A method for analyzing vibration and noise of a combined box girder bridge coupled with an axle

Abstract

The application discloses a kind of combined box girder bridge vibration noise analysis methods of axle coupling effect, belong to bridge engineering technical field.S1, the train-track-bridge coupling vibration model of high-speed railway steel-concrete combined box girder bridge is established, and based on Matlab language and Ansys finite element software, train-track-bridge coupling vibration simulation analysis program is prepared;S2, the low-frequency noise prediction model of high-speed railway steel-concrete combined box girder bridge is established, and the low-frequency noise radiation law of bridge structure is obtained;S3, the high-frequency noise prediction model of high-speed railway steel-concrete combined box girder bridge is established, and the numerical simulation of bridge structure's high-frequency radiation noise is carried out;S4, the influence parameter of high-speed railway steel-concrete combined box girder bridge vibration noise is analyzed in combination with the model established in steps S1-S3.This technical scheme is used to analyze the vibration and noise of steel-concrete combined beam applied in the field of railway bridge.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge engineering, and particularly relates to a vibration and noise analysis method for a combined box girder bridge under the coupling action of a vehicle and a bridge. BACKGROUND

[0002] The shear connector connects the steel beam and the concrete bridge deck panel to form a whole and bear force together, and this structure is called a steel-concrete composite beam. The component bears force reasonably, scientifically and economically, so that the high tensile strength of steel and the high compressive strength of concrete are fully utilized.

[0003] However, in the field of railway bridges, the construction and application of steel-concrete composite beams are still relatively small, but this bridge type is widely used in the field of highways, and the technology is mature. Therefore, it is necessary to study and analyze the construction and application of steel-concrete composite beams in the field of railway bridges. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a vibration and noise analysis method for a combined box girder bridge under the coupling action of a vehicle and a bridge, which can analyze the vibration and noise of a steel-concrete composite beam applied to the field of railway bridges.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0006] The present application provides a vibration and noise analysis method for a combined box girder bridge under the coupling action of a vehicle and a bridge, which comprises the following steps:

[0007] S1, establishing a train-track-bridge coupling vibration model of a high-speed railway steel-concrete composite box girder bridge, and based on the Matlab language and the Ansys finite element software, programming a coupling vibration simulation analysis program of the train-track-bridge;

[0008] S2, establishing a low-frequency noise prediction model of the high-speed railway steel-concrete composite box girder bridge, numerically simulating the low-frequency radiation noise of the bridge structure, and obtaining the low-frequency noise radiation law of the bridge structure;

[0009] S3, establishing a medium-high frequency noise prediction model of the high-speed railway steel-concrete composite box girder bridge, numerically simulating the medium-high frequency radiation noise of the bridge structure, and obtaining the medium-high frequency noise radiation law of the bridge structure;

[0010] S4, combining the models established in steps S1-S3, analyzing the influence parameters of the vibration and noise of the high-speed railway steel-concrete composite box girder bridge, and obtaining the analysis results.

[0011] In the step S1, the following steps are specifically provided:

[0012] S11, a vehicle dynamics model is established, the train model includes 8 vehicle consist, each vehicle includes a car body, two bogies and 4 wheelsets, and each car includes 10 degrees of freedom;

[0013] S12, a track dynamics model is established, the track model includes self-compacting concrete layer, concrete track slab, concrete base slab, steel spring fastener, steel rail component;

[0014] S13, a bridge finite element model is established, the bridge model is established by Apdl finite element software, and the dynamic behavior of the bridge structure is numerically simulated;

[0015] S14, a wheel-rail interaction model is established, and the vertical wheel-rail force is calculated through the Hertz nonlinear contact model;

[0016] S15, the track irregularity is taken as the excitation source, and the wavelength range of the track irregularity is determined as 0.04-85m;

[0017] S16, according to the bridge, vehicle and track models established in steps S11-S13, the dynamic equation of the train-track-bridge coupling large system is obtained;

[0018] S17, the train-track-bridge coupling dynamic numerical simulation analysis program model is compiled by computer simulation software and finite element software, and the solution is solved, and the results of the program running are verified;

[0019] In step S17, the dynamic equation of the train-track-bridge coupling large system is:

[0020]

[0021] In the formula, C, K and M are respectively the damping, stiffness and mass matrix of the system; Z is the generalized displacement vector of the system; the subscripts B, V and R respectively represent the bridge system, the vehicle system and the track system; F is the external load vector of the system.

[0022] Further, in step S17, the dynamic simulation calculation of the train-track-bridge system is carried out by using 50 times of asynchronous length loading rate, that is, the train and track system simulation analysis step length is taken as 0.1ms, and the bridge finite element transient response analysis step length is taken as 5ms.

[0023] Further, the motion equation of a single vehicle is:

[0024]

[0025] In the formula, M V is the mass matrix of a single vehicle;

[0026]

[0027] K V is the stiffness matrix of the single-vehicle;

[0028]

[0029] Z V is the vertical displacement column matrix of the single-vehicle;

[0030]

[0031] F V is the vertical wheel-rail force column matrix of the single-vehicle;

[0032]

[0033] Since the damping matrix has a similar content form as the stiffness matrix, only the stiffness coefficient k in the above equation is replaced by the damping coefficient c.

[0034] Further, the motion equation of the track dynamics model is:

[0035]

[0036] M R is the total mass matrix;

[0037]

[0038] K R is the total stiffness matrix;

[0039]

[0040] Z R is the total displacement matrix of the track;

[0041]

[0042] C R is the damping matrix of the track;

[0043]

[0044] wherein, , is the damping coefficient, is the damping ratio, , are the natural circular frequencies, respectively.

[0045] Further, when most of the track irregularities, the wheel-rail force F W is expressed as:

[0046] .

[0047] Further, the step S2 specifically comprises:

[0048] (1) establish the wave equation in the ideal fluid under the condition of medium static, uniform and small amplitude of sound wave;

[0049] (2) establish the Helmholtz equation for calculating the noise radiation of external field in the frequency domain, and obtain the acoustic boundary condition and the Green function expression of three-dimensional free sound field;

[0050] (3) use LMS Virtual Lab Acoustics software to obtain the simulation method of low-frequency noise radiation model under the excitation of train load.

[0051] Further, the step S3 specifically comprises:

[0052] (1) establish the theoretical formula for simulating the medium-high frequency noise of the bridge structure using the SEA method, and obtain the definition of plate sound radiation efficiency, modal density and loss factor;

[0053] (2) through Fourier transform and octave processing, the wheel-rail force and the fastener force are analyzed in detail, and the method for determining the external excitation force of the bridge deck is obtained;

[0054] (3) establish the specific steps for numerical simulation of medium-high frequency noise radiation in the software, and analyze the sound radiation contribution of different plates to different field points.

[0055] Further, the influence parameters of the vibration and noise of the high-speed railway steel-concrete composite box girder bridge in the step S4 include the web thickness, the bottom plate thickness, the vehicle speed, the number of lanes and the bottom plate material.

[0056] The beneficial effects of the present application are:

[0057] The present technical solution analyzes the vibration and noise reduction of the steel-concrete composite beam, and it is found that the influence of train speed on the radiation enhancement of medium-high frequency noise is more obvious, which is caused by the increase of train speed leading to the increase of fastener force peak value. On this basis, the influence of the change of bottom plate concrete thickness on the vibration and noise radiation of the bridge structure is analyzed, and it is found that when the bottom plate concrete thickness is 50mm, the vibration and noise reduction effect of the structure is most obvious, but if the thickness continues to increase on the basis of 50mm, the effect of vibration and noise reduction is not obvious. Therefore, the method for analyzing the vibration and noise of the steel-concrete composite bridge applied to the field of railway bridge in the present technical solution has important significance for the research and design of vibration and noise reduction of the steel-concrete composite bridge.

[0058] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0059] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0060] Figure 1 This is a schematic diagram of the vertical vehicle model in this invention;

[0061] Figure 2 This is a schematic diagram of the parameters of a single vehicle section in this invention;

[0062] Figure 3 This is a schematic diagram of the track structure in this invention;

[0063] Figure 4 This is a schematic diagram of the orbital dynamics model in this invention;

[0064] Figure 5 This is a schematic diagram of the rail stress analysis model in this invention;

[0065] Figure 6 A schematic diagram of the orbital dynamics parameters in this invention;

[0066] Figure 7 This is a schematic diagram of the parameters of track irregularity in this invention;

[0067] Figure 8 This is a schematic diagram of the dynamic model of the train-track-bridge in this invention;

[0068] Figure 9 This is a schematic diagram illustrating the asynchronous long loading efficiency in this invention;

[0069] Figures 10-12 This is a schematic diagram of the time history of the vertical displacement of the steel rails on the bridge in this invention;

[0070] Figure 13 and Figure 14 This is a time history diagram of the vertical acceleration of the rail in this invention;

[0071] Figures 15-17 This is a time history diagram of the dynamic structural response of the bridge in this invention;

[0072] Figures 18-20 This is a schematic diagram of the dynamic response spectrum of the bridge structure in this invention;

[0073] Figure 21 This is a schematic diagram of the mapping rules in this invention;

[0074] Figure 22 The schematic diagram of the boundary element modeling process in the application;

[0075] Figure 23 The schematic diagram of the acoustic field point in the application;

[0076] Figure 24 The schematic diagram of the ground reflected sound analysis in the application;

[0077] Figures 25-27 The schematic diagram of the field point transient acoustic simulation result in the application;

[0078] Figure 28 And Figure 29 The schematic diagram of the field point octave acoustic simulation result in the application;

[0079] Figures 30-33 The schematic diagram of the plate noise contribution result in the application;

[0080] Figures 34-36 The schematic diagram of the plate noise contribution frequency domain result in the application;

[0081] Figure 37 The schematic diagram of the low-frequency noise total sound pressure level field point in the application;

[0082] Figure 38 And Figure 39 The schematic diagram of the high-frequency bridge plate contribution result in the C field point in the application;

[0083] Figure 40 And Figure 41 The schematic diagram of the high-frequency bridge plate contribution result in the A field point in the application;

[0084] Figure 42 And Figure 43 The schematic diagram of the high-frequency bridge plate contribution result in the B field point in the application;

[0085] Figure 44 And Figure 45 The schematic diagram of the train speed influence on the bridge deck plate deflection result in the application;

[0086] Figure 46 The schematic diagram of the deflection peak under different train speeds in the application;

[0087] Figure 47 And Figure 48 The schematic diagram of the train speed influence on the bridge deck plate and speed result in the application;

[0088] Figure 49 The schematic diagram of the bridge deck plate acceleration index under different train speeds in the application;

[0089] Figure 50 AndFigure 51 This is a schematic diagram illustrating the effect of train speed on web acceleration in this invention;

[0090] Figure 52 This is a schematic diagram of the web acceleration index at different train speeds in this invention;

[0091] Figure 53 and Figure 54 This is a schematic diagram illustrating the effect of train speed on the acceleration of the base plate in this invention;

[0092] Figure 55 This is a schematic diagram of the acceleration index data of the base plate at different train speeds in this invention;

[0093] Figure 56 This is a schematic diagram illustrating the effect of train speed on fastener force in this invention;

[0094] Figures 57-59 This is a schematic diagram showing the effect of train speed on noise radiation at various points in this invention;

[0095] Figure 60 and Figure 61 This is a schematic diagram showing the effect of the thickness of the concrete base plate on the deflection of the base plate in this invention;

[0096] Figure 62 and Figure 63 This is a schematic diagram showing the effect of the thickness of the bottom slab concrete on the vertical vibration velocity of the bottom slab in this invention.

[0097] Figure 64 This is a schematic diagram of the fastener force spectrum under different base plate concrete thicknesses in this invention;

[0098] Figure 65 and Figure 66 This is a schematic diagram showing the effect of the thickness of the bottom slab concrete on the noise radiation at point A in this invention;

[0099] Figure 67 and Figure 68 This is a schematic diagram showing the effect of the thickness of the bottom slab concrete on the noise radiation at point B in this invention;

[0100] Figure 69 and Figure 70 This is a schematic diagram showing the effect of the thickness of the bottom slab concrete on the noise radiation at point C in this invention;

[0101] Figure 71 This is a flowchart illustrating the overall technical approach of this invention. Detailed Implementation

[0102] This invention provides a vibration and noise analysis method for a combined box girder bridge with vehicle-bridge coupling effect, which specifically includes the following steps:

[0103] The technical route analysis is shown in Fig. Figure 71 .

[0104] Train-track-bridge coupling vibration simulation model

[0105] Vehicle dynamics model

[0106] The vertical model of a single vehicle of a high-speed railway train analyzed in the present scheme is shown in Fig. Figure 1 The meanings of the parameters of the vehicle model in the figure are as follows: , Kx, Ky are the spring stiffness of the primary and secondary suspension systems in the x direction, z , , Cz, Cy are the damping coefficients of the primary and secondary suspension systems in the z direction; , Lx, Ly are the half of the longitudinal distance of the primary and secondary suspension systems. , and are the vertical motion of the wheelset, the vertical motion of the bogie and the vertical motion of the car body, and are the nodding vibration of the car body and the bogie, respectively.

[0107] When only the vertical analysis of the vibration of the vehicle is performed, the moment of inertia only needs to consider the moment of inertia . The vertical static equilibrium position of the vehicle is taken as the initial position to eliminate the influence of gravity. The motion equation of the single vehicle is:

[0108] (1-1)

[0109] In the formula, is the mass matrix of the single vehicle;

[0110] (1-2)

[0111] is the stiffness matrix of the single vehicle;

[0112] (1-3)

[0113] is the vertical displacement column matrix of the single vehicle;

[0114] (1-4)

[0115] is the vertical wheel-rail force column matrix of the single vehicle.

[0116] (1-5)

[0117] Damping matrix With stiffness matrix Having a similar form, thus, only need to replace the stiffness coefficient k in with damping coefficient c.

[0118] In this scheme, a certain type of EMU train as the research object, part of the parameters of a single vehicle can be seen in Figure 2 .

[0119] Track dynamics model

[0120] In this scheme, the dynamic characteristics of a certain type of high-speed railway slab track are studied. The track structure mainly includes self-compacting concrete layer, concrete track slab, concrete base plate, steel spring fastener and steel rail components, and its structural diagram is shown in Figure 3 .

[0121] When only vertical vibration problem is studied, the rail uses the idea of finite element, codes are written in commercial mathematical software Matlab, the fastener is simplified as vertical stiffness spring and damping spring, and each concrete component in the track structure is simulated by solid45 solid element in finite element software Ansys. The vertical model of track dynamics is shown in Figure 4 , in which, is the vertical stiffness of the fastener, is the vertical damping of the fastener.

[0122] In the track model established in this scheme, the rail is assumed to be 60kg / m standard rail, and the rail is regarded as an infinite length Euler beam supported by continuous elastic discrete point support foundation. In the process of solving practical problems, the rail should be regarded as a finite length simply supported beam. According to the existing technology, when the distance between the simply supported ends of the rail is greater than or equal to 30m, the rail can be regarded as infinite length.

[0123] Figure 5 , as shown in is the force exerted by the wheelset on the rail, which is referred to as wheel-rail force. The expression will be given in the following text. The difference between the wheel-rail force in the schematic diagram of this section and the wheel-rail force given later is that the latter is only the force between the wheel on one side of the wheelset and the rail.

[0124] is the force exerted by the fastener on the rail:

[0125] (1-6)

[0126] In the formula, , are the displacements of the rail and track slab at the fastener position , respectively.

[0127] (1-7)

[0128] where, i is the serial number of the fastener, is the spacing of the fastener, taken as 0.65m in this paper

[0129] Motion coordinates of each wheelset over time In turn:

[0130] (1-8)

[0131] where, is the initial time, the fixed coordinates of the fourth wheelset; t is the motion time variable; v is the train travel speed.

[0132] The motion equation of the rail dynamic model is:

[0133] (1-9)

[0134] The overall mass matrix The elements are as follows:

[0135] (1-10)

[0136] The overall stiffness matrix The elements are as follows:

[0137] (1-11)

[0138] The damping matrix of the rail Determined according to the proportional damping method, as shown in the formula

[0139] (1-12)

[0140] where, , is the damping coefficient, is the damping ratio, , are the natural circular frequencies, respectively. The overall displacement matrix of the rail The elements are as follows:

[0141] (1-13)

[0142] The elements of are related to the position of the external force. Assuming that the external force is between the second unit, i.e. between nodes 2 and 3, then as follows

[0143] (1-14)

[0144] The part parameters of the track dynamics structure used in the present scheme can be referred to Figure 6 .

[0145] Bridge finite element model

[0146] In the present scheme, the high-speed railway steel-concrete composite beam with a speed of 350 km / h and a span of 48 m is selected as the specific research object, and its dynamics is analyzed. The cross section of the bridge adopts a single-box single-chamber composite section, which is composed of a concrete bridge deck and a channel steel box. The steel beam adopts a single-box single-chamber channel section enclosed by a bottom plate, an upper flange top plate and a web. The bottom plate and the web are provided with longitudinal stiffening ribs. The height of the bridge is 4.005 m, and the span of the bridge is 48.6 m. The concrete bridge deck part: the top plate is 12.6 m wide, the concrete at the flange of the top plate is 0.22 m thick, the concrete at the bolted connection is 0.55 m thick, and the concrete at the midspan is 0.3 m thick. The channel steel box beam part: the upper flange is 1 m wide and 0.032 m thick; the web is 3.45 m high and 0.016 m thick; the bottom plate is 6 m wide and 0.02 m thick; vertical stiffening ribs are arranged on the web between adjacent transverse diaphragms at an interval of 1 m, and the rib plate is 0.02 m thick; the basic interval of the transverse diaphragm is 4 m, and the thickness is 0.02 m. The steel of the whole bridge adopts Q370qE steel, and the concrete selects C55 concrete. In the present scheme, fine modeling is needed for the response of the medium-high frequency vibration noise. The steel structure part is established by shell element Shell181, and the steel structure part should include transverse diaphragms, longitudinal stiffening ribs, vertical stiffening, etc. The concrete bridge deck is established by solid element Solid45.

[0147] After the geometric model is meshed, the meshing method of the finite element mesh affects the calculation accuracy and calculation efficiency of the model. In the present scheme, the factors considered in the determination of the element length of the established finite element model are:

[0148] The maximum element size of the bridge model is less than or equal to one-sixth of the wavelength of the vibration. The bridge model is mainly in bending, and the bending wave speed in the flat plate structure can be expressed as:

[0149] (1-15)

[0150] wherein, the Poisson's ratio of the material used by the structure; E represents the elastic modulus of the structure; ω represents the upper limit of the circular frequency of the problem analyzed; is the density of the material used; h represents the thickness of the structure plate; and the wavelength and the wave speed satisfy the following formula:

[0151] (1-16)

[0152] The maximum element size of the finite element model , satisfies:

[0153] (1-17)

[0154] In the subsequent text, the acoustic boundary element grid is established based on the bridge structure finite element grid established in this section to perform acoustic analysis. Under the condition of meeting certain calculation accuracy, the maximum grid size of the acoustic grid should be less than 1 / 6 of the minimum analysis wavelength length.

[0155] (1-18)

[0156] In the formula, c represents the sound speed, represents the highest frequency of calculation.

[0157] Too dense grid will cause too long model calculation time, produce larger memory occupation result file, waste too much computing resources. According to the above influencing factors, referring to the related prior art, the element length is taken as 0.25m.

[0158] The stiffness and mass of the bridge itself will affect the natural frequency, and the natural frequency is independent of the motion state of the structure. In the design process of railway bridge, the index for evaluating the dynamic performance of the bridge is the vertical natural frequency of the bridge. According to the provisions of the "Code for Design of High-speed Railway", the span of the bridge model built in this section is 48m, according to the specification, the minimum value of the first-order frequency of the simply supported beam with a span of 48m is 2.38Hz, and the first-order frequency in this scheme is 3.2Hz, which meets the specification requirements. In order to better simulate the medium and high frequency response of the structure, the complete integration method is used in Ansys to solve the transient dynamic response of the bridge structure. The bridge transient analysis in Ansys is essentially solving the dynamic equation, as shown in the following formula:

[0159] (1-19)

[0160] Rayleigh damping is used in this scheme to describe the damping size of the structure, and the damping matrix of the bridge is determined according to the proportional damping method, as shown in the following formula:

[0161] (1-20)

[0162] In the formula, , is the proportional damping coefficient; is the damping ratio, which is usually taken as 0.04 for steel-concrete composite structures.

[0163] The force exerted on the bridge structure by the fasteners is the force they provide. The elements are as follows:

[0164] (1-21)

[0165] In the formula, n is the number of fasteners on the bridge. The calculation formula has been given above.

[0166] Wheel-rail interaction model: The model established in this scheme is a vertical model, and the wheel-rail relationship only involves solving for the wheel-rail normal force. This scheme uses the Hertz nonlinear contact model to address the vertical wheel-rail force. Perform the calculation.

[0167] (1-22)

[0168] In the formula: G The contact constant between the wheel and the rail, It represents the normal elastic compression between the wheel and rail contact points.

[0169] For wheels commonly used in high-speed railway passenger cars:

[0170] (1-23)

[0171] In the formula, Let the radius of the wheel's rolling circle be (m). In this paper, we take... .

[0172] Considering only vertical vibration, the wheel-rail normal elastic compression This can be considered as the static compression of the wheel caused by the average static wheel weight S. Vertical displacement of wheelset Vertical displacement of the rail The difference is the superposition of the two parts, therefore It can be represented as:

[0173] (1-24)

[0174] In the formula, the static compression of the wheel is:

[0175] (1-25)

[0176] In the formula, the average static wheel weight (the wheel on one side of the wheelset) is calculated as follows:

[0177] (1-26)

[0178] In the formula, g is the acceleration due to gravity.

[0179] When , the wheel-rail force , indicating the occurrence of derailment phenomenon.

[0180] As Figure 7 shown, when the track irregularity exists in the wheel-rail contact interface, the expression of the wheel-rail force is:

[0181] (1-27)

[0182] The track irregularity is defined as the relative difference between the track contact surface and the theoretical track surface, which is the excitation source of the large system vibration mechanics in this chapter. According to the track irregularity in different directions, the track irregularity can be divided into direction, high-low, gauge and horizontal irregularities. The left and right track y-direction irregularities are defined as , and the left and right track z-direction irregularities are defined as The high-low irregularity, direction irregularity, horizontal irregularity, gauge irregularity, left-right track direction irregularity and left-right track high-low irregularity can be expressed as:

[0183] (1-28)

[0184] (1-29)

[0185] (1-30)

[0186] (1-31)

[0187] (1-32)

[0188] (1-33)

[0189] (1-34)

[0190] (1-35)

[0191] The main track irregularity spectrum used in this paper is the high-speed railway ballastless track irregularity spectrum, which is segmented and fitted according to the following formula:

[0192] (1-36)

[0193] In the formula, f is the spatial frequency; S(f) is the power spectral density; A, K are fitting coefficients, which are segmented and valued according to Table 2-5.

[0194] The wavelength range of the irregularity spectrum of the high-speed railway ballastless track is . In order to meet the simulation requirement of the noise in the high frequency in the scheme, the vibration response in the high frequency is obtained, and the short-wave irregularity of the wheel-rail interface contact needs to be considered. In the scheme, the track high-low short-wave irregularity spectrum proposed by Sato is used, the wavelength range of the spectrum is , and the power spectrum density function expression is:

[0195] (1-37)

[0196] In the formula, is the power spectrum density , is the spatial circular frequency , .

[0197] The wavelength range of the track irregularity as the external excitation affects the frequency range of the solution of the vehicle-track-bridge coupling problem. From the perspective of driving comfort, the long-wave wavelength of the track irregularity should reach 85 m. From the perspective of the maximum research frequency of the steel-concrete composite structure vibration noise, the short-wave wavelength of the track irregularity should be less than 0.04 m. Therefore, the wavelength range of the track irregularity in the scheme is .

[0198] Establishment and solution of the vehicle-track-bridge system equation: according to the bridge, vehicle and track dynamic models established in the chapter, the dynamic equation of the coupling large system in the chapter can be obtained, as shown in the following formula:

[0199] (1-38)

[0200] In the formula, C , K , M respectively are the damping, stiffness and mass matrices of the system; Z is the generalized displacement vector of the system; the subscripts B , V , R respectively represent the bridge system, vehicle system and track system; F is the external load vector of the system. For the vehicle system, the external load vector is the vertical wheel-rail force. For the track system, the external load vector is the vertical wheel-rail force and the support force provided by the bridge through the fastener. For the bridge system, the external load vector is the vertical force applied by the track through the fastener to the bridge.

[0201] The dynamic equation of vehicle-track-bridge coupling system is a large and complex equation set involving nonlinearity, including the nonlinearity of wheel-rail contact force, etc., and needs to be solved by using an accurate and stable numerical simulation algorithm. In the present scheme, for the finite element structures such as bridge and track slab, the Newmark integration method in Ansys software is used for complete transient response analysis and solution; as for the vehicle-track system, the Newmark integration method programmed by Matlab is used for solution. As can be seen from the above theoretical analysis, the vehicle-track-bridge coupling vibration is extremely complex, and needs to be calculated and solved by using computer simulation software. Figure 8

[0202] Analysis method considering asynchronous long loading

[0203] In the process of structural transient dynamic analysis, the selection of appropriate time integration step determines the running time of the model and the accuracy and convergence effect of the solution of the problem. For general problems, the smaller the integration time step, the higher the calculation result precision, and the higher the configuration of the computer hardware and the power consumption required; the larger the integration time step, the solution precision of the higher order response simulation will be inevitably affected. Therefore, according to the characteristics of the problem to be solved in the present scheme, the following two factors will be considered in determining the time step of transient analysis:

[0204] (1) Relationship between time step and highest response frequency of structure

[0205] The dynamic response of structure can be regarded as the response of each order of dynamic modal combined with each other, and the maximum value of time step should be able to solve the highest order modal response of structure, then satisfies the following formula:

[0206] (1-39)

[0207] The above formula: f is the highest order frequency of the structure required by the problem to be analyzed.

[0208] (2) Relationship between integration time step and grid size, driving speed

[0209] In the present scheme, the fastener force load applied on the bridge varies with time, the size of the grid element has been determined in the previous section, assuming that the length of the finite element grid element is L, and the driving speed of the train is V , then satisfies the following formula:

[0210] (1-40)

[0211] ​In the vehicle-track-bridge coupling dynamic analysis model, the wheel-rail contact frequency is high, and after several calculations, the maximum stable step length of the wheel-rail contact algorithm in the program is about 0.1 ms. After every n analysis steps, the bridge finite element structure is analyzed for transient response. Considering the problem solving accuracy and solving efficiency, the asynchronous length loading ratio of 50 times is used in the dynamic simulation calculation of the vehicle-track-bridge system in this scheme, that is, the simulation analysis step length of the train and track system is 0.1 ms, and the bridge finite element transient response analysis step length is 5 ms.

[0212] The relevant comparison of the simulation results of the dynamic behavior of the train, track and bridge under different asynchronous length ratios is shown in Figure 9 . It can be analyzed that the asynchronous length loading ratio has a significant effect on the calculation efficiency. If the model in this scheme is calculated using equal time steps, the single model calculation time is expected to be 8 days, and if the 50 times asynchronous length calculation method proposed in this scheme is used, the calculation time can be reduced to 4 hours.

[0213] Program running results and verification

[0214] In order to judge the accuracy of the calculation results of the high-speed railway vehicle-track-bridge coupling dynamic simulation analysis simulation program written in this chapter, an 8-car train with a speed of 300 km / h passing through a 48m-span simply supported steel-concrete composite box girder bridge is taken as an example, and the program written in this chapter based on Matlab language is used for verification. The results show that the simulation results in this scheme meet certain accuracy requirements, and the relative error is due to the difference of several input parameters.

[0215] Time domain result analysis: as Figures 10-12 shown, the part of the time domain results of the program in this scheme extracts the displacement, velocity and acceleration data of the bridge, rail and train at any time. Under the action of train load, the vertical displacement of the mid-span node of the bridge deck is 3.2mm; the periodicity of the vertical displacement time history of the rail on the subgrade (not on the bridge) is obvious, and the maximum vertical deflection can reach 0.8mm; the displacement time history of the rail at the mid-span of the bridge is extracted, and it can be analyzed that Figure 12 The results can be considered as Figure 10 and Figure 11 superimposed, that is, the total displacement of the rail on the bridge under the train load is equal to the sum of the displacements of the bridge and the rail under the train load. And from the curve in Figure 12 , the whole process of the train on the bridge and off the bridge can be clearly seen; the displacement of the rail is smaller than that of the bridge, which also reflects that the stiffness of the rail structure is much greater than that of the bridge structure.

[0216] As Figure 13 and Figure 14 shown, the wheel-rail force time history curve Figure 13The curve is generally fluctuating around 56kN, which is related to the static wheel load of the wheel. The fluctuation range of-50~50kN reflects the medium-high frequency of the analyzed vehicle-bridge coupling problem. Under the direct action of the high-frequency exciting force, the vibration of the rail also reflects the characteristics of high frequency and obvious periodicity. The peak value of the acceleration of the rail node can even reach 500m / s².

[0217] As Figures 15-17 The time history curve of the bridge shows that the vibration amplitude of the bridge deck flange is significantly larger than that of the mid-span position, which is related to the thickness of the plate and the distance from the exciting position. In this scheme, the train load is unidirectional loading, and the bridge deck flange is closer to the loading position. The vibration intensity of the steel structure part of the bottom plate is stronger than that of the web, which provides a way for the study of vibration reduction and noise reduction of this bridge type. The displacement curves of the concrete parts are almost overlapped, but it can be seen that the vertical displacement of the upper component is larger than that of the lower component, which reflects the vibration reduction and isolation characteristics of the concrete structure.

[0218] Frequency domain result analysis: The time domain vibration signal of the vehicle-track-bridge dynamic analysis result is expanded in the frequency domain, and the output is the frequency correlation function. The distribution law of the signal is studied, which is called dynamic spectrum analysis. The vibration signal can be decomposed into several frequency components, and the frequency structure and amplitude information of each harmonic of the signal can be obtained. Further, the noise elimination filter function of the input signal can be realized.

[0219] The application of the fast algorithm of discrete Fourier transform (FFT) has been very mature in the vibration signal frequency domain processing of vehicle-bridge coupling results. In this scheme, the vibration time domain data of the bridge components are processed by using the self-programming of Matlab, and the frequency domain results of the bridge structure dynamic behavior are obtained as Figures 18-20 .

[0220] The frequency domain results of the asynchronous long loading ratio of 25 are selected for analysis, that is, the transient analysis time step in Ansys is 2.5ms. According to the sampling theorem, the frequency spectrum results within 200Hz can be obtained. Analysis shows that the dynamic response curves of the bridge components with different material properties present the phenomenon of overlapping due to the low frequency of the analyzed frequency. And the whole shows the characteristics of low frequency, that is, the main energy is concentrated in the low frequency band on the left of the frequency spectrum. The frequency spectrum of displacement and velocity mainly concentrates on 10Hz below, while the acceleration frequency spectrum mainly concentrates on 100Hz below. The peak value of 128Hz is caused by the modeling method of the rail, which is related to the spacing of the fastener and the speed of the train. The calculation formula will be given later.

[0221] In summary, based on the theory of vehicle-track-bridge coupling dynamics, this chapter establishes a simulation model of vehicle-track-bridge coupling vibration for high-speed railway steel-concrete composite structure bridge, and verifies the accuracy of the program based on Matlab language and Ansys finite element software. Specifically:

[0222] (1) Based on the theory of vehicle-track-bridge coupling dynamics, a simulation model of vehicle-track-bridge coupling vibration for high-speed railway steel-concrete composite structure bridge is established. In the model, a high-speed railway four-axle locomotive model with 10 degrees of freedom is established based on multi-rigid-body dynamics; the dynamic model of the commonly used 60 kg / m steel rail is established by finite element method, and the high-speed railway plate-type ballastless track structure is established in Ansys finite element software; the high-speed railway steel-concrete composite structure bridge is established by Ansys finite element software, the steel structure is simulated by SHELL element, the concrete deck slab is established by SOLID element, and the connection between steel and concrete is realized by MPC algorithm; the track irregularity is fitted by the high-speed railway ballastless track irregularity spectrum, and the short-wave track irregularity is considered; the vertical wheel-rail force is calculated by Hertz nonlinear elastic contact theory; the Newmark integration method is used to solve the dynamic response of the bridge and the vehicle-track system.

[0223] (2) Based on Matlab language, a simulation program of high-speed railway vehicle-track-bridge coupling vibration dynamics is developed. By building the overall calculation framework in Matlab language, the train and track models are established, and the Ansys software is used to establish the bridge finite element model. Through the data exchange of the contact points between the track and the bridge in the analysis step, the dynamic simulation of the train-track-bridge system is realized. In order to improve the calculation efficiency of the program, the asynchronous long loading analysis method is considered, and the influence of different asynchronous long loading ratios on the system dynamic response results is compared. After comparing the calculation accuracy and efficiency, an asynchronous long loading ratio of 50 times is selected for the dynamic simulation analysis of the train-track-bridge system.

[0224] (3) Taking a high-speed railway simply supported composite box girder bridge with a span of 48 m and a train speed of 300 km / h as an example, the dynamic vibration simulation analysis of the large system is carried out, and the response results are compared with the related existing technology. The results show that the simulation accuracy of the self-programming is reliable.

[0225] (4) The simulation results of vehicle-track-bridge are analyzed in time domain and frequency domain, and some time-frequency rules of vehicle-bridge coupling vibration response are given.

[0226] High-speed railway steel-concrete composite beam low-frequency noise prediction model

[0227] Basic assumptions of low-frequency noise numerical simulation

[0228] (1) The simulated sound wave is a small-amplitude wave in a uniform and stationary ideal fluid in air.

[0229] (2) The sound-solid coupling interaction is not considered.

[0230] (3) Other sound sources other than the bridge structure are not considered.

[0231] In this scheme, the acoustic boundary element module in LMS Virtual.lab is used to simulate the low-frequency noise of the bridge structure. The LMS boundary element method requires that the element size of the acoustic mesh satisfy formula (1-18): the upper limit frequency of the boundary element analysis method in this scheme is 100 Hz, which is brought into formula (1-18) to obtain the maximum element size of the acoustic mesh is about 0.56m, in order to ensure the simulation accuracy, the acoustic mesh size in this scheme is controlled to 0.25m.

[0232] The number of influence nodes is set to 4 and the maximum distance is set to 0.3m. This means that within a circular range of 300mm radius centered on the acoustic mesh node, the four nearest finite element mesh nodes are found to map the data. As shown in Figure 21

[0233] The value of the target node can be determined according to the value of the source node according to the following mapping relationship:

[0234] (1-41)

[0235] The specific acoustic boundary element simulation process is shown in Figure 22 In order to explore the spatial distribution law of the radiation noise of the simply supported composite box girder bridge structure, the mid-span section of the bridge is taken as the reference plane, and the spatial noise calculation points are selected as shown in Figure 23 The bridge centerline bottom plate is taken as the origin, and the field points are selected at the height of 4.0m, 0m, 3.5m, 5m, 10m and 20m along the horizontal direction of the bridge centerline, track centerline, respectively, a total of 28 noise calculation points. In order to show the distribution law of noise in detail, the interval of the field points is refined to 1 meter. The reflection of the ground greatly affects the distribution of the sound field. In this scheme, only the reflection of the rigid ground to the sound wave is considered. In order to simplify the analysis, as Figure 24 ​As shown, the reflected sound from the sound source S to the field point P is equivalent to the direct propagation from the mirror sound source S1 to the field point P. The distance between the bridge bottom plate and the ground is 10 meters, which is simulated by a symmetrical plate in the model. The train takes 2.5 seconds from the upper bridge to the lower bridge, and the time-domain transient acoustic radiation is taken at three time points, i.e. when the train is on the bridge (t=0.05s), when the train is on the bridge (t=1.5s), and when the train is off the bridge (t=3.5s) to compare the bridge structure noise radiation at different times.

[0236] As can be clearly seen from the sound field pressure cloud map at different times, with the passing of the train, the bridge structure noise radiation changes from small to large, and then from large to small. The spatial distribution of sound radiation can be clearly seen, and the value of sound radiation decreases with the increase of the distance from the bridge. The vehicle load of the model is unidirectional loading, which is the reason for the asymmetry of the sound field cloud map. The noise level of the field point on the side where the vehicle load is applied is obviously larger than that on the other side. During the process of the train on the bridge, it can be seen that the sound radiation has not reached the measuring points far from the bridge, and the sound pressure level is still 0 dB. When the train is on the bridge, the maximum sound pressure level of the field point can reach 100 dB. After the train leaves the bridge, the bridge members vibrate freely with damping. It can be seen that the sound pressure level inside the bridge is significantly higher than that outside.

[0237] As shown in Figures 25-27 , the noise time-frequency curves of A, B and C field points are extracted for analysis. The following conclusions can be drawn. By analyzing the time-domain graph, the sound pressure level curve decreases rapidly from 2.5s, which can be judged that the train is in the process of leaving the bridge. By observing the curve amplitude, the A and B field points are relatively close in the time-domain graph, and it is difficult to compare the size, but they are much larger than the C field point result, which conforms to the basic law that noise decreases with distance. By analyzing the frequency spectrum, it can be seen that the energy is mainly concentrated in the low frequency band, and the sound pressure level amplitude of the three curves decreases with the increase of frequency, which is consistent with the law that the vibration energy is concentrated in the low frequency band as described in the previous chapter. Figure 26 The result of A-weighting processing is obtained Figure 27 , which can be seen as the suppression effect of A-weighting on low frequency noise. The A-weighting result in this scheme is only for comparison, and the rest of the noise radiation results are given without weighting.

[0238] The solution range of bridge low-frequency noise is 0~100Hz, but the hearing range of human ear is above 20Hz, so the effective range of the analysis result is 20~100Hz. The noise spectrum is processed by one-third octave band, as shown in Figure 28 , and A-weighting processing is performed on the basis of Figure 28 , as shown in Figure 29The sound radiation curves of the three field points are basically the same, the A-weighting has obvious inhibitory effect on low-frequency noise, and the curve drops obviously at about 80Hz. The maximum value of the sound pressure level in the three field points appears in the B field point. The dynamic analysis results in the previous chapter also show that the vibration amplitude of the bottom plate is larger, and this field point is close to the bottom plate. The sound pressure level is 80dB under the linear weighting, and is 45dB under the A-weighting, which reflects the great contribution of the steel bottom plate in the steel-concrete composite beam to the low-frequency vibration noise radiation. The contributions of different plate elements of the bridge structure to the low-frequency noise radiation of the A, B and C field points at the frequencies of 12.5Hz, 25Hz, 50Hz and 100Hz are analyzed, and the following results are obtained. As shown in Figures 30-33

[0239] The results show that, except at 100Hz, the noise contribution of the web plate and the bottom plate to the field point is negative, and the rest is positive. The negative value means that the contribution is smaller, which is lower than the reference sound pressure. Compared with the positive value, it also has physical meaning. Analysis shows that the top plate has the largest contribution to the A field point, and the bottom plate has the largest contribution to the B field point. The total contribution of the plate noise mainly comes from the lower frequency band.

[0240] Figures 34-36 The noise contribution of different plate elements to the A, B and C field points at each single frequency in the frequency range is given. The plate element contribution curve close to the total sound pressure level curve indicates that this plate element has the largest contribution to the sound pressure level of the field point, and the plate element contribution curve located in the lower part of the total sound pressure level curve and far away from it indicates that the plate element has smaller contribution or negative contribution to the sound pressure level of the field point. The A field point is located in the upper part of the top plate, Figure 34 which shows that the top plate has the largest noise radiation contribution to the field point; the B field point is located in the lower part of the bottom plate, Figure 35 which shows that the bottom plate has the largest noise radiation contribution to the field point; the C field point is far away from the bridge structure sound source, and the simulation result Figure 36 which shows that the concrete top plate has larger contribution to the noise radiation of the point at lower frequencies, and the steel bottom plate has larger contribution to the noise radiation of the field point at medium and high frequencies. Comparison of the positive and negative contributions of different plate elements to the field point at different frequencies can provide ideas for reducing the bridge structure noise.

[0241] The software can give the sound pressure level values of any field point at different frequencies, but cannot give the total sound pressure level cloud map. In this scheme, the method of manually superimposing the sound pressure levels at different frequencies according to the total sound pressure level formula of the acoustic field point (prior art) is used to calculate the total sound pressure level of each field point. The total sound pressure level calculation results of each field point are summarized to obtain the total sound pressure level cloud map as shown in Figure 37 ​The results show that the total sound pressure level near the middle of the bridge floor is the maximum, the maximum value of the total sound pressure level is 100 dB, and the total sound pressure level of the acoustic field point on the left side of the bridge is obviously greater than that on the right side, which is related to the simulated one-way driving of the train in the scheme. The noise radiation value near the lower part of the bridge structure is greater than that near the top plate, showing that the noise radiation capacity of the steel web and steel floor is stronger than that of the concrete top plate. The farther away from the bridge structure, the weaker the degree of sound radiation attenuation.

[0242] In summary, by using the basic parameters of acoustics and the basic formula of acoustic field radiation problem in the prior art, the low-frequency radiation noise of the bridge structure is numerically simulated by using the boundary element method based on LMS software, and the low-frequency noise radiation law of the bridge structure is given. The low-frequency noise radiation model of a 48m steel-concrete composite simply supported beam under the excitation of a train load at 300km / h is simulated by using LMS Virtual. Lab Acoustics software. The noise radiation simulation results show that the total sound pressure level field point diagram is symmetrically distributed as a whole; the maximum noise sound pressure level appears in the middle of the bridge floor, which is 100dB; the farther away from the bridge structure, the weaker the degree of sound radiation attenuation; the bottom plate and the web of the steel structure part of the bridge contribute greatly to the noise of each field point, and each plate contributes greatly to the noise of the nearby field point; the low-frequency total sound pressure level value of the established acoustic field point is distributed in the range of 70dB-100dB.

[0243] High-noise prediction model for high-speed railway steel-concrete composite beam

[0244] Bridge structure plate sound radiation: In order to obtain the noise radiation of a point at a certain distance from the bridge plate, the following simplifications need to be made, that is, the steel-concrete composite beam bridge is regarded as a system composed of multiple rectangular plates with length m and width n. Then for each subsystem, the radiation sound power is:

[0245] (1-42)

[0246] In the formula, is the density of air, is the propagation speed of sound in air, and are the radiation efficiency and surface area, respectively, is the mean square velocity. Let the vertical distance from the measuring point M to the subsystem be r .

[0247] When , it indicates that the measuring point M is close to the sound source, at this time, the sound wave is regarded as a plane wave with constant sound pressure, then:

[0248] (1-43)

[0249] When , it indicates that the measuring point M is far away from the sound source, at this time, the sound pressure level of the sound wave will decrease linearly with the increase of the distance, then:

[0250] (1-44)

[0251] When , it indicates that the measuring point M is far away from the sound source, at this time, the sound pressure mean square value of the measuring point C is:

[0252] (1-45)

[0253] The sound pressure level at any point in the external sound field of the bridge structure can be obtained by linear superposition according to the above formula. The noise contribution of the plate refers to the sound pressure caused by each plate of the bridge structure at the field point. By comparing and analyzing the noise contribution of the plate with the total structure noise, it can be analyzed which type of plate plays a major role in the bridge structure noise, thereby providing ideas for bridge structure vibration reduction and noise reduction.

[0254] The structure noise of the steel box composite beam is mainly composed of three types of plates, i.e. top plate, bottom plate and web plate, and the contribution of the transverse plate and stiffening rib is small. The noise contribution of a certain plate to a certain acoustic field point at a certain frequency can be represented by the following formula:

[0255] (1-46)

[0256] In the formula, is the structure noise contribution of a certain plate at frequency i, and respectively represent the sound pressure level and the sound pressure generated by a certain plate at the measuring point at frequency i, and respectively represent the total sound pressure level and the total sound pressure generated by all plates at the measuring point at frequency i.

[0257] Modal density: the number of modes in a unit frequency bandwidth is called modal density. It can reflect the energy storage capacity of the system. For the bridge noise radiation problem analyzed in this scheme, most structures can be simplified as plate structures, and the modal density analytical expression of a simple substructure can be given by mathematical method. For a vibrating flat plate, the modal density expression is as follows:

[0258] (1-47)

[0259] In the formula, represents the bending wave speed, S represents the area of the plate, and t represents the thickness of the plate.

[0260] It can be seen that the modal density is proportional to the area of the plate and inversely proportional to the thickness of the plate. In the medium and high frequency range, the boundary conditions have no effect on the modal density. Therefore, the simply supported bridge model established in this chapter is different from the finite element method or the boundary element method in that the SEA method only establishes the plate without constraints.

[0261] Internal loss factor The internal loss factor is defined as the ratio of the energy dissipated per unit time to the average stored energy in a vibration cycle of the subsystem. It is generally believed that the damping of any subsystem is usually determined by no more than three damping mechanisms. The internal loss factor of a structural subsystem can be expressed as:

[0262] (1-48)

[0263] In the formula, is the boundary connection damping of the structural subsystem; is the damping formed by the internal friction of the structural subsystem; is the vibration and sound radiation damping of the structural subsystem. In this scheme, the internal loss factor of the concrete structure is taken as 1.5%, and the internal loss factor of the steel structure is taken as 0.1%.

[0264] Coupling loss factor: the coupling between subsystems is formed by mutual connection, and relying on the coupling, the energy of the directly excited subsystem is directly transmitted to the subsystem not directly excited. The coupling loss factor is defined as the transmission loss energy at the connection between subsystem i and subsystem j. In this scheme, the formula for calculating the coupling loss factor is given in the book by R.H. Lyon et al. The formula for calculating the coupling loss factor between plates through line connection is given.

[0265] (1-49)

[0266] In the formula, : wave propagation coefficient from structure 1 to structure 2; l: length of line connection; : group velocity; surface area of substructure 1; ω: center frequency of frequency band.

[0267] Determination of external excitation force of bridge deck plate subsystem. The high-frequency wheel-rail force between the train wheelset and the rail directly affects the external excitation force of the bridge deck plate subsystem, so it is necessary to analyze the wheel-rail force data. First, the wheel-rail force time history of a wheelset is extracted, and the fast Fourier transform and octave data processing are performed.

[0268] The time history of wheel-rail force after processing shows that the curve is relatively dense. The spectrum of the data is analyzed, and the data is distributed within 2000 Hz, which is related to the lower cut-off wavelength of the short-wave track irregularity. It is observed that the image has obvious peaks at 128 Hz and 256 Hz, which is related to the modeling method of the steel rail, and is affected by the length of the steel rail unit. The periodic passing of the wheel set through the steel rail unit is subjected to periodic wheel-rail force, and the frequency can be calculated as follows:

[0269] (1-50)

[0270] Therefore, the spectrum has peaks at multiples of 128 Hz.

[0271] To effectively analyze the frequency domain data of wheel-rail force, the data is processed by one-third octave band, and the results show that the image has an obvious upward trend within 200 Hz, which verifies the existing technology. The time history of the fastener force shows that the maximum fastener force is 40 kN, and it has obvious periodic characteristics. The spectrum shows that the fastener force has peaks within 10 Hz, reaching 5.5 kN, and the octave band shows that the fastener force still has data distribution after 1000 Hz, showing the medium-high frequency characteristics of the fastener force. Combined with the frequency band analyzed in this section, the spectrum data of 100-1000 Hz is extracted for solving the external excitation force of the bridge deck. The original fastener force data is filtered by a 100 Hz high-pass filter, and the filtered wheel-rail force time history curve is obtained by inverse Fourier transform. It can be concluded that the excitation force of the steel rail on the bridge has obvious periodic characteristics.

[0272] The longitudinal length of the bridge deck in the VAONE model is 4 m, and the longitudinal spacing of the fastener is 0.65 m. Considering the symmetrical distribution of the fastener along the center line of the track, the number of fasteners in one bridge deck is 12. According to the principle of SEA, the load position does not affect the stress of a certain SEA panel, i.e. the force applied to the same SEA panel system can be superimposed, so the force of all support springs in the same bridge deck system can be superimposed and applied to the corresponding panel system in the form of concentrated force. The force transmitted to the bridge is defined as the square root of the square sum of the forces of each support spring when the train load acts on the steel rail, and the specific calculation method is shown in the following formula:

[0273] (1-51)

[0274] In the formula, is the external force of the bridge deck system, M represents the number of fasteners on the bridge deck, is the force of the nth fastener spring acting on the bridge deck system.

[0275] The simulation results of the medium and high frequency noise: compared with the C field point, the A field point and the B field point are closer to the sound source, and the radiated sound pressure level is also significantly greater than the sound pressure level of the C field point. The variation law of the sound pressure level with frequency, that is, the law of the sudden increase at 100 Hz and 1000 Hz, is similar to the variation of the external excitation force of the bridge with frequency, that is, the energy is mainly distributed in the low frequency band. Among them, the A field point has a maximum value of 88 dB at 100 Hz. The values of the three field points in each frequency band are all above 65 dB. And at the end of the analysis frequency range, 1000 Hz, a sudden change occurs, indicating that the noise prediction value at this point has inaccuracy.

[0276] The vibration velocity data of each plate of the bridge are extracted, and it is found that the average vibration velocity of the concrete plate is much smaller than that of the steel structure part. The total vibration level of the concrete plate is 127 dB, and the steel plate has similar vibration conditions due to the same thickness and similar size, and no load is directly loaded, so the average total vibration level is about 138 dB.

[0277] Figures 38-43 The noise radiation contribution of different plate parts of the bridge structure to the A, B and C acoustic field points is given. The A field point is located at the top of the bridge structure, and the bottom plate has a small contribution to the field point in the full frequency band. The noise contribution of the concrete top plate to the field point plays a major role, and the noise contribution value of the concrete top plate to the field point can reach 92 dB.

[0278] The B field point is located at the bottom of the bridge structure, and the contribution of the bottom plate to the field point is greater than that of the A field point. In the low frequency band, the noise radiation value of the concrete top plate to the field point plays a major role, and after 250 Hz, the radiation efficiency of the steel structure part increases, and the contribution to the field point is greater than that of the concrete part.

[0279] Regarding the medium and high frequency noise radiation contribution of the bridge bottom plate, the bridge top plate and the bridge web to the A, B and C field points, according to formula 1-46, the calculation results show that the bottom plate has the largest contribution to the B field point among the three acoustic field points, which is 24%, the web has a similar contribution to the noise of the three field points, and the average contribution rate is 17%; the plate part with the largest contribution rate to the three field points is the concrete top plate, and the contribution rates to the A, B and C field points are 61%, 56% and 36%, respectively.

[0280] In summary, the basic parameters of the statistical energy method are introduced, the power flow balance equation of the bridge structure is derived, the VAONE software is used, and the medium and high frequency radiation noise of the bridge structure is numerically simulated based on the statistical energy method. The medium and high frequency noise radiation law of the bridge structure is given, and the main content and conclusions of this chapter are:

[0281] (1) Firstly, the theoretical formula of simulating the mid-high frequency noise of bridge structure using SEA method is derived, including the definition of plate sound radiation efficiency, modal density and loss factor. (2) The wheel-rail force and fastener force mentioned in the previous section are extracted, and a detailed comparative analysis is carried out on the two data through Fourier transform and octave processing. The method of determining the external excitation force of bridge deck is given, and the results show that the spectrum of fastener force is at 128 Hz, and it is pointed out that the reason for the peak value appearing is related to the train running speed and the length of the rail unit. (3) The specific steps of numerical simulation of mid-high frequency noise radiation in the software are introduced in detail. After obtaining the results of mid-high frequency noise radiation, the sound radiation contribution of different plates to different field points is analyzed, and the following conclusions are drawn: the radiation efficiency of concrete top plate is obviously greater than that of steel structure plate below 500 Hz, and the radiation efficiency of steel structure is greater than that of concrete top plate after 500 Hz; Overall, the sound radiation contribution of the top plate is greater than that of the steel structure part, and the average contribution of the concrete top plate to the three acoustic field points in this scheme is as high as 50%; the contribution of the bottom plate and web plate of the steel structure part to the noise cannot be ignored, and it is necessary to conduct in-depth research on the vibration and noise reduction performance of the steel bottom plate.

[0282] Analysis of vibration and noise influence parameters of composite box girder bridge

[0283] When the train passes through the bridge at high speed, it will produce a huge impact force on the bridge, which will in turn cause structural noise of the bridge, and have a negative impact on the normal life of residents along the line. When the train passes through the bridge at different speeds, the structural sound radiation of the bridge structure is different. Therefore, it is of great significance to study the influence law of different train speeds on noise for vibration reduction and noise reduction. In this section, the vibration and sound radiation results of the train passing through the bridge at 200 km / h, 250 km / h, 300 km / h and 350 km / h are obtained through model calculation with an interval of 50 km / h.

[0284] Influence of train speed on vibration: In this scheme, the peak speed and root mean square speed are used as indicators to evaluate vibration. The peak value is the maximum value of the absolute value of the speed in the vibration signal, and the root mean square value is the effective value, which means that the speed is squared and then summed in a certain time, and finally the operation is taken. The calculation formulas of vibration peak speed and speed effective value are as follows:

[0285] (1-52)

[0286] Figure 44 The vertical displacement response time history of the mid-span node of the bridge deck under different train speeds is given, and the maximum vertical deflection under different speeds is extracted for comparison; Figure 45 The numerical value of the vertical maximum deflection changes with the speed as shown in the figure; the specific values are shown in Figure 46 . Figure 44It can be seen from the figure that when the train runs at a low speed, the displacement-time curve is relatively smooth and the waveform is complete. It can be clearly seen that with the increase of train speed, the train crossing time is shortened and the vibration amplitude is also significantly reduced. Figure 45 It can be seen from the figure that when the train runs at a low speed, the displacement-time curve is relatively smooth and the waveform is complete. It can be clearly seen that with the increase of train speed, the train crossing time is shortened and the vibration amplitude is also significantly reduced. Figures 47-49 The vertical acceleration response time history of the mid-span node of the bridge deck under different train speeds is given, and the acceleration peak value and the acceleration effective value under different speeds are compared. The acceleration peak value under different speeds and the train crossing time at this time are shown in Figure 49 .

[0287] Figure 47 It can be seen from the figure that when the train runs at a low speed, the displacement-time curve is relatively smooth and the waveform is complete. It can be clearly seen that with the increase of train speed, the train crossing time is shortened and the vibration amplitude is also significantly reduced. Figure 48 It can be seen from the figure that when the train runs at a low speed, the displacement-time curve is relatively smooth and the waveform is complete. It can be clearly seen that with the increase of train speed, the train crossing time is shortened and the vibration amplitude is also significantly reduced. Figures 50-52 The vertical acceleration response time history of the mid-span node of the bridge deck under different train speeds is given, and the acceleration peak value and the acceleration effective value under different speeds are compared. The acceleration peak value under different speeds and the train crossing time at this time are shown in Figure 52 . Figures 53-55 The vertical acceleration response time history of the mid-span node of the bridge deck under different train speeds is given, and the acceleration peak value and the acceleration effective value under different speeds are compared. The acceleration peak value under different speeds and the train crossing time at this time are shown in Figure 55 .

[0288] The influence of train speed on noise: the low-frequency noise response of the bridge structure under different speeds is simulated according to the method described in Chapter 3; the medium and high-frequency noise radiation under different speeds is simulated, only the external excitation force of the bridge deck subsystem needs to be changed, Figure 56 The fastener force frequency spectrum data of a single fastener under different train speeds is given. With the increase of speed, the amplitude of the fastener force frequency spectrum is significantly improved, and the peak frequency also increases with the increase of speed, which is consistent with the calculation formula of the peak frequency of the fastener force proposed before.

[0289] Combining the low-frequency noise simulation method and the high-frequency noise numerical simulation method, the noise radiation of A, B and C field points under the influence of different train speeds is given as Figures 57-59The low frequency band and the medium-high frequency band have obvious mutations at the segmentation point 100 Hz, which is slightly different from the actual situation. After analysis, it is found that this is related to the modeling method of the vehicle-track-bridge model. The results of the fastener force obtained in this scheme are slightly larger than those of the related existing technology, which leads to the slightly larger noise radiation results in the medium-high frequency band presented in this section. The vehicle-track-bridge model in this scheme is a vertical model, which ignores the contribution of the lateral force between the wheel and the rail to the vibration of the bridge, which leads to the slightly smaller noise amplitude in the low frequency band. These two main factors lead to the obvious mutation of the noise radiation full frequency band simulation results at 100 Hz.

[0290] Influence of the thickness of the bottom plate concrete on vibration: Figure 60 and Figure 61 The influence of different thicknesses of the bottom plate poured concrete on the vertical displacement of the bottom plate at the midspan is given. It can be seen from the figure that compared with the concrete not poured, the peak value of the vertical deflection at the midspan is reduced from 3 mm to 1 mm, and during the process of increasing the concrete thickness from 50 mm to 150 mm, the time history curve of the vertical deflection at the midspan has almost no change in the deflection peak value index. Figure 62 and Figure 63 The influence of different thicknesses of the bottom plate poured concrete on the vertical vibration speed of the bottom plate at the midspan is given. It can be seen from the figure that compared with the concrete not poured, the peak value of the vertical speed at the midspan and the effective value of the vertical speed are both obviously decreased, and during the process of increasing the concrete thickness from 50 mm to 150 mm, the time history curve of the vertical speed at the midspan and the index of the vertical speed of the bottom plate show little change. In this section, the peak value index of the speed is slightly decreased, and the effective value index of the speed is slightly increased.

[0291] Influence of the thickness of the bottom plate concrete on noise: Figure 64 The influence of different thicknesses of the bottom plate concrete on the frequency spectrum of the fastener force is given. From the figure, the following conclusions can be drawn: with the increase of the concrete thickness from 0 mm to 150 mm, the peak value of the fastener force is almost not affected, so the frequency spectrum data of the external excitation force of the bridge deck is not changed when simulating the influence of the bottom plate concrete thickness on the medium-high frequency noise. Figures 65-70 The change of the structure noise radiation of A, B and C three field points under different thicknesses of the bottom plate concrete is given. From the figure, the following rules can be analyzed: in the low frequency stage, i.e. below 100 Hz, the influence of the thickness of the bottom plate concrete on the noise radiation of the field point is not obvious, and the frequency spectrum graph presents a relatively chaotic feature; in the medium-high frequency band, i.e. 100 Hz~1000 Hz, the increase of the thickness of the bottom plate concrete has a relatively obvious influence on the noise radiation reduction result. Among them, the noise reduction effect of the bottom plate concrete pouring thickness of 50 mm is the most obvious, which makes the average total sound pressure level of the three field points decrease by 1 dB. The change of the thickness of the bottom plate concrete has the most obvious noise reduction effect on the B field point which is close to the bottom plate.

[0292] In summary, by parameter analysis, the vibration and noise reduction of steel-concrete composite beam are analyzed. In the process of increasing train speed from 200 km / h to 350 km / h, the peak value of mid-span vertical deflection of the bridge is reduced from 3.5 mm to about 3.0 mm; the peak value of acceleration is increased from 1 m / s² to 2 m / s², and the effective value of mid-span vertical acceleration is also increased; the increase of train speed has the most obvious effect on the acceleration of steel web plate and steel bottom plate. In terms of the influence of train speed on noise, the increase of train speed has a more obvious effect on the radiation of medium and high frequency noise, which is caused by the increase of the peak value of fastener force caused by the increase of train speed. On this basis, this chapter studies the influence of the change of bottom plate concrete thickness on the vibration and noise radiation of the bridge structure, and the results show that when the thickness of the bottom plate concrete is 50 mm, the vibration and noise reduction effect of the structure is the most obvious, among which the peak value of mid-span vertical deflection of the bottom plate is reduced from 3.0 mm to 0.9 mm, and the effective value and peak value of the bottom plate speed are reduced, which shows the vibration reduction characteristics of the bottom plate concrete. The simulation of the bottom plate concrete in noise reduction shows that the pouring of 50 mm thick bottom plate concrete reduces the average total sound pressure level of the three field points by 1 dB. However, if the thickness is increased on the basis of 50 mm, the effect of vibration and noise reduction is not obvious.

[0293] Finally, it should be pointed out that the above preferred embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present application.

Claims

1. A method for analyzing the vibration and noise of a combined box girder bridge under vehicle-bridge coupling, characterized in that: Includes the following steps: S1. Establish a train-track-bridge coupled vibration model for a high-speed railway steel-concrete composite box girder bridge, and develop a train-track-bridge coupled vibration simulation analysis program based on Matlab language and Ansys finite element software. S2. Establish a low-frequency noise prediction model for high-speed railway steel-concrete composite box girder bridges, conduct numerical simulation of low-frequency radiated noise of bridge structures, and obtain the low-frequency noise radiation law of bridge structures. S3. Establish a high-frequency noise prediction model for high-speed railway steel-concrete composite box girder bridges, conduct numerical simulation of the high-frequency radiated noise of the bridge structure, and obtain the high-frequency noise radiation law of the bridge structure. S4. Based on the models established in steps S1-S3, analyze the impact parameters of vibration and noise on high-speed railway steel-concrete composite box girder bridges and obtain the analysis results. Specifically, step S1 is as follows: S11. Establish a vehicle dynamics model. The train model consists of 8 cars. Each car includes a car body, two bogies and four wheelsets, and each car has 10 degrees of freedom. S12. Establish a track dynamics model, which includes a self-compacting concrete layer, a concrete track slab, a concrete base slab, steel spring fasteners, and rail components. S13. Establish a finite element model of the bridge. The bridge model is established using Apdl finite element software, and the dynamic behavior of the bridge structure is numerically simulated. S14. Establish a wheel-rail interaction model and calculate the vertical wheel-rail force using the Hertz nonlinear contact model; S15. The track irregularity is determined as the excitation source, and the wavelength range of the track irregularity is determined to be 0.04-85m; S16. Based on the bridge, vehicle and track models established in steps S11-S13, derive the dynamic equations of the train-track-bridge coupled large system. S17. Using computer simulation software and finite element software, develop a numerical simulation analysis program model for the coupled dynamics of train-track-bridge, solve the problem, and verify the results of the program. The dynamic equations of the train-track-bridge coupled system in step S17 are as follows: In the formula, C, K, and M are the damping, stiffness, and mass matrices of the system, respectively; Z is the generalized displacement vector of the system; subscripts B, V, and R represent the bridge system, vehicle system, and track system, respectively; and F is the external load vector of the system.

2. The method for analyzing the vibration and noise of a combined box girder bridge under vehicle-bridge coupling according to claim 1, characterized in that: In step S17, a dynamic simulation calculation of the train-track-bridge system is performed using an asynchronous long loading ratio of 50 times. Specifically, the simulation analysis step size for the train and track system is 0.1 ms, and the finite element transient response analysis step size for the bridge is 5 ms.

3. The method for analyzing the vibration and noise of a combined box girder bridge under vehicle-bridge coupling according to claim 1, characterized in that: The equation of motion for a single vehicle is: In the formula, M V The mass matrix of a single vehicle; K V This represents the stiffness matrix of a single vehicle section. Z V This is the column matrix representing the vertical displacement of a single vehicle section; F V The vertical wheel-rail force matrix for a single vehicle section; Since the damping matrix and the stiffness matrix have similar content forms, it is only necessary to replace the stiffness coefficient k in the matrix with the damping coefficient c.

4. The vibration and noise analysis method for a combined box girder bridge with vehicle-bridge coupling effect according to claim 1, characterized in that: The equations of motion for the orbital dynamics model are: M R This is the overall quality matrix; K R Overall stiffness matrix; Z R Overall orbital displacement matrix; C R The damping matrix of the track; In the formula, , The damping coefficient is... For the damping ratio, , These are the natural circular frequencies.

5. The method for vibration and noise analysis of a combined box girder bridge with vehicle-bridge coupling effect according to claim 1, characterized in that: When the track is uneven, the wheel-rail force F W The expression is: 。 6. The method for vibration and noise analysis of a combined box girder bridge with vehicle-bridge coupling effect according to claim 1, characterized in that: Step S2 specifically includes: (1) Establish the wave equation in an ideal fluid under the condition that the medium is static and homogeneous and the sound wave has a small amplitude; (2) Establish the Helmholtz equation for external noise radiation in the frequency domain, and derive the Green's function expressions for acoustic boundary conditions and three-dimensional free sound field; (3) Using LMS Virtual.Lab Acoustics software, a simulation method for low-frequency noise radiation model under train load excitation was obtained.

7. The method for vibration and noise analysis of a combined box girder bridge with vehicle-bridge coupling effect according to claim 1, characterized in that: Step S3 specifically includes: (1) Establish the theoretical formula for simulating the mid-to-high frequency noise of bridge structures using the SEA method, and derive the definitions of plate acoustic radiation efficiency, modal density, and loss factor; (2) Through Fourier transform and octave band processing, a detailed comparative analysis of wheel-rail force and fastener force was conducted, and a method for determining the external excitation force of the bridge deck was derived. (3) Establish specific steps for numerical simulation of mid-to-high frequency noise radiation in the software, and analyze the contribution of different plates to the sound radiation at different field points.

8. The method for vibration and noise analysis of a combined box girder bridge with vehicle-bridge coupling effect according to claim 1, characterized in that: The parameters affecting the vibration and noise of high-speed railway steel-concrete composite box girder bridges in step S4 include web thickness, bottom plate thickness, vehicle speed, number of lanes, and bottom plate material.

Images