A method for analyzing vibration and noise characteristics of a single-slit bridge expansion joint under vehicle excitation

Abstract

This invention provides a method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation. The method includes: S1 constructing a finite element model of the vehicle-slot-bridge coupled structure; S2 calculating the vibration response of the bridge expansion joint under vehicle excitation; S3 establishing an acoustic boundary element model and sound field points, and calculating the vibration and noise of the expansion joint when a vehicle passes through it based on acoustic-vibration coupling analysis, thus obtaining the expansion joint vibration and noise model; and S4 analyzing the sound contribution of three sound sources: the finite-length main beam, the bridge expansion joint, and the vehicle tire finite element model. This invention, by considering the nonlinearity of the contact between the vehicle tire and the expansion joint during vibration analysis and simultaneously considering the acoustic contributions of the vehicle tire and the main beam during acoustic analysis, can obtain more accurate sound source contributions, laying the foundation for vibration reduction and noise reduction design of bridge expansion joints. Compared with existing technologies, the accuracy of analyzing the vibration and noise characteristics of bridge expansion joints when vehicles pass through them is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of transportation technology, and more specifically to a method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation. Background Technology

[0002] Bridge expansion joints are crucial components for ensuring vehicle safety and comfort, accommodating bridge expansion and contraction caused by diurnal and seasonal temperature variations, bridge movement due to vehicle traffic, and earthquakes. To accommodate these deformations, expansion joints are typically installed at the beam ends to seal the gaps between adjacent spans. However, the discontinuities created by these expansion joints often result in significant impact forces from passing vehicles, leading to excessive noise radiation. With the rapid development of transportation systems, residents are increasingly complaining about the vibrations and noise generated when vehicles pass over bridge expansion joints. Furthermore, the noise generated by vehicles passing over expansion joints has become one of the main sources of noise from highway bridges, urgently requiring a solution. Therefore, it is essential to study the vibration characteristics and noise radiation mechanisms of expansion joints and explore potential control measures for the former.

[0003] Current research on vehicle-induced vibration and noise at bridge expansion joints only models the bridge expansion joints themselves, and vehicle loads are simplified. Based on these assumptions, these numerical models struggle to capture the highly nonlinear interaction between vehicle tires and the expansion joint, thus failing to consider the acoustic contributions of vehicle tires and the main beam in acoustic analysis. Furthermore, numerous studies have shown that tire noise dominates when vehicles are traveling at high speeds. Therefore, to comprehensively evaluate the vibration and noise characteristics of vehicles passing over bridge expansion joints and optimize the vibration and noise reduction design of bridge expansion joints, a method for analyzing the vibration and noise characteristics of single-slot bridge expansion joints under vehicle excitation is needed. Summary of the Invention

[0004] The purpose of this invention is to disclose a method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation, which solves the problems of low accuracy, insufficient consideration of sound sources, and difficulty in accurately analyzing the vibration and noise characteristics of vehicles passing through the bridge expansion joint in the existing technology.

[0005] To achieve the above objectives, this invention provides a method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation, comprising the following steps:

[0006] S1. Establish a vehicle-joint-bridge coupled structure finite element model based on the longitudinal section structure of the bridge expansion joint location, including the finite length main beam, bridge expansion joint and vehicle tire finite element model, and mesh the vehicle-joint-bridge coupled structure finite element model.

[0007] S2. Calculate the vibration response of the bridge expansion joint under vehicle excitation, specifically including the following sub-steps:

[0008] S21. Perform steady-state analysis by inflating the inner tube of the vehicle tire finite element model until deformation stops and a stable state is reached.

[0009] S22. Perform steady-state-transient analysis. Apply gravity effect to the vehicle tire finite element model to simulate the actual gravity conditions of the vehicle. Ensure that the outer tread layer of the vehicle tire finite element model is in full contact with the main beam of finite length. Under the combined action of gravity and contact force, the vehicle tire finite element model reaches a state of mechanical equilibrium.

[0010] S23. Perform transient analysis by applying translational and rotational velocities to the finite element model of the vehicle tires to simulate the actual situation of the vehicle passing through the bridge expansion joint. Obtain the vibration response of each node of the vehicle-joint-bridge coupled structure model and compare it with the acceleration data collected by the measured vibration acceleration sensor arranged on the bridge expansion joint in the time and frequency domains.

[0011] S3. Extract the surface mesh of the vehicle-joint-bridge coupled structure finite element model in step S1, establish the acoustic boundary element model and sound field points, set the acoustic boundary element model parameters, import the vibration response analysis results in step S2 as the boundary conditions of the acoustic boundary element model, calculate the vibration noise of the vehicle passing through the bridge expansion joint based on the acoustic-vibration coupling analysis, and obtain the expansion joint vibration noise model.

[0012] S4. Based on the expansion joint vibration noise model obtained in step S3, derive the field point sound pressure calculated by the acoustic boundary element model, calculate the 1 / 3 octave band sound pressure level, draw the sound pressure spatial distribution cloud map and analyze the noise law, and analyze the sound contribution of the three sound sources: the finite length main beam, the bridge expansion joint and the vehicle tire finite element model.

[0013] Preferably, in S1, the bridge expansion joint and the finite-length main beam are connected by a common node, and the vehicle tire finite element model is in surface-to-surface contact with the finite-length main beam and the bridge expansion joint, wherein the outer tread layer of the vehicle tire finite element model is set as a follower surface.

[0014] Preferably, in S1, the meshing process for the finite element model of the car-seam-bridge coupled structure is as follows:

[0015] S11. Determine the grid size of the bridge expansion joint and add a grid to it, and the grid size of the bridge expansion joint meets the requirement that the minimum wavelength contains at least six elements;

[0016] S12. Determine the mesh size of the vehicle tire finite element model and add meshes to it, and the mesh size of the vehicle tire finite element model is less than or equal to the mesh size of the bridge expansion joint.

[0017] S13. Determine the grid size of the finite-length main beam and add a grid to it, and ensure that the grid size of the finite-length main beam matches the grid size of the bridge expansion joint.

[0018] Preferably, in S21, an independent node is created at the center of the vehicle tire finite element model to represent the centroid, and is rigidly connected to the rim layer inside the vehicle tire finite element model. During the inflation stage, constraints are applied to the vehicle tire finite element model to constrain all degrees of freedom of the centroid, so that it does not move under the inflation load.

[0019] Preferably, in S22, before applying gravity to the finite element model of the vehicle tire, the vertical degree of freedom constraint at its center of mass is released, allowing it to move in the vertical direction.

[0020] The state switching process in steady-state-transient analysis is as follows:

[0021] S221. Steady-state analysis makes the tire model approach a state of mechanical equilibrium under the action of gravity;

[0022] S221. Switch to transient analysis. Add a mass damper of 10 Ns / m to the model to control it to reach equilibrium quickly within 0.5 s. Perform transient analysis calculations during this stage.

[0023] S223. Before the transient analysis calculation ends, set the mass damping to zero.

[0024] Preferably, the number of acceleration sensors on the bridge expansion joint is set to multiple, all of which are high-frequency acceleration sensors. The multiple acceleration sensors are evenly arranged at different positions in the actual test area of ​​the structure, and the multiple acceleration sensors are installed in different directions, both vertical and longitudinal.

[0025] Preferably, in S23, during transient analysis, the output time interval Δt for simulation calculation is determined based on the maximum frequency measured in the actual structure, and its calculation formula is as follows:

[0026] Δt=12f max

[0027] Among them, f max This represents the maximum frequency measured in the experiment.

[0028] The simulation vibration calculation results are made to correspond with the measured frequencies; the measured time-domain response is converted to the frequency domain through fast Fourier transform and verified with the numerical simulation results, and then the finite element model of the car-seam-bridge coupled structure is further adjusted.

[0029] Preferably, the comparison and verification between the simulated vibration calculation results and the measured results has the following characteristics:

[0030] a) If the simulated vibration calculation results and the measured results are in high agreement near the peak frequency, the acceleration level change trend is generally consistent across the entire analysis frequency band, and the acceleration level error at the peak frequency is <10%, then it indicates that the finite element model of the vehicle-seam-bridge coupled structure can accurately simulate the vibration of the vehicle passing through the expansion joint and can be used for subsequent noise analysis.

[0031] b) If there is at least one of the following: low agreement between the simulated vibration calculation results and the measured results near the peak frequency, large difference in the acceleration level change trend across the entire analysis frequency band, and acceleration level error at the peak frequency ≥10%, it indicates that the experimental results have a large error. In this case, the validity of the finite element model of the car-seam-bridge coupled structure needs to be re-examined.

[0032] Preferably, in S3, the surface mesh of the finite element model of the car-seam-bridge coupled structure is extracted as a rectangular mesh, and then the rectangular mesh is re-divided into triangular meshes while retaining the rectangular mesh. The rectangular mesh is used as planar sound field points, and the triangular mesh is used as the acoustic boundary element model.

[0033] A closed acoustic mesh is added to the outer rim layer of the vehicle tire finite element model.

[0034] Preferably, in S4, when analyzing the magnitude of the sound contribution of each sound source, based on the original vehicle-seam-bridge coupled acoustic boundary element model, acoustic models containing only these three sound sources are established by retaining only the acoustic meshes of the finite length main beam, bridge expansion joint, and vehicle tire finite element model respectively.

[0035] The method used to assess the sound contribution is as follows:

[0036] S41. By using fast Fourier transform, the acoustic models of the three sound sources—the finite-length main beam, the bridge expansion joint, and the vehicle tire finite element model—are obtained at the 1 / 3 octave band sound pressure level at the sound field point.

[0037] S42. Determine the dominant frequency range of each sound source based on the 1 / 3 octave band sound pressure level at the sound field point according to the acoustic model corresponding to the three sound sources;

[0038] S43. Compare the dominant frequency range of each sound source with the 1 / 3 octave band sound pressure level calculated at the sound field point by the corresponding car-seam-bridge coupled acoustic boundary element model to determine the sound contribution of the three sound sources.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] 1. A coupled system model of vehicle-expansion joint-bridge is constructed, and a refined finite element model of vehicle tires is established. The nonlinearity of the contact between vehicle tires and expansion joints is considered in the vibration analysis. The acoustic contribution of vehicle tires and main beams is considered in the acoustic analysis, which can obtain more accurate sound source contribution. This lays the foundation for the vibration reduction and noise reduction design of bridge expansion joints. Compared with the existing technology, the accuracy of the vibration and noise characteristics analysis of vehicles passing through bridge expansion joints is significantly improved.

[0041] 2. In vibration analysis, the real-time process of a vehicle passing through a bridge expansion joint is dynamically simulated through steady-state and transient analysis. The coupled model is adjusted with reference to the structural vibration response tested in the field, which improves the accuracy and reliability of the numerical simulation model.

[0042] 3. In acoustic analysis, an acoustic boundary element model is established based on the vehicle-joint-bridge coupled finite element model to simulate the noise characteristics of vehicle tires passing through bridge expansion joints. The sound contribution of the three sound sources—vehicle tires, main beam, and bridge expansion joints—is considered to make the noise calculation results more consistent with the measured data. Attached Figure Description

[0043] Figure 1 A flowchart illustrating the noise characteristic analysis method provided by this invention;

[0044] Figure 2 Finite element model diagram of the noise characteristic analysis method provided by this invention;

[0045] Figure 3 This is a schematic diagram of the measured-simulated acceleration level spectrum in the noise characteristic analysis method provided by the present invention.

[0046] Figure 4 A schematic diagram of the acoustic boundary element model and planar sound field points in the noise characteristic analysis method provided by this invention;

[0047] Figure 5 This is a schematic diagram of the measured-simulated sound pressure level spectrum in the noise characteristic analysis method provided by the present invention.

[0048] Figure 6 This is a schematic diagram of the sound source contribution in the noise characteristic analysis method provided by the present invention.

[0049] In the picture:

[0050] Finite-length main beam-1; Bridge expansion joint-2; Vehicle tire finite element model-3; External support surface-4;

[0051] Tread layer - 31; Belt layer - 32; Carcass layer - 33; Sidewall layer - 34; Rim layer - 35;

[0052] Center of mass -o. Detailed Implementation

[0053] The present invention will be described in detail below with reference to the embodiments shown in the accompanying drawings. It should be noted, however, that these embodiments are not intended to limit the present invention, and any equivalent transformation or substitution in terms of function, method or structure made by those of ordinary skill in the art based on these embodiments shall fall within the protection scope of the present invention.

[0054] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant accompanying drawings. The preferred embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the disclosure of the present invention more thorough and comprehensive.

[0055] Refer Figure 1 As shown, the present invention discloses a method for analyzing the vibration and noise characteristics of a single - slit bridge expansion joint under vehicle excitation, including the following steps:

[0056] S1. Establish a vehicle - joint - bridge coupled - structure finite - element model according to the longitudinal section structure of the position where the bridge expansion joint structure is located, including a finite - length main beam 1, a bridge expansion joint 2, and a vehicle - tire finite - element model 3. The bridge expansion joint 2 is connected to the finite - length main beam 1 by co - nodes, and the vehicle - tire finite - element model 3 is in surface - to - surface contact with the finite - length main beam 1 and the bridge expansion joint 2. The outer tread layer 31 of the vehicle - tire finite - element model 3 is set as the slave surface;

[0057] The number of acceleration sensors on the bridge expansion joint 2 is set to be multiple, and all are high - frequency acceleration sensors. The multiple acceleration sensors are evenly arranged at different positions in the actual measurement area of the structural field test, and the multiple acceleration sensors are installed in different vertical and longitudinal directions;

[0058] In the contact analysis between the vehicle - tire finite - element model 3 and the bridge expansion joint 2, a mesh convergence analysis must be carried out to ensure the accuracy of the analysis. The vehicle - joint - bridge coupled - structure finite - element model is meshed, and the process is as follows:

[0059] S11. Determine the mesh size of the bridge expansion joint 2 and add a mesh to it. The mesh size of the bridge expansion joint 2 meets the requirement that the minimum wavelength contains at least six elements to avoid truncation - frequency errors in subsequent noise analysis;

[0060] S12. Determine the mesh size of the vehicle tire finite element model 3 and add meshes to it. The mesh size of the vehicle tire finite element model 3 should be less than or equal to the mesh size of the bridge expansion joint 2. This will control the vibration response error of the bridge expansion joint 2 within 5%. Therefore, it is necessary to first determine the mesh size of the bridge expansion joint 2, and then further determine the final mesh size of the vehicle tire finite element model 3 based on the mesh size of the bridge expansion joint 2.

[0061] S13. Determine the grid size of the finite-length main beam 1 and add a grid to it, and the grid size of the finite-length main beam 1 matches the grid size of the bridge expansion joint 2;

[0062] S2. Calculate the vibration response of bridge expansion joint 2 under vehicle excitation, specifically including the following sub-steps:

[0063] S21. Perform steady-state analysis. Create an independent node at the center of the vehicle tire finite element model 3 to represent the centroid o, and rigidly connect it to the rim layer 35 inside the vehicle tire finite element model 3. Apply constraints to the vehicle tire finite element model 3 during the inflation stage to constrain all degrees of freedom of the centroid o so that it does not move under the inflation load.

[0064] Inflate the inner tube of the vehicle tire finite element model 3 until deformation stops and a stable state is reached. Depending on the vehicle type and load conditions, when applying inflation pressure to the inner tube of the vehicle tire finite element model 3, if the main body of the vehicle tire finite element model 3 is a passenger car, the tire pressure range is controlled between 0.2-0.25 MPa; if the main body of the vehicle tire finite element model 3 is a truck, the tire pressure range is controlled between 0.92-1.0 MPa.

[0065] S22. Perform steady-state-transient analysis. Before applying gravity to the finite element model 3 of the vehicle tire, release the vertical degree of freedom constraint at its center of mass o so that it can move in the vertical direction.

[0066] Gravity is applied to the top of the vehicle tire finite element model 3 to simulate the actual gravity conditions of the vehicle, so that the outer tread layer 31 of the vehicle tire finite element model 3 is in full contact with the main beam 1 of finite length. Under the combined action of gravity and contact force, the vehicle tire finite element model 3 reaches a state of mechanical equilibrium. Under this state, the displacement response of the vehicle tire finite element model 3 tends to be stable.

[0067] The state switching process in steady-state-transient analysis is as follows:

[0068] S221. Steady-state analysis makes the tire model approach a state of mechanical equilibrium under the action of gravity;

[0069] S221. Switch to transient analysis. Add a mass damper of 10 Ns / m to the model to control it to reach equilibrium quickly within 0.5 s. Perform transient analysis calculations during this stage to reduce calculation time.

[0070] S223. Before the transient analysis calculation is completed, the mass damping is set to zero to avoid affecting subsequent calculations.

[0071] S23. Perform transient analysis by applying translational and rotational velocities to the vehicle tire finite element model 3 to simulate the actual situation of the vehicle passing through the bridge expansion joint 2. Obtain the vibration response of each node in the vehicle-joint-bridge coupled structural model. Based on this, analyze and obtain the structural acceleration level spectrum results. Compare and verify the acceleration data collected by the measured vibration acceleration sensor arranged on the bridge expansion joint 2 in the time domain and frequency domain. The acceleration data collected by the measured vibration acceleration sensor is processed into the measured acceleration level spectrum results.

[0072] During transient analysis, the output time interval Δt for simulation calculation is determined based on the maximum frequency measured in the actual structure. The calculation formula is as follows:

[0073] Δt=12f max

[0074] Among them, f max This represents the maximum frequency measured in the experiment.

[0075] To ensure that the simulated vibration calculation results correspond to the measured frequencies, the measured time-domain response is converted to the frequency domain using a fast Fourier transform and verified against the numerical simulation results. The comparison and verification between the simulated vibration calculation results and the measured results have the following characteristics:

[0076] a) If the simulated vibration calculation results and the measured results are in high agreement near the peak frequency, the acceleration level change trend is generally consistent across the entire analysis frequency band, and the acceleration level error at the peak frequency is <10%, then it indicates that the finite element model of the vehicle-seam-bridge coupled structure can accurately simulate the vibration of the vehicle passing through the expansion joint and can be used for subsequent noise analysis.

[0077] b) If there is at least one of the following: low agreement between the simulated vibration calculation results and the measured results near the peak frequency, large difference in the acceleration level change trend across the entire analysis frequency band, and acceleration level error at the peak frequency ≥10%, it indicates that the experimental results have a large error. In this case, the validity of the finite element model of the car-seam-bridge coupled structure needs to be re-examined; and the finite element model of the car-seam-bridge coupled structure needs to be further adjusted.

[0078] S3. Extract the surface mesh of the finite element model of the car-seam-bridge coupled structure in step S1, establish the acoustic boundary element model and sound field points, extract the surface mesh of the car-seam-bridge coupled structure finite element model as a rectangular mesh, and then re-divide the rectangular mesh into triangular meshes while retaining the rectangular meshes. The rectangular meshes are used as planar sound field points, and the triangular meshes are used as the acoustic boundary element model.

[0079] The closed nature of the acoustic mesh is crucial for ensuring the accuracy of the acoustic model. A closed acoustic mesh prevents the unrestricted diffusion of sound waves at the model boundaries, which is particularly important for simulating the propagation of sound waves in a finite space. Adding a closed acoustic mesh to the outer rim layer 35 of the vehicle tire finite element model 3, and assigning it an acoustic impedance value of 416.5 kg / (m²·s), allows for accurate simulation of the propagation and reflection of sound waves within the model, while avoiding non-physical leakage of sound waves at the model boundaries, thus ensuring the accuracy and integrity of the acoustic model.

[0080] Set the acoustic boundary element model parameters, import the vibration response analysis results from step S2 as the boundary conditions of the acoustic boundary element model, calculate the vibration noise of the vehicle passing through the bridge expansion joint 2 based on acoustic-vibration coupling analysis, and obtain the expansion joint vibration noise model.

[0081] S4. Based on the expansion joint vibration noise model obtained in step S3, derive the field point sound pressure calculated by the acoustic boundary element model, calculate the 1 / 3 octave band sound pressure level, draw the sound pressure spatial distribution cloud map and analyze the noise law, and analyze the sound contribution of the three sound sources: finite length main beam 1, bridge expansion joint 2 and vehicle tire finite element model 3 respectively.

[0082] Based on the original vehicle-seam-bridge coupled acoustic boundary element model, acoustic models containing only these three sound sources are established by retaining only the acoustic meshes of the finite length main beam 1, bridge expansion joint 2, and vehicle tire finite element model 3.

[0083] The method used to assess the sound contribution is as follows:

[0084] S41. By using fast Fourier transform, the acoustic models of the three sound sources—the finite-length main beam 1, the bridge expansion joint 2, and the vehicle tire finite element model 3—are obtained at the 1 / 3 octave band sound pressure level at the sound field point.

[0085] S42. Determine the dominant frequency range of each sound source based on the 1 / 3 octave band sound pressure level at the sound field point according to the acoustic model corresponding to the three sound sources;

[0086] S43. Compare the dominant frequency range of each sound source with the 1 / 3 octave band sound pressure level calculated at the sound field point by the corresponding car-seam-bridge coupled acoustic boundary element model to determine the sound contribution of the three sound sources.

[0087] The method of this invention can be used to analyze the vibration and noise characteristics of vehicles passing through the expansion joint structure of bridges, obtain the noise impact of vehicles on the expansion joint structure of bridges, and provide a theoretical basis for reducing the vibration and noise of vehicles passing through the expansion joint structure of bridges.

[0088] The following example, using the expansion joint structure of a bridge on a highway, illustrates the method of this invention for analyzing the vibration and noise characteristics of bridge expansion joints under vehicle excitation:

[0089] 1) Constructing a finite element model of the coupled vehicle-seam-bridge structure

[0090] Reference Figure 2 As shown, a detailed vehicle-joint-bridge coupled model is established based on the actual design drawings. First, the geometric models corresponding to the finite-length main beam 1, the bridge expansion joint 2, and the vehicle tire finite element model 3 are established. The vehicle tire finite element model 3 includes the tread layer 31, belt layer 32, carcass layer 33, sidewall layer 34, and rim layer 35. The finite-length main beam 1 includes the box girder structure located on both sides of the bridge expansion joint 2. The bridge expansion joint 2 includes the anchorage zone concrete and the expansion joint side beam. In addition, external support surfaces 4 are added to the left and right ends of the vehicle-joint-bridge coupled model.

[0091] Except for the rim layer 35, which uses shell element Shell163, the rest of the above structure uses solid element Solid164. The element division is performed after the geometric model is established.

[0092] The axle load of the vehicle is simulated using the method of adding mass. The mass is directly applied to the node, and the node is connected to the tire center of mass o through a spring damping unit. The spring stiffness is set to k = 20 N / mm, the damping coefficient is set to c = 3 N s / mm, and the tire center of mass o is rigidly connected to the rim layer 35.

[0093] In terms of mesh generation, the element size needs to meet the requirement of 6 elements within the minimum wavelength. At the same time, the element size is gradually widened at the position away from the bridge expansion joint 2 to reduce the calculation time and improve efficiency while ensuring accuracy. The maximum mesh size of the bridge expansion joint 2 is set to 20mm, the maximum frequency of noise analysis is 2800Hz, the maximum mesh size of the finite length main beam 1 is set to 80mm, and the maximum mesh size of the vehicle tire finite element model 3 is set to 10mm through mesh convergence analysis.

[0094] 2) Calculate the vibration response of bridge expansion joints under vehicle excitation.

[0095] It is divided into 3 stages:

[0096] 2.1) In stage 1 (time is 0-1s), steady-state analysis is adopted. The centroid o of the vehicle tire finite element model 3 is fixed, and inflation pressure is applied to the inner surface of the vehicle tire finite element model 3. The pressure increases from 0 to 220kPa within 0-0.5s, and then the pressure remains constant within 0.5-1s.

[0097] 2.2) Stage 2 (time period 1-3s): Steady-state and transient analysis are adopted. Steady-state analysis is performed within 1-2s, and transient analysis is performed within 2-3s. During the analysis, the vertical degree of freedom at the centroid o of the vehicle tire finite element model 3 is released, allowing it to move freely along the vertical direction. At the same time, the surface-to-surface contact between the vehicle tire finite element model 3 and the finite-length main beam 1 is set, and the contact algorithm is set to a penalty function. The dynamic and static friction coefficients are set to 0.2 and 0.3, respectively.

[0098] The finite element model 3 of the vehicle tire is subjected to its own gravity (the magnitude of gravity increases from 0 to 9.8 m / s² within 1-1.5 s). 2 (Then kept constant) it makes further full contact with the finite length main beam 1, and makes the vehicle tire finite element model 3 obtain initial deformation;

[0099] Then, within 2-3 seconds, the transient analysis is initiated, and within 2-2.6 seconds, a mass damping of 10 N s / mm is added to the finite element model 3 of the vehicle tire, so that the displacement response of the finite element model 3 of the vehicle tire tends to stabilize and reach a state of mechanical equilibrium.

[0100] 2.3) Stage 3 (time period 3-3.3s): Transient analysis is used to release the rotational and translational degrees of freedom at the center of mass o of the finite element model 3 of the vehicle tire, allowing it to move longitudinally along the main beam 1 of finite length and rotate around the central axis. At the same time, the translational velocity and rotational angular velocity corresponding to the vehicle tire are given. Within 3-3.1s, both the translational velocity and rotational velocity increase from 0 to the target velocity and then remain unchanged. The vibration response of the measuring point when passing through the bridge expansion joint 2 is recorded, and the analysis results of the coupled model are saved.

[0101] A vertical acceleration sensor was installed on the bridge expansion joint 2 structure. The measured time-domain response was converted to the frequency domain using a fast Fourier transform, and compared with the numerical simulation results at various frequency points. Figure 3 The simulated-measured acceleration spectrum is shown. If the simulation and measured results agree well near the peak frequency and are generally consistent, it indicates that the frequency domain coupling model accurately simulates the vibration of the train during operation; if the agreement is poor, the validity of the finite element model needs to be re-examined.

[0102] 3) Establish an acoustic boundary element model

[0103] The surface meshes of the vehicle tire finite element model 3, the finite-length main beam 1, and the bridge expansion joint 2 are extracted as acoustic boundary element meshes. The vibration displacements of each node in the obtained vehicle-joint-bridge coupled model are used as boundary conditions and input into the acoustic boundary element model to calculate the vibration noise of the vehicle tire finite element model 3 when passing through the bridge expansion joint 2. Field points are set along the outward normal direction according to the coordinates of the actual measurement points. The field point plane is 12m × 12m, the spacing between each field point is 1.5m, and the center of the field point plane is located at the middle of the expansion joint; (Refer to...) Figure 4 The acoustic boundary element model and schematic diagram of the planar sound field points are shown.

[0104] 4) Calculation of vibration noise from expansion joints and analysis of sound source contribution

[0105] Based on the expansion joint vibration noise model obtained in step S3, the sound pressure at the field point calculated by the acoustic boundary element model is derived. The 1 / 3 octave band sound pressure level is calculated, and one octave band is divided into three adjacent 1 / 3 octave bands. The sound domain is divided into 30 1 / 3 octave bands, and the sound pressure level spectrum diagrams of the measuring point and the planar field point are plotted. (Refer to...) Figure 5 The simulated-measured sound pressure level spectrum comparison diagram shown indicates that if the simulation and measured results show a high degree of agreement near the peak frequency and are generally consistent, it means that the acoustic boundary element model can accurately simulate the vibration and noise situation when a vehicle passes through the bridge expansion joint 2. (Refer to...) Figure 6 The sound pressure spectrum diagrams of the three sound sources at various field points are shown. By drawing sound pressure spatial distribution cloud maps and analyzing noise propagation patterns, the acoustic contribution of the three sound sources is evaluated.

[0106] Based on the calculation results, the 1 / 3 octave band sound pressure level of each sound source at each sound field point was obtained. Near-field and far-field points were selected for comparative analysis. Taking the near-field point as an example, the acoustic contribution of the main beam vibration noise within 200Hz is comparable to that of tire noise; however, the acoustic contribution of the expansion joint vibration noise across the entire frequency band (0-1000Hz) is much smaller than that of tire noise and main beam vibration noise, indicating that the acoustic contribution of the structural vibration noise of bridge expansion joint 2 is negligible.

[0107] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation, characterized in that: Includes the following steps: S1. Based on the longitudinal section structure of the bridge expansion joint (2), establish a vehicle-joint-bridge coupled structure finite element model, including a finite length main beam (1), a bridge expansion joint (2), and a vehicle tire finite element model (3). Mesh the vehicle-joint-bridge coupled structure finite element model. S2. Calculate the vibration response of the bridge expansion joint (2) under vehicle excitation, specifically including the following sub-steps: S21. Perform steady-state analysis by inflating the inner tube of the vehicle tire finite element model (3) until deformation stops and a stable state is reached. S22. Perform steady-state-transient analysis. Apply gravity effect to the vehicle tire finite element model (3) to simulate the actual gravity conditions of the vehicle. Make the outer tread layer (31) of the vehicle tire finite element model (3) fully contact with the main beam (1) of finite length. Under the combined action of gravity and contact force, the vehicle tire finite element model (3) reaches the mechanical equilibrium state. S23. Perform transient analysis, apply translational and rotational velocities to the vehicle tire finite element model (3), simulate the actual situation of the vehicle passing through the bridge expansion joint (2), obtain the vibration response of each node of the vehicle-joint-bridge coupled structure model, and compare and verify the acceleration data collected by the measured vibration acceleration sensor arranged on the bridge expansion joint (2) in the time domain and frequency domain. S3. Extract the surface mesh of the vehicle-seam-bridge coupled structure finite element model in step S1, establish the acoustic boundary element model and sound field points, set the acoustic boundary element model parameters, import the analysis results of vibration response in step S2 as the boundary conditions of the acoustic boundary element model, calculate the vibration noise of the vehicle passing through the bridge expansion joint (2) based on the acoustic-vibration coupling analysis, and obtain the expansion joint vibration noise model. S4. Based on the expansion joint vibration noise model obtained in step S3, derive the field point sound pressure calculated by the acoustic boundary element model, calculate the 1 / 3 octave band sound pressure level, draw the sound pressure spatial distribution cloud map and analyze the noise law, and analyze the sound contribution of the three sound sources: the finite length main beam (1), the bridge expansion joint (2) and the vehicle tire finite element model (3).

2. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S1, the bridge expansion joint (2) and the finite length main beam (1) are connected by a common node. The vehicle tire finite element model (3) is in surface contact with the finite length main beam (1) and the bridge expansion joint (2). The outer tread layer (31) of the vehicle tire finite element model (3) is set as a slave surface.

3. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S1, the meshing process for the finite element model of the car-seam-bridge coupled structure is as follows: S11. Determine the grid size of the bridge expansion joint (2) and add a grid to it, and the grid size of the bridge expansion joint (2) meets the requirement that the minimum wavelength contains at least six elements; S12. Determine the mesh size of the vehicle tire finite element model (3) and add a mesh to it, and the mesh size of the vehicle tire finite element model (3) is ≤ the mesh size of the bridge expansion joint (2); S13. Determine the grid size of the finite length main beam (1) and add a grid to it, and the grid size of the finite length main beam (1) matches the grid size of the bridge expansion joint (2).

4. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S21, an independent node is created at the center of the vehicle tire finite element model (3) to represent the centroid (o), and is rigidly connected to the rim layer (35) inside the vehicle tire finite element model (3). During the inflation stage, constraints are applied to the vehicle tire finite element model (3) to constrain all degrees of freedom of the centroid (o) so that it does not move under the inflation load.

5. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S22, before applying gravity to the finite element model (3) of the vehicle tire, the vertical degree of freedom constraint at its center of mass (o) is released so that it can move in the vertical direction; The state switching process in steady-state-transient analysis is as follows: S221. Steady-state analysis makes the tire model approach a state of mechanical equilibrium under the action of gravity; S221. Switch to transient analysis. Add a mass damper of 10 Ns / m to the model to control it to reach equilibrium quickly within 0.5 s. Perform transient analysis calculations during this stage. S223. Before the transient analysis calculation ends, set the mass damping to zero.

6. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: The number of acceleration sensors on the bridge expansion joint (2) is set to multiple, all of which are high-frequency acceleration sensors. The multiple acceleration sensors are evenly arranged in different positions in the actual test area of ​​the structure, and the multiple acceleration sensors are installed in different directions, vertical and longitudinal.

7. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 6, characterized in that: In S23, during transient analysis, the output time interval Δt for simulation calculation is determined based on the maximum frequency measured in the actual structure. The calculation formula is as follows: Δt=12f max Among them, f max This represents the maximum frequency measured in the experiment. The simulation vibration calculation results are made to correspond with the measured frequencies; the measured time-domain response is converted to the frequency domain through fast Fourier transform and verified with the numerical simulation results, and then the finite element model of the car-seam-bridge coupled structure is further adjusted.

8. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 7, characterized in that: The simulation vibration calculation results were compared and verified with the measured results, and the following conditions were observed: a) If the simulated vibration calculation results and the measured results are in high agreement near the peak frequency, the acceleration level change trend is generally consistent across the entire analysis frequency band, and the acceleration level error at the peak frequency is <10%, then it indicates that the finite element model of the vehicle-seam-bridge coupled structure can accurately simulate the vibration of the vehicle passing through the expansion joint and can be used for subsequent noise analysis. b) If there is at least one of the following: low agreement between the simulated vibration calculation results and the measured results near the peak frequency, large difference in the acceleration level change trend across the entire analysis frequency band, and acceleration level error at the peak frequency ≥10%, it indicates that the experimental results have a large error. In this case, the validity of the finite element model of the car-seam-bridge coupled structure needs to be re-examined.

9. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S3, the surface mesh of the car-seam-bridge coupled structure finite element model is extracted as a rectangular mesh, and then the rectangular mesh is re-divided into triangular meshes while retaining the rectangular mesh. The rectangular mesh is used as the planar sound field points, and the triangular mesh is used as the acoustic boundary element model. A closed acoustic mesh is added to the outer rim layer (35) of the vehicle tire finite element model (3).

10. The method for analyzing the vibration and noise characteristics of a single-slot bridge expansion joint under vehicle excitation as described in claim 1, characterized in that: In S4, when analyzing the magnitude of the sound contribution of each sound source, based on the original vehicle-seam-bridge coupled acoustic boundary element model, acoustic models containing only these three sound sources are established by retaining only the acoustic meshes of the finite length main beam (1), bridge expansion joint (2), and vehicle tire finite element model (3). The method used to assess the sound contribution is as follows: S41. By using fast Fourier transform, the acoustic models of the three sound sources—the finite-length main beam (1), the bridge expansion joint (2), and the vehicle tire finite element model (3)—are obtained at the 1 / 3 octave band sound pressure level at the sound field point. S42. Determine the dominant frequency range of each sound source based on the 1 / 3 octave band sound pressure level at the sound field point according to the acoustic model corresponding to the three sound sources; S43. Compare the dominant frequency range of each sound source with the 1 / 3 octave band sound pressure level calculated at the sound field point by the corresponding car-seam-bridge coupled acoustic boundary element model to determine the sound contribution of the three sound sources.

Images