200Hz, and the SEA is used to solve the acoustic response in the range of 200-2000Hz.

[0090] The specific steps of step S1 are:

[0091] S11. Based on the finite element method, construct the structural multi-degree-of-freedom motion differential equations of the finite element model;

[0092] S12, calculating the maximum element size of the finite element model and the boundary element model;

[0093] S13, based on prediction accuracy and computational efficiency, selecting the upper cutoff frequency of the boundary element model;

[0094] S14. Based on the maximum unit size and the upper cutoff frequency, select the mesh size of the finite element model and the boundary element model.

[0095] The expression of the structural multi-degree-of-freedom motion differential equation in step S11 is:

[0096]

[0097] Where M, C and K represent the mass, damping and stiffness matrices of the structure respectively. and x represent acceleration, velocity and displacement vectors respectively, and F represents the external load vector.

[0098] The calculation formula of the maximum unit size in step S12 is:

[0099]

[0100] Where Δd represents the maximum element size of the finite element model, Δd' represents the maximum element size of the boundary element model, and λ min represents the minimum vibration wavelength, C v represents the wave speed of vibration waves propagating in the structure, f u represents the upper cutoff frequency, ρ, E and μ represent the density, elastic modulus and Poisson's ratio of the material respectively, C s Represents the speed of sound at which vibration waves propagate in a structure.

[0101] In the air, C s Usually 340m / s is taken.

[0102] In this embodiment 1, the unit size of the finite element model has a significant impact on the calculation efficiency and calculation accuracy. And when the boundary element method is used for acoustic simulation calculations, in order to ensure the simulation accuracy of higher frequency bands, it is often necessary to set a more refined grid division, which leads to a surge in the amount of calculation, increases the consumption and occupation of computing resources, and makes numerical simulation difficult. Considering the calculation efficiency and calculation accuracy, it is necessary to select a more appropriate upper cutoff frequency, so as to determine the grid division size through the above formula.

[0103] The specific steps of step S2 are:

[0104] S21. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems;

[0105] S22, construct the power flow balance equation of each subsystem;

[0106] S23, based on the power flow balance equation, all subsystems are coupled to obtain the total statistical energy analysis matrix;

[0107] S24, calculating the modal number of each subsystem;

[0108] S25. Based on the modal number, determine the lower limit starting frequency of statistical energy analysis.

[0109] In this embodiment 1, it is first necessary to divide the structural subsystems to ensure the modal similarity of the same component subsystems, so as to clearly describe the entire process and characteristics of energy reception, storage, transmission, and loss in the structure.

[0110] The expression of the power flow balance equation in step S22 is:

[0111]

[0112] Among them, Φ m represents the input power of the mth subsystem, represents the center frequency of the analysis band, ξ m represents the damping loss factor of the mth subsystem, E m and E n denote the vibration energy of the mth subsystem and the nth subsystem, ξ mn represents the coupling loss factor between the mth subsystem and the nth subsystem, and N represents the number of subsystems;

[0113] The expression of the total statistical energy analysis matrix in step S23 is:

[0114]

[0115] Among them, Φ represents the column vector of input power, ξ represents the loss factor matrix of the entire system, and E represents the column vector of vibration energy;

[0116] In this embodiment 1, It is the simplified vector form of the total statistical energy analysis matrix, and its original matrix is ​​as follows:

[0117]

[0118] Among them, m=1,...,N, n=1,...,N.

[0119] The calculation formula of the modal number in step S24 is:

[0120]

[0121] Among them, N m represents the mode number of the mth subsystem, δ m represents the modal density of the mth subsystem, Indicates the analysis bandwidth.

[0122] In this embodiment 1, for N m <1 in the low frequency region, the subsystem modes are sparse and often cannot meet the accuracy requirements of statistical energy analysis. m <5 mid-frequency area and N m In the high frequency region of ≥5, the subsystem contains more modes, which is an ideal area for calculation using statistical energy analysis.

[0123] The bridge-related parameters include component size, material density and unit type; when the train passes the bridge, a vehicle-track-bridge system coupling model needs to be constructed.

[0124] In this embodiment 1, the calculation model of the wheel-rail force when the train passes the bridge and the force transmitted to the bridge can be simplified to a vehicle-track-bridge system coupling model. For the track subsystem, it is simplified to a half-width track based on the structural symmetry during analysis, wherein the rail is regarded as an infinitely long Timoshenko beam, the fastener is simulated as a series of discrete springs with complex stiffness, the sleeper is simulated as a series of discrete mass blocks connecting the fastener and the ballast, and the ballast is simulated as a series of discrete mass-spring damping pairs. For the bridge subsystem, since its vertical stiffness is much greater than that of the track subsystem, the bridge is regarded as a rigid foundation during analysis.

[0125] On this basis, a series of frequency spectra of the forces transmitted to the bridge can be obtained, and the vibration response calculation of the bridge when the train passes through the bridge can be completed through the frequency spectra.

[0126] The specific steps of step S5 are:

[0127] S51, select the acoustic equation of the boundary element model, and combine the Green function and the Neumann boundary condition to obtain the conventional Helmholtz integral equation of the boundary element model;

[0128] S52, based on the grid size of the boundary element model, setting the field point grid and the sound reflection surface of the boundary element model to obtain a bridge boundary element model of the bridge structure;

[0129] S53, using the vibration response as the acoustic mesh of the bridge boundary element model;

[0130] S54. Based on the bridge boundary element model, calculate the acoustic response within the range below the boundary frequency when the train passes the bridge.

[0131] In this embodiment 1, considering that most bridge types are non-closed structures, an indirect boundary element solver is configured and selected in the boundary element analysis.

[0132] The expression of the acoustic equation in step S51 is:

[0133]

[0134] Among them, s(·) represents the space The steady-state sound pressure at the position, κ represents the spatial angular wave number, represents the Laplace operator, r, θ and Together they represent spatial position coordinates;

[0135] The expression of the conventional Helmholtz integral equation in step S51 is:

[0136]

[0137] Among them, G f (·) represents the free field space Green function, m represents the surface normal vector, P a and P b represent the field points of the observation position and the sound source position respectively, S - , S and S + Respectively represent the interior space, surface and exterior space of the structure;

[0138] The expression of the acoustic response in step S54 is:

[0139]

[0140] Among them, s(P a ) represents the steady-state sound pressure at the observation location, P b1 and P b2 They represent the field points on the inside and outside of the sound source surface respectively.

[0141] The specific steps of step S6 are:

[0142] S61. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established;

[0143] S62. Calculate the sound radiation efficiency of the bridge structure by using a bridge statistical energy analysis model;

[0144] S63. Calculate the radiated sound power of the bridge structure;

[0145] S64. Calculate the acoustic response above the cut-off frequency by using the acoustic radiation efficiency and the radiated acoustic power;

[0146] In this embodiment 1, the bending wave propagating in the structure is the main source of noise, and the propagation speed of the bending wave is c B The center frequency of the analysis band It can be written in the following form:

[0147]

[0148] Where D = Eh 3 / 12(1-v 2 ), E, ​​v, ρ and h represent the elastic modulus, Poisson's ratio, density and thickness of the plate respectively, m' represents the surface density of the plate, m'=ρh.

[0149] When the bending wave speed c B When it is equal to the speed of sound c, the frequency at this time is the matching frequency, that is, the intermediate variable f c :

[0150]

[0151] For a rectangular plate with a size of a×b, its sound radiation efficiency σ can be solved using the following formula.

[0152] The expression of the sound radiation efficiency is:

[0153]

[0154] Where σ represents the sound radiation efficiency, f represents the frequency, and f 1,1 、f e and f c All represent intermediate variables, a and b represent the length and width of the plate respectively, S' represents the surface area of ​​the plate, D represents the bending stiffness of the plate, c represents the speed of sound, ρ represents the density of the plate, h represents the thickness of the plate, and α represents the intermediate parameter;

[0155] In this embodiment 1, for the mean square velocity Calculate the radiated sound power for the board system i.

[0156] The expression of the radiated sound power is:

[0157]

[0158] Among them, W rad,i represents the radiated sound power of plate i, ρ0 represents the air density, σ i represents the acoustic radiation efficiency of plate i, S i represents the surface area of ​​plate i, represents the mean square velocity of plate i;

[0159] The expression of the acoustic response is:

[0160]

[0161] in, represents the sound pressure at the observation point, and d represents the distance from the observation point p to the bridge.

[0162] Example 2

[0163] This embodiment 2 is described by taking a railway steel-concrete composite beam bridge as an example. Figure 2 shown.

[0164] In this Example 2, in order to ensure the prediction accuracy and calculation efficiency, 240 Hz is selected as the upper cutoff frequency of the boundary element model. The wavelength of each vibration wave and sound wave should contain at least 6 linear units. Considering that the analysis frequencies of the finite element method and the boundary element method in this Example 2 are 20-2000 Hz and 20-240 Hz, respectively, the maximum grid unit is integrated, and the grid size of the analysis model is finally determined to be 250 mm, and the division method is free quadrilateral to meet the above requirements. After grid division, a total of 46177 nodes and 46213 units are generated.

[0165] In this embodiment 2, the bridge structure is divided into multiple subsystems, and the energy transfer between subsystems is studied by establishing a power flow balance equation. To ensure that the simulation results are not distorted, the model needs to have a sufficient number of modes. For the statistical energy model of the railway steel-concrete composite beam bridge in this embodiment 2, a total of 4845 nodes and 410 plate subsystems are included, including 80 bridge deck subsystems, 56 I-beam web subsystems, 112 I-beam flange subsystems, and 162 diaphragm subsystems.

[0166] Through calculation, the modal number of each subsystem is as follows Figure 3 As shown. Figure 3 It can be seen that when the analysis frequency is higher than 200 Hz, the modal numbers of all component subsystems are greater than 1; when the analysis frequency is higher than 1000 Hz, the modal numbers of all component subsystems are greater than 5, that is, above 200 Hz is the ideal area for calculation using the statistical energy analysis method.

[0167] Therefore, the more appropriate solution frequency range for the finite element-boundary element model corresponding to this bridge is 20 to 240 Hz, so 200 Hz is selected as the dividing frequency for boundary element and statistical energy analysis calculations.

[0168] The material properties of the bridge finite element model are shown in Table 1. The bridge main beam is simulated using 4-node plate element Shell 181. After meshing, a total of 46177 nodes and 46213 elements are generated.

[0169] Table 1

[0170]

[0171] This embodiment 2 is constructed as Figure 4 The vehicle-track-bridge system coupling model is shown in Figure 2, and the main design parameters of the vehicle are shown in Table 2.

[0172] Table 2

[0173]

[0174]

[0175] Through calculation, the frequency spectra of the dynamic wheel-rail force and the force transmitted to the bridge as well as the corresponding force transmission rate are given, such as Figure 5 As shown. Figure 5 It can be seen that the dynamic wheel-rail force and the force transmitted to the bridge both reach their peak values ​​at 55 Hz, that is, their peak frequencies match well. Subsequently, the dynamic wheel-rail force reaches a valley at 120 Hz, but since this frequency is close to the peak frequency of the force transfer rate of 116 Hz, the force transmitted to the bridge has a smooth transition near this frequency, and no obvious peak or valley effect occurs. In the medium and high frequency bands, there are many small peaks in the dynamic wheel-rail force and the force transmitted to the bridge, and the peak frequencies also match well. At the same time, since the force transfer rate decays rapidly in this frequency band, the force transmitted to the bridge also shows an obvious downward trend overall.

[0176] In this embodiment 2, a bridge boundary element model of the bridge structure, that is, a finite element-boundary element numerical simulation analysis model, is constructed. Figure 6 As shown in the figure, it is necessary to arrange the field point grid and acoustic reflection surface according to the actual engineering requirements, and then use the vibration response as the acoustic grid to further solve the acoustic response in the bridge boundary element model.

[0177] In this embodiment 2, Figure 7 For the statistical energy analysis model of the steel-concrete composite beam bridge established in this embodiment, a mirror model is created with the ground as the symmetry plane to simulate the sound reflection effect of the rigid ground, and the acoustic response in the high-frequency range above the boundary frequency is solved.

[0178] Based on the calculation results of step S4, step S5 and step S6, the measured results of each measuring point are compared with the predicted results to verify the reliability and accuracy of the proposed prediction method and the established prediction model. By arranging the calculated data and drawing a line point graph, the detailed measurement point layout is shown in the figure. Figure 8 As shown in the figure, a total of 6 measuring points including 3 normal vibration acceleration measuring points (V-1~V-3) and 3 sound pressure measuring points (S-1~S-3) are arranged. For the acceleration measuring point, V-1 is located at the center of the bottom of the bridge deck to monitor the vibration of the bridge deck, and V-2 and V-3 are located at the center of the web and flange of the I-beam respectively to monitor the vibration of the I-beam; for the sound pressure measuring point, S-1 is located at the left span, 1.5m above the ground, just below the center line of the bridge, to monitor the noise at the bottom of the beam, and S-2 and S-3 are located at the middle of the main span, 7.5m and 25m from the center line of the westbound track, respectively, and are also 1.5m above the ground to measure near-field and far-field noise.

[0179] Fig. 9The test average value and simulation value comparison of the vibration acceleration measurement point V-1 and the sound pressure measurement point S-1 are given. The results show that the test average value is consistent with the simulation value results.

[0180] In summary, by analyzing the boundary frequency, the finite element-boundary element calculation method is used to predict low-frequency noise, and the statistical energy analysis method is used to predict medium and high-frequency noise. This combined analysis method takes advantage of each method and effectively combines the advantages of each method to achieve a balance between calculation efficiency and accuracy. The present invention can provide technical support for calculating and predicting broadband vehicle-induced structural vibration noise in the field of bridges.

Claims

1. A method for calculating the acoustic vibration of steel-concrete composite beams based on FEM-BEM-SEA. It is characterized in that The following steps are involved: S1. Based on the finite element method and boundary element method, the mesh size of the finite element model and the boundary element model is selected, and the upper cutoff frequency of the boundary element calculation is determined; S2. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems, and the total statistical energy analysis matrix and the modal number of each subsystem are calculated, and the lower limit starting frequency of the statistical energy analysis is determined according to the modal number; S3, determining the demarcation frequency based on the upper limit cut-off frequency and the lower limit starting frequency; S4. Based on the mesh size of the finite element model, the bridge-related parameters are input into the finite element model to obtain a bridge finite element model of the bridge structure, and the vibration response of the train passing the bridge in the full frequency range is calculated by the bridge finite element model; S5. constructing a bridge boundary element model of the bridge structure based on the mesh size of the boundary element model, and inputting the vibration response into the bridge boundary element model to calculate the acoustic response within a range below the boundary frequency when the train passes over the bridge; S6. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established, and statistical energy analysis is performed through the bridge statistical energy analysis model to calculate the acoustic response within a range above the demarcation frequency; S7. The acoustic response within the range below the demarcation frequency, the acoustic response within the range above the demarcation frequency, and the vibration response within the full frequency range are taken together as the acoustic-vibration calculation results of the steel-concrete composite beam.

2. According to the FEM-BEM-SEA based acoustic vibration calculation method for steel-concrete composite beams in claim 1, It is characterized in that The specific steps of step S1 are: S11. Based on the finite element method, construct the structural multi-degree-of-freedom motion differential equations of the finite element model; S12, calculating the maximum element size of the finite element model and the boundary element model; S13, based on prediction accuracy and computational efficiency, selecting the upper cutoff frequency of the boundary element model; S14. Based on the maximum unit size and the upper cutoff frequency, select the mesh size of the finite element model and the boundary element model.

3. According to claim 2, the acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA, It is characterized in that The expression of the structural multi-degree-of-freedom motion differential equation in step S11 is: Where M, C and K represent the mass, damping and stiffness matrices of the structure respectively. and x represent acceleration, velocity and displacement vectors respectively, and F represents the external load vector.

4. According to claim 2, the acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA, It is characterized in that The calculation formula of the maximum unit size in step S12 is: Where Δd represents the maximum element size of the finite element model, Δd' represents the maximum element size of the boundary element model, and λ min represents the minimum vibration wavelength, C v represents the wave speed of vibration waves propagating in the structure, f u represents the upper cutoff frequency, ρ, E and μ represent the density, elastic modulus and Poisson's ratio of the material respectively, C s Represents the speed of sound at which vibration waves propagate in a structure.

5. According to the FEM-BEM-SEA based acoustic vibration calculation method for steel-concrete composite beams in claim 1, It is characterized in that The specific steps of step S2 are: S21. Based on the statistical energy analysis method, the bridge structure is divided into multiple subsystems; S22, construct the power flow balance equation of each subsystem; S23, based on the power flow balance equation, all subsystems are coupled to obtain the total statistical energy analysis matrix; S24, calculating the modal number of each subsystem; S25. Based on the modal number, determine the lower limit starting frequency of statistical energy analysis.

6. The acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA according to claim 5, It is characterized in that The expression of the power flow balance equation in step S22 is: Among them, Φ m represents the input power of the mth subsystem, represents the center frequency of the analysis band, ξ m represents the damping loss factor of the mth subsystem, E m and E n denote the vibration energy of the mth subsystem and the nth subsystem, ξ mn represents the coupling loss factor between the mth subsystem and the nth subsystem, and N represents the number of subsystems; The expression of the total statistical energy analysis matrix in step S23 is: Among them, Φ represents the column vector of input power, ξ represents the loss factor matrix of the entire system, and E represents the column vector of vibration energy; The calculation formula of the modal number in step S24 is: Among them, N m represents the mode number of the mth subsystem, δ m represents the modal density of the mth subsystem, Indicates the analysis bandwidth.

7. The acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA according to claim 1, It is characterized in that The bridge-related parameters include component size, material density and unit type; when the train passes the bridge, a vehicle-track-bridge system coupling model needs to be constructed.

8. The acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA according to claim 1, It is characterized in that The specific steps of step S5 are: S51, select the acoustic equation of the boundary element model, and combine the Green function and the Neumann boundary condition to obtain the conventional Helmholtz integral equation of the boundary element model; S52, based on the grid size of the boundary element model, setting the field point grid and the sound reflection surface of the boundary element model to obtain a bridge boundary element model of the bridge structure; S53, using the vibration response as the acoustic mesh of the bridge boundary element model; S54. Based on the bridge boundary element model, calculate the acoustic response within the range below the boundary frequency when the train passes the bridge.

9. The acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA according to claim 8, It is characterized in that The expression of the acoustic equation in step S51 is: Among them, s(·) represents the space The steady-state sound pressure at the position, κ represents the spatial angular wave number, represents the Laplace operator, r, θ and Together they represent spatial position coordinates; The expression of the conventional Helmholtz integral equation in step S51 is: Among them, G f (·) represents the free field space Green function, m represents the surface normal vector, P a and P b represent the field points of the observation position and the sound source position respectively, S - , S and S + Respectively represent the interior space, surface and exterior space of the structure; The expression of the acoustic response in step S54 is: Among them, s(P a ) represents the steady-state sound pressure at the observation location, P b1 and P b2 They represent the field points on the inside and outside of the sound source surface respectively.

10. The acoustic vibration calculation method of steel-concrete composite beam based on FEM-BEM-SEA according to claim 1, It is characterized in that The specific steps of step S6 are: S61. Based on the total statistical energy analysis matrix, a bridge statistical energy analysis model of the bridge structure is established; S62. Calculate the sound radiation efficiency of the bridge structure by using a bridge statistical energy analysis model; S63. Calculate the radiated sound power of the bridge structure; S64. Calculate the acoustic response above the cut-off frequency by using the acoustic radiation efficiency and radiated acoustic power; The expression of the sound radiation efficiency is: Where σ represents the sound radiation efficiency, f represents the frequency, and f 1,1 、f e and f c All represent intermediate variables, a and b represent the length and width of the plate respectively, S' represents the surface area of ​​the plate, D represents the bending stiffness of the plate, c represents the speed of sound, ρ represents the density of the plate, h represents the thickness of the plate, and α represents the intermediate parameter; The expression of the radiated sound power is: Among them, W rad,i is the radiated sound power of panel i, ρ 0 represents the air density, σ i represents the acoustic radiation efficiency of plate i, S i represents the surface area of ​​plate i, represents the mean square velocity of plate i; The expression of the acoustic response is: in, represents the sound pressure at the observation point, and d represents the distance from the observation point p to the bridge.

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