Method for analyzing vibration noise of combined box girder bridge under axle coupling effect

Abstract

The invention discloses a vibration noise analysis method for a combined box girder bridge with an axle coupling effect, and belongs to the technical field of bridge engineering. The method comprises the following steps: S1, establishing a train-track-bridge coupled vibration model of a high-speed railway steel-concrete combined box girder bridge, and compiling a train-track-bridge coupled vibration simulation analysis program based on a Matlab language and Ansys finite element software; s2, establishing a low-frequency noise prediction model in the steel-concrete combined box girder bridge of the high-speed railway, and obtaining a low-frequency noise radiation rule of a bridge structure; s3, establishing a medium-high noise prediction model of the steel-concrete combined box girder bridge of the high-speed railway, and performing numerical simulation on medium-high frequency radiation noise of a bridge structure; and S4, analyzing the influence parameters of the vibration noise of the steel-concrete combined box girder bridge of the high-speed railway in combination with the models established in the steps S1 to S3. The technical scheme is used for analyzing vibration and noise conditions of the steel-concrete composite beam applied to the field of railroad bridges.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a vibration noise analysis method for a combined box girder bridge with vehicle-bridge coupling. Background Art

[0002] Shear connectors connect the steel beam and concrete bridge deck to form a whole and bear the force together. This structural form is called a steel-concrete composite beam. The force of this component is reasonable, scientific and economical, making full use of the high tensile strength of steel and the high compressive strength of concrete.

[0003] However, in the field of railway bridges, the construction and application of steel-concrete composite beams are still relatively rare, but this type of bridge is widely used in the highway field and the technology is becoming 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 of the invention

[0004] In view of this, the purpose of the present invention is to provide a vibration and noise analysis method for a composite box girder bridge with vehicle-bridge coupling, so as to analyze the vibration and noise of a steel-concrete composite beam applied in the field of railway bridges.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention provides a vibration noise analysis method for a combined box girder bridge with vehicle-bridge coupling, comprising the following steps:

[0007] S1. Establish a train-track-bridge coupled vibration model for high-speed railway steel-concrete composite box girder bridges, and compile a train-track-bridge coupled vibration simulation analysis program based on Matlab language and Ansys finite element software;

[0008] S2. Establish a low-frequency noise prediction model for high-speed railway steel-concrete composite box girder bridges, conduct numerical simulations on the low-frequency radiation noise of bridge structures, and derive the low-frequency noise radiation law of bridge structures;

[0009] S3. Establish a prediction model for medium and high frequency noise of high-speed railway steel-concrete composite box girder bridges, conduct numerical simulation of medium and high frequency radiation noise of bridge structures, and derive the laws of medium and high frequency noise radiation of bridge structures;

[0010] S4. In combination with the model established in steps S1-S3, the influencing parameters of the vibration noise of the high-speed railway steel-concrete composite box girder bridge are analyzed, and the analysis results are obtained.

[0011] Wherein, the step S1 is specifically as follows:

[0012] S11, establishing a vehicle dynamics model, the train model includes 8 vehicle trains, each vehicle includes a car body, two bogies and 4 wheel pairs, and each car includes 10 degrees of freedom;

[0013] S12, establishing a track dynamics model, the track model including self-compacting concrete layer, concrete track slab, concrete base slab, steel spring fasteners, rails and other components;

[0014] S13, establishing a bridge finite element model, establishing the bridge model by using the Apdl finite element software, and numerically simulating the dynamic behavior of the bridge structure;

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

[0016] S15, taking track irregularity as an excitation source, and determining that the wavelength range of track irregularity is 0.04-85m;

[0017] S16. Based on the bridge, vehicle and track models established in (1)-(3), the dynamic equations of the train-track-bridge coupling system are obtained;

[0018] S17. Using computer simulation software and finite element software, compile a numerical simulation analysis program model for train-track-bridge coupling dynamics, solve it, and verify the results of the program operation;

[0019] The dynamic equation of the train-track-bridge coupling system in step S17 is:

[0020]

[0021] Where 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.

[0022] Furthermore, in step (7), a 50-fold asynchronous long loading ratio is used to perform dynamic simulation calculations of the train-track-bridge system, that is, the simulation analysis step size of the train and track system is 0.1 ms, and the finite element transient response analysis step size of the bridge is 5 ms.

[0023] Furthermore, the motion equation of a single-section vehicle is:

[0024]

[0025] Where M V is the mass matrix of a single vehicle;

[0026] MV =diag(m w m w m w m w m t J t m t J t m c J c )

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

[0028]

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

[0030]

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

[0032] F V =(2(F w1 -S) 2(F w2 -S) 2(F w3 -S) 2(F w4 -S) 0 0 0 0 0 0)

[0033] Since the damping matrix and the stiffness matrix have similar content forms, we only need to replace the stiffness coefficient k with the damping coefficient c.

[0034] Furthermore, the equation of motion of the orbital dynamics model is:

[0035]

[0036] M R is the overall mass matrix;

[0037]

[0038] K R Overall stiffness matrix;

[0039]

[0040] Z R Track overall displacement matrix;

[0041]

[0042] C RThe damping matrix of the track;

[0043]

[0044] In the formula, α 0,R , α 1，R is the damping coefficient, ξ R is the damping ratio, ω 1，R ,ω 2，R are the self-oscillating circular frequencies respectively.

[0045] Furthermore, when most tracks are not smooth, the wheel-rail force F W The expression is:

[0046]

[0047] Further, the step S2 specifically includes:

[0048] (1) Establish the wave equation in an ideal fluid when the medium is stationary and uniform and the sound wave has a small amplitude;

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

[0050] (3) Using LMS Virtual.Lab Acoustics software, a simulation method for the low-frequency noise radiation model under train load excitation was obtained.

[0051] Further, the step S3 specifically includes:

[0052] (1) Establish theoretical formulas for simulating mid- and high-frequency noise of bridge structures using the SEA method, and derive definitions of the acoustic radiation efficiency, modal density, and loss factor of panels;

[0053] (2) Through Fourier transform and octave processing, a detailed comparative analysis of wheel-rail force and fastener force was carried out, and a method for determining the external excitation force of the bridge deck was derived;

[0054] (3) The specific steps for numerical simulation of medium and high frequency noise radiation were established in the software, and the contribution of different panels to the sound radiation at different field points was analyzed.

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

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

[0057] This technical solution analyzes the vibration and noise reduction of steel-concrete composite beams, and finds that the influence of train speed on the radiation enhancement of medium and high frequency noise is relatively obvious. This is caused by the increase in the peak value data of the fastener force caused by the increase in train speed. On this basis, the influence of the change in the thickness of the bottom slab concrete on the vibration and noise radiation of the bridge structure is analyzed, and it is found that when the thickness of the bottom slab concrete 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 on the vibration and noise reduction effect is not obvious; therefore, the method of analyzing the vibration and noise of steel-concrete composite bridges applied to the field of railway bridges in this technical solution is of great significance to the research and development and design of vibration and noise reduction of steel-concrete composite bridges.

[0058] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art may be taught from the practice of the present invention. The objectives and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

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

[0061] Figure 2 It is a parameter diagram of a single-section vehicle in the present invention;

[0062] Figure 3 is a schematic diagram of the track structure of the present invention;

[0063] Figure 4 is a schematic diagram of the track dynamics model of the present invention;

[0064] Figure 5 It is a schematic diagram of the rail force analysis model in the present invention;

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

[0066] Figure 7 It is a schematic diagram of parameters of track unevenness in the present invention;

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

[0068] Fig. 9 This is a schematic diagram of the asynchronous long loading efficiency in the present invention;

[0069] Figure 10-12It is a schematic diagram of the vertical displacement time history of the rail on the bridge in the present invention;

[0070] Fig.13 and Fig.14 It is the time history diagram of the vertical acceleration of the rail in the present invention;

[0071] Figure 15-17 It is a time history diagram of the dynamic structure response of the bridge in the present invention;

[0072] Figure 18-Figure 20 It is a schematic diagram of the dynamic response spectrum of the bridge structure in the present invention;

[0073] Fig.21 It is a schematic diagram of the mapping rules in the present invention;

[0074] Fig. 22 It is a schematic diagram of the boundary element modeling process in the present invention;

[0075] Fig.23 Schematic diagram of acoustic field points in the present invention;

[0076] Fig.24 It is a schematic diagram of the ground reflected sound analysis in the present invention;

[0077] Figure 25-27 It is a schematic diagram of the transient acoustic simulation results of the field point in the present invention;

[0078] Fig.28 and Fig.29 It is a schematic diagram of the octave-band acoustic simulation results of a mid-point in the present invention;

[0079] Figure 30-Figure 33 This is a schematic diagram of the panel noise contribution result in the present invention;

[0080] Figure 34-Figure 36 This is a schematic diagram of the frequency domain results of the panel noise contribution in the present invention;

[0081] Fig.37 It is a schematic diagram of the total sound pressure level field point of low-frequency noise in the present invention;

[0082] Fig.38 and Fig.39 This is a schematic diagram of the contribution results of the high frequency bridge plate at the C field point in the present invention;

[0083] Fig.40 and Fig.41 This is a schematic diagram of the contribution results of the high-frequency bridge plate at the A field point in the present invention;

[0084] Fig.42 and Fig.43 This is a schematic diagram of the contribution results of the high frequency bridge plate at the B field point in the present invention;

[0085] Fig.44 and Fig.45It is a schematic diagram of the effect of train speed on bridge deck deflection in the present invention;

[0086] Fig.46 It is a schematic diagram of the peak deflection at different train speeds in the present invention;

[0087] Fig.47 and Fig.48 It is a schematic diagram of the effect of train speed on bridge deck and speed in the present invention;

[0088] Fig.49 It is a schematic diagram of the acceleration index of the bridge deck at different train speeds in the present invention;

[0089] Fig.50 and Fig.51 It is a schematic diagram of the effect of train speed on web acceleration in the present invention;

[0090] Fig.52 It is a schematic diagram of the web acceleration index at different train speeds in the present invention;

[0091] Fig.53 and Fig.54 It is a schematic diagram of the effect of train speed on floor acceleration in the present invention;

[0092] Fig.55 It is a schematic diagram of the base acceleration index data at different train speeds in the present invention;

[0093] Fig.56 It is a schematic diagram of the effect of train speed on fastener force in the present invention;

[0094] Figure 57-Figure 59 It is a schematic diagram of the noise radiation results of each field point due to the train speed in the present invention;

[0095] Fig.60 and Fig.61 This is a schematic diagram of the effect of the thickness of the bottom slab concrete on the bottom slab deflection in the present invention;

[0096] Fig.62 and Fig.63 It is a schematic diagram of the effect of the thickness of the bottom plate concrete on the vertical vibration velocity of the bottom plate in the present invention;

[0097] Fig.64 It is a schematic diagram of the fastener force spectrum under different bottom slab concrete thicknesses in the present invention;

[0098] Fig.65 and Fig.66 This is a schematic diagram of the noise radiation result of the bottom plate concrete thickness on the A field point in the present invention;

[0099] Fig.67 and Fig.68This is a schematic diagram of the noise radiation result of the bottom plate concrete thickness on the B field point in the present invention;

[0100] Fig.69 and Fig.70 It is a schematic diagram of the noise radiation result of the bottom plate concrete thickness on the C field point in the present invention;

[0101] Fig.71 It is a schematic diagram of the overall technical route of the present invention. DETAILED DESCRIPTION

[0102] The present invention provides a vibration noise analysis method for a combined box girder bridge with vehicle-bridge coupling, which specifically comprises the following steps:

[0103] Technical route analysis, specific analysis routes such as Fig.71 shown.

[0104] Train-Track-Bridge Coupled Vibration Simulation Model

[0105] Vehicle dynamics model

[0106] The vertical model of a single vehicle of a high-speed railway train analyzed in this scheme is as follows: Figure 1 As shown in the figure, the meanings of the parameters of the vehicle model are as follows: k1 and k2 are the spring stiffness of the primary and secondary suspension systems in the z direction, c1 and c2 are the damping coefficients of the primary and secondary suspension systems in the z direction; d1 and d2 are half of the longitudinal spacing of the primary and secondary suspensions. w 、z t and z c is the vertical motion of wheelset, bogie and car body, and They are the nodding vibration of the car body and the bogie respectively.

[0107] When only the vertical vibration of the vehicle is analyzed, the moment of inertia only needs to be considered. Y The vertical static equilibrium position of the vehicle is taken as the initial position to eliminate the influence of gravity. The motion equation of a single-section vehicle is:

[0108]

[0109] Where M V is the mass matrix of a single vehicle;

[0110] M V =diag(m w m w m w m w m t J t m t J tm c J c ) (1-2)

[0111] K V is the stiffness matrix of a single vehicle;

[0112]

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

[0114]

[0115] F V is the vertical wheel-rail force matrix of a single-section vehicle.

[0116] F V =(2(F w1 -S) 2(F w2 -S) 2(F w3 -S) 2(F w4 -S) 0 0 0 0 0 0) (1-5)

[0117] Damping matrix C V With the stiffness matrix K V has a similar content form, whereby only K needs to be replaced by the damping coefficient c V The stiffness coefficient k in can be used.

[0118] In this proposal, a certain type of EMU train is taken as the research object. Some parameters of a single vehicle can be found in Figure 2 .

[0119] Orbital dynamics model

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

[0121] When only the vertical vibration problem is studied, the rail uses the finite element concept and writes the code in the commercial mathematical software Matlab. The fasteners are simplified to vertical stiffness springs and damping springs. Each concrete component in the track structure is simulated using solid45 entity units in the finite element software Ansys. Figure 4 As shown in the figure, k r is the vertical stiffness of the fastener, c r is the vertical damping of the fastener.

[0122] In the track model established in this plan, the rails are planned to use 60kg / m standard rails. The rails are regarded as infinitely long Euler beams supported by continuous elastic discrete point support foundations. In the process of solving practical problems, the rails should be regarded as finite-length simply supported beams. According to the existing technology, when the distance between the front and rear simply supported ends of the rails is greater than or equal to 30m from the calculated length, the rails can be regarded as infinitely long.

[0123] Figure 5 As shown, F wi It is the force exerted by the wheelset on the rail, referred to as wheel-rail force, and its expression will be given later. The difference between the wheel-rail force in the diagram of this section and the wheel-rail force given later is that the force given later is only the force between the wheel and the rail on one side of the wheelset.

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

[0125]

[0126] In the formula, X Ri , X Bi They are the fastener position x i The displacement of rails and track plates at the location.

[0127] x i =il s (i=1~N) (1-7)

[0128] Where i is the serial number of the fastener, l s is the spacing of the fasteners, which is taken as 0.65m in this paper

[0129] The motion coordinates x of each wheel pair over time wj (j=1,2,3,4) are:

[0130]

[0131] Where x0 is the starting time, the fixed coordinate of the fourth wheelset; t is the motion time variable; and v is the train speed.

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

[0133]

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

[0135]

[0136] Overall stiffness matrix K R The elements are as follows:

[0137]

[0138] The damping matrix C of the rail R Determined by the proportional damping method, as shown in the formula

[0139]

[0140] In the formula, α 0,R , α 1,R is the damping coefficient, ξ R is the damping ratio, ω 1,R ,ω 2,R are the natural circular frequencies respectively. The overall displacement matrix Z of the rail R , the elements are as follows:

[0141]

[0142] F R The elements of are related to the location of the external force. Assuming that the external force F m In the second unit, that is, between nodes 2 and 3, then F R as follows

[0143]

[0144] Some parameters of the orbital dynamics structure used in this scheme can be found in Figure 6 .

[0145] Bridge Finite Element Model

[0146] In this scheme, a high-speed railway ballastless track steel-concrete composite beam with a speed of 350km / h and a span of 48m is selected as the specific research object, and a dynamic analysis is performed on it. The cross section of the bridge adopts a single-box single-chamber composite section, which is composed of a concrete bridge deck and a trough steel box. The steel beam adopts a single-box single-chamber trough section enclosed by a bottom plate, an upper flange top plate and a web plate. Longitudinal stiffening ribs are set on the bottom plate and the web plate. The bridge height is 4.005m and the bridge span is 48.6m. Concrete bridge deck part: the top plate is 12.6m wide, the concrete thickness at the top plate flange is 0.22m, the concrete thickness at the bolt connection is 0.55m, and the concrete thickness at the mid-span is 0.3m. The trough steel box girder part: the upper flange is 1m wide and 0.032m thick; the web is 3.45m high and 0.016m thick; the bottom plate is 6m wide and 0.02m thick; and vertical stiffening ribs are set on the webs between adjacent diaphragms at intervals of 1m, where the ribs are 0.02m thick; the basic spacing of the diaphragms is 4m and the thickness is 0.02m. The steel material of the entire bridge is Q370qE steel, and the concrete is C55 concrete. This scheme involves medium and high frequency vibration and noise responses, which require refined modeling. The steel structure is established using the shell element Shell181, and the steel structure should include diaphragms, longitudinal stiffening ribs, vertical stiffening, etc. The concrete bridge deck is established using the solid element Solid45.

[0147] After the geometric model is meshed, the finite element mesh division method affects the calculation accuracy and efficiency of the model. The factors considered in determining the unit length of the finite element model established in this scheme are:

[0148] The maximum unit size of the bridge model is less than or equal to one sixth of the vibration wavelength. The bridge model is mainly subjected to bending, and the bending wave velocity C in the plate structure is b It can be expressed as:

[0149]

[0150] Among them, μ represents the Poisson's ratio of the material used in the structure; E represents the elastic modulus of the structure; ω represents the upper limit of the circular frequency of the problem being analyzed; ρ is the density of the material used; and h represents the thickness of the structural plate. And the wavelength and wave speed satisfy the following formula:

[0151]

[0152] Then the maximum element size e of the finite element model is max ,satisfy:

[0153]

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

[0155]

[0156] In the formula, c represents the speed of sound, f max Represents the highest frequency calculated.

[0157] Too dense a grid will cause a long model calculation time, generate a result file that occupies a large amount of memory, and waste too much computing resources. Based on the above influencing factors and referring to relevant existing technologies, the unit length is taken as 0.25m.

[0158] The stiffness and mass of the bridge itself will affect the natural frequency, and the natural frequency has nothing to do with the motion state of the structure. In the design process of railway bridges, the indicator for evaluating the dynamic performance of bridges is the vertical natural frequency of the bridge. According to the provisions of the "High-speed Railway Design Code", the span of the bridge model built in this section is 48m. According to the code, the minimum limit of the first-order frequency of a simply supported beam with a span of 48m is 2.38Hz. The first-order frequency in this scheme is 3.2Hz, which meets the requirements of the code. In order to better simulate the medium and high frequency responses of the structure, the complete integration method is used in Ansys to solve the transient dynamic response of the bridge structure. The transient analysis of bridges performed in Ansys is essentially still solving the dynamic equations, as shown in the following formula:

[0159]

[0160] In this scheme, Rayleigh damping is used to describe the damping size of the structure. The damping matrix C of the bridge is B Determined according to the proportional damping method, as shown in the following formula:

[0161]

[0162] In the formula, α 0,B , α 1,B is the proportional damping coefficient; ξ B is the damping ratio, which is usually taken as 0.04 for steel-concrete composite structures.

[0163] F B is the force exerted by the fastener on the bridge structure, F B The elements are as follows:

[0164] F B =(F k1 F k2 F k3 F k4 Fk5 … … F kn ) (1-21)

[0165] Where n is the number of fasteners on the bridge, F ki The calculation formula has been given in the previous article.

[0166] Wheel-rail interaction model: The model constructed in this scheme is a vertical model, and the wheel-rail relationship only involves the solution of the wheel-rail normal force.

[0167] In this scheme, the Hertz nonlinear contact model is used to calculate the vertical wheel-rail force F w Perform calculations.

[0168]

[0169] Where G is the contact constant between the wheel and rail, and Δ is the normal elastic compression between the wheel and rail contact points.

[0170] Common wheels for high-speed railway passenger cars:

[0171] G=4.57R w -0.115 ×10 -8 (1-23)

[0172] In the formula, R w is the radius of the wheel rolling circle (m), in this paper, R w =0.46m.

[0173] When only vertical vibration is considered, the wheel-rail normal elastic compression Δ can be regarded as the wheel static compression Δ0 caused by the average static wheel weight S and the vertical displacement Zw of the wheelset and the vertical displacement Z r (x w ) is the superposition of the difference between the two parts, so Δ can be expressed as:

[0174] Δ=Z r (x w )-Z w +Δ0 (1-24)

[0175] In the formula, the static compression of the wheel is:

[0176]

[0177] In the formula, the calculation formula for the average static wheel weight (wheel on one side of the wheelset) is:

[0178]

[0179] Where g is the acceleration due to gravity.

[0180] When Δ<0, the wheel-rail force F w=0, indicating derailment.

[0181] like Figure 7 As shown in the figure, when track irregularity δ(x) exists at the wheel-rail contact interface, the wheel-rail force F w The expression is:

[0182]

[0183] Track irregularity is defined as the relative difference between the track contact surface and the theoretical track surface, and is the excitation source of the large system vibration dynamics in this chapter. According to the track irregularity in different directions, track irregularity can be divided into direction, height, gauge and horizontal irregularity. The y direction irregularity of the left and right rails is defined as y l ,y r , the unevenness of the left and right rails in the z direction is z l 、z r , height unevenness, direction unevenness, level unevenness, track gauge unevenness, left-right track direction unevenness, left-right track height unevenness can be expressed as:

[0184]

[0185] Δz i =z l -z r (1-30)

[0186] Δy i =y l -y r (1-31)

[0187]

[0188] The main track irregularity spectrum used in this paper is the irregularity spectrum of high-speed railway ballastless track, which is fitted piecewise according to the following formula:

[0189]

[0190] In the formula, f is the spatial frequency; S(f) is the power spectrum density; A and K are fitting coefficients, which are divided into sections according to Table 2-5.

[0191] The applicable range of the unevenness wavelength of the ballastless track unevenness spectrum of high-speed railway is 2 to 200m. In order to meet the simulation requirements of the medium and high frequencies of noise in this scheme, the vibration response of the medium and high frequencies needs to be obtained, so the short-wave unevenness of the wheel-rail interface contact needs to be considered. This scheme intends to adopt the track high and low short-wave unevenness spectrum proposed by Sato. The wavelength range of this spectrum is 0.01 to 2m, and its power spectrum density function expression is:

[0192] S c (Ω)=A0Ω-3 (1-37)

[0193] In the formula, S c (Ω) is the power spectral density (m 2 / (1 / m)), Ω is the spatial circular frequency (rad / m), A0=2.41×10 -8 .

[0194] Track irregularity is used as an external excitation, and the range of wavelengths affects the frequency range for solving the vehicle-track-bridge coupling problem. From the perspective of driving comfort, the long-wave wavelength of track irregularity should reach 85m. Considering the maximum research frequency of 2000Hz of the vibration noise of the steel-concrete composite structure, the short-wave wavelength of track irregularity should be less than 0.04m. Therefore, the wavelength range of track irregularity in this scheme is 0.04~85m.

[0195] Establishment and solution of vehicle-track-bridge system equations: Based on the bridge, vehicle and track dynamics models established in this chapter, the dynamics equations of the coupled large system in this chapter can be obtained, as shown in the following equation:

[0196]

[0197] Where 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. 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 fasteners; for the bridge system, the external load vector is the vertical force applied to the bridge by the track through fasteners.

[0198] The dynamic equations of the vehicle-track-bridge coupling system are a large and complex set of equations involving nonlinearities, including nonlinearities in the contact force between the wheel and the rail, and require an accurate and stable numerical simulation algorithm to solve. In this solution, for finite element structures such as bridges and track plates, the Newmark integration method built into the Ansys software is used to perform a complete transient response analysis and solution; as for the vehicle-track system, the Newmark integration method programmed in Matlab is used to solve it. From the above theoretical analysis, it can be seen that the vehicle-track-bridge coupling vibration is extremely complex, such as Figure 8 As shown, it is necessary to use computer simulation software to calculate and solve.

[0199] Analysis method considering asynchronous long loading

[0200] In the process of structural transient dynamic analysis, choosing the appropriate time integration step determines the running time of the model and the correctness of the problem solving and the accuracy of the convergence effect. For general problems, the smaller the integration time step, the higher the accuracy of the calculation results, which requires higher-configuration computer hardware and greater power consumption; the larger the integration time step, the more accurate the solution of higher-order response simulations will inevitably be affected. Therefore, according to the characteristics of the problem to be solved in this solution, the following two factors will be considered in determining the time step of transient analysis:

[0201] (1) Relationship between time step and maximum response frequency of the structure

[0202] The dynamic response of the structure can be regarded as the combined dynamic modal responses of various orders. The maximum value of the time step should be able to solve the structural response of the highest-order mode, then Δt satisfies the following formula:

[0203]

[0204] In the above formula: f is the highest-order frequency of the structure required for the problem being analyzed.

[0205] (2) Relationship between integration time step, grid size, and driving speed

[0206] In this scheme, the fastener force load applied to the bridge changes with time. The size of the grid unit has been determined in the previous section. Assuming that the length of the finite element grid unit is L and the train speed is V, Δt satisfies the following formula:

[0207]

[0208] In the vehicle-track-bridge coupling dynamic analysis model, the wheel-rail contact frequency is relatively high. After multiple calculations, the maximum stable step length of the wheel-track contact algorithm in this program is about 0.1ms. After every n analysis steps, a transient response analysis is performed on the bridge finite element structure. Considering the problem solving accuracy and solution efficiency, this solution uses a 50-fold asynchronous long loading ratio for the dynamic simulation calculation of the vehicle-track-bridge system, that is, the simulation analysis step length of the train and track system is 0.1ms, and the transient response analysis step length of the bridge finite element is 5ms.

[0209] Comparison of the simulation results of the dynamic behavior of trains, tracks and bridges under different asynchronous length ratios. Fig. 9 It can be analyzed that the asynchronous long loading ratio has a significant impact on the calculation efficiency. If the model in this scheme is calculated with an equal time step, the single model calculation time is expected to be up to 8 days. If the 50-fold asynchronous length calculation method proposed in this scheme is used, the calculation time can be reduced to 4 hours.

[0210] Program running results and verification

[0211] In order to judge the accuracy of the calculation results of the high-speed railway vehicle-track-bridge coupling dynamics simulation analysis program written in this chapter, an 8-car train with a speed of 300km / h passing through a 48m span simply supported steel-concrete composite box girder bridge is used as an example to verify the program written in this chapter based on the Matlab language. The results show that the simulated results in this scheme meet certain accuracy requirements, and the relative error comes from the differences in several input parameters.

[0212] Time domain result analysis: Figure 10-12 The program compiled in this scheme extracts some time domain results of the displacement, velocity and acceleration data of the bridge, rail and train at any time. As shown in the figure, under the action of the train load, the maximum vertical displacement of the mid-span node of the bridge deck is 3.2mm; the vertical displacement time history of the rail on the roadbed (not on the bridge) is more periodic, 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 the analysis shows that Fig.12 The result can be regarded as Fig.10 and Fig.11 That is, the total displacement of the rails on the bridge under train load is equal to the sum of the displacements of the bridge and rails under train load. Fig.12 The middle curve clearly shows the entire process of the train going up and down the bridge; the displacement of the rails 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.

[0213] like Fig.13 and Fig.14 It is concluded that the wheel-rail force time history curve Fig.13 It is relatively dense, indicating the contact force between a single wheel on the wheelset and the rail, rather than the wheel-rail contact force of the entire wheelset. The curve generally fluctuates around 56kN, which is related to the static wheel weight of the wheel. The fluctuation range of -50 to 50kN reflects the medium and high frequency characteristics of the vehicle-bridge coupling problem analyzed in this solution. Under the direct action of this high-frequency excitation force, the vibration of the rail also shows the characteristics of high frequency and obvious periodicity. The peak value of the acceleration of the rail node can even reach 500m / s 2 .

[0214] like Figure 15-17 The result time history curve of the bridge shows that the vibration amplitude of the bridge deck flange is significantly greater than that of the mid-span position. This is related to the thickness of the plate and the distance from the applied excitation position. The train load of the model in this scheme is unidirectional loading, and the bridge deck flange is closer to the loading position. In the steel structure part, the vibration intensity of the bottom plate is stronger than that of the web, which provides ideas for studying the vibration reduction and noise reduction of this type of bridge. The displacement curves of the various components of the concrete part are almost overlapping, but it can still be seen that the vertical displacement of the upper component is greater than that of the lower component, reflecting the vibration reduction and isolation characteristics of the concrete structure.

[0215] Frequency domain result analysis: The time domain vibration signal of the vehicle-track-bridge dynamic analysis result is expanded in the frequency domain, output as a frequency-related function, and the distribution law of the signal is studied, which is called dynamic spectrum analysis. The vehicle-track-bridge vibration signal is decomposed into several frequency components to obtain the frequency structure of the vibration signal and the amplitude information of each harmonic of the signal. Furthermore, the filter function of eliminating noise on the input signal can be realized.

[0216] The application of fast discrete Fourier transform (FFT) algorithm has been very mature and applied to the frequency domain processing of vibration signals of vehicle-bridge coupling results. In this scheme, Matlab self-written program is used to process the vibration time domain data of bridge components, and the frequency domain results of bridge structure dynamic behavior are obtained as follows: Figure 18-Figure 20 .

[0217] This technical solution selects the frequency domain results of asynchronous long loading ratio of 25 for analysis, that is, the transient analysis time step in Ansys is 2.5ms. According to the sampling theorem, the spectrum results within 200Hz can be obtained. Analysis shows that because the analyzed frequency is relatively low frequency, the dynamic response curves of bridge components with different material properties overlap; and the overall low-frequency characteristics are shown, that is, the main energy is concentrated in the low-frequency band on the left side of the spectrum; among them, the main energy of the displacement and velocity spectrum is concentrated below 10Hz, and the acceleration spectrum energy is mainly concentrated within 100Hz. Its peak at 128Hz is caused by the modeling method of the rails, which is related to the spacing of the fasteners and the speed of the train. The calculation formula will be given later.

[0218] In summary, this chapter, based on the vehicle-track-bridge large system coupling dynamics analysis theory, established a vehicle-track-bridge coupling vibration simulation analysis model for high-speed railway steel-concrete composite structure bridges, compiled a high-speed railway vehicle-track-bridge coupling vibration simulation analysis program based on Matlab language and Ansys finite element software, and verified the accuracy of the program. Specifically:

[0219] (1) Based on the vehicle-track-bridge coupled dynamic analysis theory, a vehicle-track-bridge coupled vibration simulation analysis model for a high-speed railway steel-concrete composite bridge was established. In the model, a high-speed railway four-axle locomotive model with 10 degrees of freedom was established based on multi-rigid body dynamics; the rails were simplified by the finite element method, and the 60kg / m rail dynamic model commonly used in railways was established. A certain type of slab track structure of high-speed railway was established in the finite element software Ansys; the high-speed railway steel-concrete composite bridge was established using the Ansys finite element software. The steel structure was simulated using SHELL units, the concrete bridge deck was established using SOLID units, and the steel and concrete were connected using the MPC algorithm; the track unevenness was fitted using the high-speed railway ballastless track unevenness spectrum, and the track short-wave unevenness was considered; the vertical wheel-rail force was calculated using the Hertz nonlinear elastic contact theory; the model used the Newmark integral method to solve the bridge dynamic response and the vehicle-track system dynamic response.

[0220] (2) A high-speed railway vehicle-track-bridge coupled vibration dynamics simulation analysis program was compiled based on the Matlab language. By building an overall calculation framework in the Matlab language, establishing a train and track model, and calling the Ansys software to build a bridge finite element model, the dynamic simulation solution of the train-track-bridge system is realized through the data exchange of the contact points between the track and the bridge within the analysis step. In order to improve the calculation efficiency of the program, the analysis method of asynchronous long loading is considered, and the influence of different asynchronous long loading ratios on the system dynamic response results is compared. After comprehensively comparing the calculation accuracy and calculation efficiency, a 50-fold asynchronous long loading ratio is selected for the dynamic simulation analysis of the train-track-bridge system.

[0221] (3) Taking a train running at a speed of 300 km / h passing through a high-speed railway simply supported composite box girder bridge with a span of 48 m as an example, a large system dynamic vibration simulation analysis was carried out, and the response results were compared with relevant existing technologies. The results showed that the simulation accuracy of the self-compiled program is reliable.

[0222] (4) The simulation results of the vehicle-track-bridge are analyzed in the time domain and frequency domain, and some time-frequency laws of the vehicle-bridge coupled vibration response are given.

[0223] Low-frequency noise prediction model for high-speed railway steel-concrete composite beams

[0224] Basic assumptions of numerical simulation of low-frequency noise

[0225] (1) The simulated sound waves are small amplitude waves in a uniform, stationary ideal fluid in the air.

[0226] (2) The acoustic-solid coupling interaction is not considered.

[0227] (3) Noise sources other than the bridge structure are not considered.

[0228] In this scheme, the acoustic boundary element module in LMS Virtual.lab is used to numerically simulate the low-frequency noise of the bridge structure. The LMS boundary element method requires that the unit size of the acoustic grid satisfies formula (1-18): The upper limit frequency of the boundary element analysis method in this scheme is 100Hz. Substituting it into formula (1-18), the maximum unit size of the acoustic grid is about 0.56m. To ensure the simulation accuracy, the acoustic grid size is controlled to 0.25m in this scheme.

[0229] Set the number of influencing nodes to 4 and the maximum distance to 0.3m. This means that with the acoustic mesh node as the center, the four finite element mesh nodes closest to the point are searched within a circular range of 300mm in radius for data mapping. Fig.21 As shown:

[0230] The value of the target node can be determined according to the value of the source node based on the following mapping relationship:

[0231]

[0232] The specific acoustic boundary element simulation process is as follows: Fig. 22 In order to explore the spatial distribution law of radiation noise of simply supported composite box girder bridge structure, the cross section of the bridge span is taken as the reference plane, and the spatial noise calculation points are selected as follows Fig.23 As shown. Taking the bottom plate of the bridge centerline as the origin, the field points are selected along the height direction at 4.0m at the bottom of the beam, the bottom of the beam, the top of the beam and 3.5m at the top of the beam, and along the horizontal direction at 5m, 10m and 20m at the center line of the bridge and the center line of the track, for a total of 28 noise calculation points. In order to display the distribution law of noise in detail in the software, the interval between 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 effect of the rigid ground on sound waves is considered. To simplify the analysis. As Fig.24 As shown in the figure, the reflected sound from the sound source S to the field point P is equivalent to the sound from the image sound source S1 directly propagating to the field point P. The distance between the bridge bottom plate and the ground is 10 meters, and a symmetrical plate is used to simulate the ground in the model. It takes 2.5 seconds for the train to go from the bridge to the bridge. The time domain transient acoustic radiation is taken at three moments, namely the moment when the train goes on the bridge (t = 0.05s), the moment when the train is on the bridge (t = 1.5s), and the moment when the train goes off the bridge (t = 3.5s) to compare the bridge structure noise radiation at different moments.

[0233] From the sound field sound pressure cloud map at different times, it can be clearly seen that as the train passes, the noise radiated by the bridge structure changes from small to large, and then from large to small. The distribution law of sound radiation in space can be clearly seen. The value of sound radiation decreases with the increase of the distance from the bridge. The vehicle load of this model is unidirectional loading, which is also the reason for the asymmetry of the sound field cloud map. The field point noise on one side of the vehicle load is significantly greater than the other side. During the process of the train going up the bridge, it can be seen that the sound radiation has not yet reached the measuring point far from the bridge and is still 0dB. When the train is on the bridge, the maximum sound pressure level of the field point can reach 100dB. After the train goes down the bridge, the various plates of the bridge undergo damped free vibration. It can be seen that the sound pressure level inside the bridge is significantly greater than that outside.

[0234] like Figure 25-27 As shown in the figure, the noise time-frequency curves of the three field points A, B, and C are extracted and analyzed, and the following conclusions can be drawn. Analyzing the time domain diagram, from the 2.5s moment, the sound pressure level curve drops rapidly, which can be judged that the train is in the stage of getting off the bridge during this period. Observing the amplitude of the curve, the field points A and B are relatively close in the time domain diagram, and it is difficult to compare the size, but it is much larger than the result of the field point C, which is in line with the basic law that noise decreases with increasing distance. Analyzing the spectrum diagram, it can be seen that the energy is mainly concentrated in the low-frequency band. As the frequency increases, the sound pressure level amplitudes of the three curves are all decreasing, which is consistent with the law described in the previous chapter that the vibration energy is concentrated in the low-frequency band. Fig.26 The result of linear weighting is obtained by performing A weighting on the data. Fig. 27 From the results, we can see the suppression effect of A-weighting on low-frequency noise. The A-weighted results in this scheme are only for comparison, and the other noise radiation results are given as unweighted results.

[0235] The solution range of bridge low-frequency noise is 0-100Hz, but the hearing range of human ears is above 20Hz, so the effective range of the analysis result is 20-100Hz. The noise spectrum is processed into one-third octave band, such as Fig.28 shown and in Fig.28 Based on the A weighting treatment, Fig.29 As shown. The trends of the sound radiation curves of the three field points are basically the same. The A-weighting has a significant suppressive effect on low-frequency noise, and the curve drops significantly around 80Hz. The maximum sound pressure level among the three field points appears at field point B. The dynamic analysis results in the previous chapter also show that the vibration amplitude of the bottom plate is large. This field point is close to the bottom plate. It is 80dB under linear weighting and 45dB under A-weighting, reflecting the huge contribution of the steel bottom plate in the steel-concrete composite beam to the low-frequency vibration noise radiation. The contribution of different plates of the bridge structure to the low-frequency noise radiation of field points A, B, and C at frequencies of 12.5Hz, 25Hz, 50Hz, and 100Hz was analyzed, and the following results were obtained. Figure 30-Figure 33 shown.

[0236] The results show that except for the negative value of the web and bottom plate noise contribution to the field point at 100Hz, the rest are positive values. The negative value means that the contribution is small and lower than the reference sound pressure. Compared with the positive value, it also has physical meaning. Analysis shows that the top plate contributes the most to the A field point, and the bottom plate contributes the most to the B field point. The total contribution of the panel noise mainly comes from the lower frequency band.

[0237] Figure 34-Figure 36 The noise contribution of different panels to the A, B, and C field points at each single frequency within the solution frequency range is given. Among them, the panel contribution curve that is closer to the total sound pressure level curve indicates that this panel contributes the most to the sound pressure level of the field point. The panel contribution curve located at the lower part of the total sound pressure level curve and farther away indicates that it contributes less to the sound pressure level of the field point, or plays a negative role. Field point A is located at the upper part of the top plate. Fig.34 It shows that the top plate contributes the most to the noise radiation of this field point; field point B is located at the bottom of the bottom plate. Fig.35 It shows that the bottom plate contributes the most to the noise radiation of this point; the C point is far away from the bridge structure sound source, and its simulation results Fig.36 It shows that in the lower frequency band, the concrete top plate contributes more to the noise radiation of the point, while in the medium and high frequency bands, the steel bottom plate contributes more to the noise radiation of the field point. Comparing the positive and negative contributions of different plates to the field points at different frequencies can provide ideas for reducing bridge structure noise.

[0238] The software can give the sound pressure level value at any field point at different frequencies, but cannot obtain the total sound pressure level cloud map. In this scheme, the sound pressure levels at different frequencies are manually superimposed according to the total sound pressure level formula of the acoustic field point (existing technology), and the total sound pressure level of each field point can be calculated. The calculation results of the total sound pressure level of each field point are summarized to obtain the following: Fig.37 The total sound pressure level field point diagram of acoustic radiation. The results show that the total sound pressure level near the mid-span of the bridge bottom plate is the largest, with a maximum total sound pressure level of 100dB, and the total sound pressure level of the acoustic field point on the left side of the bridge is significantly greater than that on the right side, which is related to the one-way train driving mode simulated in this scheme. In addition, the noise radiation value near the middle and lower part of the bridge structure is greater than the noise radiation result near the top plate, indicating that the noise radiation capacity of the steel web and steel bottom plate is stronger than that of the concrete top plate. The farther away from the bridge structure, the weaker the sound radiation attenuation.

[0239] In summary, based on the basic parameters of acoustics and the basic formulas of acoustic external field radiation problems in the existing technology, using the LMS software and relying on the boundary element method, the numerical simulation of the low-frequency radiation noise of the bridge structure was carried out, and the low-frequency noise radiation law of the bridge structure was given. Using the LMS Virtual.Lab Acoustics software, the low-frequency noise radiation model of a 48m steel-concrete composite simply supported beam under the excitation of a train load of 300km / h was simulated. The simulation results of the noise radiation show that the overall total sound pressure level field point map is symmetrically distributed; 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 attenuation degree of the sound radiation; the floor and web of the steel structure part in the bridge contribute more to the noise at each field point, and each plate contributes more to the noise at the nearby field points; the established low-frequency total sound pressure level values of the acoustic field points are distributed in the range of 70dB to 100dB.

[0240] High-noise prediction model for steel-concrete composite beams in high-speed railways

[0241] Sound radiation of bridge structure plates: In order to obtain the noise radiation situation at a certain point at a certain distance from the bridge plates, the following simplifications are needed, that is, the steel-concrete composite beam bridge is regarded as composed of a subsystem of multiple rectangular plates with a length of m and a width of n. Then, for each subsystem, the radiated sound power is:

[0242]

[0243] In the formula, ρ a is the density of air, c a is the speed of sound in air, σ i and S i are the radiation efficiency and surface area respectively, is the mean square velocity. Let the vertical distance from the measurement point M to the subsystem be r.

[0244] When r ≤ n / π, it indicates that the measurement point M is close to the sound source. At this time, the sound wave is regarded as a plane wave with a constant sound pressure, then:

[0245]

[0246] When n / π < r ≤ m / π, it indicates that the measurement point M is far 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:

[0247]

[0248] When m / π < r, it indicates that the measurement point M is very far from the sound source. At this time, the mean square value of the sound pressure at the measurement point C is:

[0249]

[0250] The sound pressure level at any point in the sound field outside the bridge structure can be obtained by linear superposition according to the above formula. The plate noise contribution refers to the sound pressure caused by each plate of the bridge structure at the field point. By comparing and analyzing the plate noise contribution with the total structural noise, it is possible to analyze which type of plate plays a major role in the bridge structure noise, thereby providing ideas for vibration and noise reduction of the bridge structure.

[0251] The noise of steel box composite beam structure is mainly composed of three types of plates: top plate, bottom plate and web plate. The contribution of plates such as diaphragm and stiffening rib is relatively small. The noise contribution of a certain plate to a certain acoustic field point at a certain frequency can be expressed by the following formula:

[0252]

[0253] Where η i Lp is the structural noise contribution of a panel at frequency i. 1,i and p 1,i They represent the sound pressure level and sound pressure generated by a panel at the measuring point at frequency i, respectively. Lp i and p i They respectively represent the total sound pressure level and total sound pressure generated by all panels at the measuring point at frequency i.

[0254] Modal density: The number of modes within a unit frequency bandwidth is called modal density. It can reflect the system's ability to store energy. For the bridge noise radiation problem analyzed in this solution, most structures can be simplified into plate structures, and mathematical methods can be used to give the modal density analytical expression of simple substructures. For a vibrating plate, its modal density expression is as follows:

[0255]

[0256] In the formula, c B represents the bending wave velocity, S represents the area of ​​the plate, and t represents the thickness of the plate.

[0257] It can be seen that the modal density is proportional to the plate area and inversely proportional to the plate thickness. In the medium and high frequency range, the boundary conditions have no effect on the modal density. Therefore, the SEA simply supported bridge model established in this chapter is different from the finite element method or boundary element method in that the SEA method only establishes the plate without any constraints.

[0258] Internal loss factor η i is defined as the ratio of energy loss per unit time to average stored energy during the vibration period of the subsystem. It is generally believed that for any subsystem, the damping of the system is usually determined by no more than three damping mechanisms. The internal loss factor of the structural subsystem can be expressed as:

[0259] η i =η is +ηir +η ib (1-48)

[0260] Where η ib is the boundary connection damping of the structural subsystem; η is is the damping caused by friction in the structural subsystem; η ir is the vibration and acoustic 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%.

[0261] Coupling loss factor: The subsystems are coupled through mutual connection. Based on the coupling, the energy of the directly excited subsystem is transferred to the subsystem that is not directly excited. Coupling loss factor η ij is defined as the transmission loss energy of two mutually coupled subsystems i and j at the connection. The calculation formula of the coupling loss factor used in this scheme refers to the calculation expression of the coupling loss factor between boards connected by lines given in the works of RHLyon et al.

[0262]

[0263] In the formula, τ 12 : wave propagation coefficient from structure 1 to structure 2; l: length of line connection; C g : group velocity; surface area of ​​A1 substructure 1; ω: center frequency of the frequency band.

[0264] Determination of the external excitation force of the bridge deck subsystem. The high-frequency wheel-rail force between the train wheelset and the rail directly affects the external excitation force on the bridge deck subsystem, so it is necessary to analyze the wheel-rail force data. First, the wheel-rail force time history of a certain wheelset is extracted, and fast Fourier transform and octave band data processing are performed.

[0265] The wheel-rail force time history diagram obtained after processing shows that the curve is relatively dense. The spectrum diagram is analyzed and the data is distributed within 2000Hz, which is related to the lower cutoff wavelength of the short-wave track unevenness. It is observed that the image has obvious peaks at 128Hz and 256Hz, which is related to the modeling method of the rail and is specifically affected by the length of the rail unit. The wheelset passes through the rail unit periodically and is subject to periodic wheel-rail force. The frequency can be calculated using the following formula:

[0266]

[0267] Therefore, the spectrum graph has peaks at frequencies that are multiples of 128 Hz.

[0268] In order to effectively analyze the frequency domain data of wheel-rail force, the data was processed by one-third octave band. The results showed that the image had an obvious upward trend within 200Hz, which was mutually verified with the existing technology. The fastener force time history diagram shows that the fastener force can reach a maximum of 40kN, showing obvious periodic characteristics. The spectrum diagram shows that the fastener force has a peak value within 10Hz, which can reach 5.5kN. The octave band diagram shows that the fastener force still has data distribution after 1000Hz, showing the medium and high frequency characteristics of the fastener force. At the same time, combined with the frequency band analyzed in this section, the spectrum data of 100~1000Hz is extracted for solving the external excitation force of the bridge deck. The original fastener force data is subjected to 100Hz high-pass filtering and Fourier inverse transformation to obtain the filtered rail force time history curve. It can be concluded that the exciting force applied by the rail to the bridge has an obvious periodic law.

[0269] The longitudinal length of the bridge deck built in the VAONE model is 4m, and the longitudinal spacing of the fasteners is 0.65m. Considering that the fasteners are symmetrically distributed along the center line of the track, the number of fasteners in a bridge deck is 12. According to the principle of SEA, the position of the load does not affect the force of a certain SEA plate, that is, the force applied to the same SEA plate subsystem can be superimposed, so the force of all support springs on the same bridge deck subsystem can be superimposed and applied to the corresponding plate subsystem in the form of concentrated force. The force transmitted to the bridge is defined as: when the train load acts on the rail, the square root of the sum of the squares of the forces of each support spring. The specific calculation method is shown in the formula:

[0270]

[0271] In the formula, F b is the external force on the bridge deck subsystem, M is the number of fasteners on the bridge deck, and f n is the force exerted by the nth fastener spring on the bridge deck subsystem.

[0272] Simulation results of medium and high frequency noise: Compared with field points A, B and C, field points A are closer to the sound source, and the radiated sound pressure level is also significantly greater than that of field point C. The law of sound pressure level changing with frequency, that is, the law of upward surge at 100Hz and 1000Hz, is similar to the change 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 maximum value of field point A is 88dB at 100Hz. The values ​​of the three field points in each frequency band are all above 65dB. And at the end of the analysis frequency range, 1000Hz, there is a sudden change, indicating that the noise prediction value at this point is inaccurate.

[0273] The vibration velocity data of each bridge plate was extracted, and it was found that the average vibration velocity of the concrete plate was much smaller than that of the steel structure. The total vibration level of the concrete plate was 127dB. The steel plates had similar vibration conditions due to the same thickness, similar size, and no direct load, and their average total vibration level was about 138dB.

[0274] Figure 38-Figure 43 The noise radiation contribution of different bridge structure plates to the three acoustic field points A, B and C is given. Field point A is located at the top of the bridge structure, and the contribution of the bottom plate to this field point is relatively small in the whole frequency band. The concrete top plate plays a major role in the noise contribution to this field point, and the noise contribution value of the concrete top plate to this field point can reach 92dB.

[0275] Field point B is located at the bottom of the bridge structure, and the contribution of the bottom plate to this field point is greater than that of field point A. In the low-frequency band, the concrete top plate plays a major role in the noise radiation value of this field point. After 250Hz, the radiation efficiency of the steel structure part increases, and its contribution to this field point is greater than that of the concrete part.

[0276] Regarding the contribution of the bridge bottom plate, bridge top plate and bridge web to the medium and high frequency noise radiation of the A, B and C field points, according to formula 1-46, the calculation results show that the bottom plate contributes the most to the B field point among the three acoustic field points, which is 24%, and the noise contribution ratio of the web to the three field points is relatively close, with an average contribution rate of 17%; the plates with the largest contribution rate to the three field points are all concrete top plates, and their contribution rates to the A, B and C field points are 61%, 56% and 36% respectively.

[0277] In summary, the basic parameters of the statistical energy method are introduced, the power flow balance equation of the bridge structure is derived, and the medium and high frequency radiation noise of the bridge structure is numerically simulated using the VAONE software based on the statistical energy method, and the medium and high frequency noise radiation law of the bridge structure is given. The main contents and conclusions of this chapter are:

[0278] (1) First, the theoretical formula for simulating the medium and high frequency noise of bridge structures using the SEA method was derived, including the definitions of the acoustic radiation efficiency, modal density, and loss factor of the plate. (2) The wheel-rail force and fastener force mentioned in the previous section were extracted, and a detailed comparative analysis of the two data was conducted through Fourier transform and octave processing. A method for determining the external excitation force of the bridge deck was given, and the results showed that the fastener force spectrum was at 128 Hz, and it was pointed out that the reason for the peak was related to the train speed and the length of the rail unit. (3) The specific steps of numerical simulation of medium and high frequency noise radiation in the software are introduced in detail. After obtaining the results of medium and high frequency noise radiation, the contribution of different plates to the sound radiation of different field points is analyzed, and the following conclusions are drawn: the radiation efficiency of the concrete top plate is significantly greater than that of the steel structure plate below 500Hz. After 500Hz, the radiation efficiency of the steel structure is greater than that of the concrete top plate; in general, the contribution of the top plate to the sound radiation is greater than that of the steel structure. The average contribution of the concrete top plate to the three acoustic field points built in this scheme is as high as 50%; the contribution of the bottom plate and web of the steel structure to noise cannot be ignored. It is necessary to conduct an in-depth study on the vibration reduction and noise reduction performance of the steel bottom plate.

[0279] Analysis of parameters affecting vibration and noise of composite box girder bridge

[0280] When a train passes through a bridge at high speed, it will produce a huge impact force on the bridge, which will cause the bridge to generate structural noise, which will 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 generated by the bridge structure is different. Therefore, studying the influence of different speeds on noise is of great significance for vibration reduction and noise reduction. This section uses 50km / h as an interval and calculates the vibration sound radiation results of the train passing the bridge at 200km / h, 250km / h, 300km / h and 350km / h through the model.

[0281] The impact of train speed on vibration: In this scheme, peak speed and root mean square speed are used as indicators to evaluate vibration. The peak value is the maximum 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, summed, and finally squared within a certain period of time. The calculation formulas for the peak vibration speed and the effective speed are as follows:

[0282]

[0283] Fig.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; Fig.45 The figure shows the change of the maximum vertical deflection value with vehicle speed; the specific value is shown in Fig.46 . Fig.44It is shown in the figure that when the train runs at a lower speed, the displacement time history curve is relatively smooth and the waveform is relatively complete. It can be clearly seen that as the speed increases, the train bridge crossing time is shortened and the vibration amplitude is significantly reduced; Fig.45 It is shown that within the train speed range simulated in this scheme, that is, within the range of 200 to 350 km / h, as the train speed increases, the peak mid-span deflection decreases from 3.5 mm to 3 mm. Figure 47-Figure 49 The vertical acceleration response time history of the mid-span node of the bridge deck under different train speeds is given, and the peak acceleration value and the effective value of acceleration under different speeds are extracted for comparison. The peak acceleration value under different speeds and the time when the train enters the bridge at this time are shown in Fig.49 .

[0284] Fig.47 It is shown in the figure that as the vehicle speed increases, the vibration amplitude of the acceleration time history curve increases significantly; Fig.48 It is shown that within the train speed range simulated in this scheme, that is, within the range of 200 to 300 km / h, the increasing trend of the effective value of acceleration is not obvious as the speed increases. However, within the range of 300 to 350 km / h, the effective value of acceleration and the peak value of acceleration change dramatically, almost increasing exponentially, and it is speculated that resonance may occur. Figure 50-Figure 52 The acceleration response time history of a node on the web under different train speeds is given, and the peak acceleration value and effective acceleration value under different speeds are extracted for comparison. The peak acceleration value under different speeds and the time when the train goes on the bridge at this time are shown in Fig.52 . Figure 53-Figure 55 The acceleration response time history of a node on the floor at different train speeds is given, and the peak acceleration value and effective acceleration value at different speeds are extracted for comparison. The peak acceleration value at different speeds and the time when the train goes on the bridge are shown in Fig.55 .

[0285] The influence of train speed on noise: The low-frequency noise response of the bridge structure at different speeds is simulated as described in Chapter 3. To simulate the medium and high frequency noise radiation at different speeds, it is only necessary to change the external excitation force of the bridge deck subsystem. Fig.56 The fastener force spectrum data of a single fastener at different train speeds are given. As the speed increases, the amplitude of the fastener force spectrum increases significantly, and the peak frequency also increases with the increase in speed, which is consistent with the calculation formula of the fastener force peak frequency proposed above.

[0286] Combining the low-frequency noise simulation method and the high-frequency noise numerical simulation method, the noise radiation of the A, B, and C points under the influence of different train speeds is given as follows: Figure 57-Figure 59As shown. There is an obvious mutation in the low-frequency band and the medium-high frequency band at the segmentation point of 100Hz, which is slightly different from the actual situation. After analysis, it can be seen that this is related to the modeling method of the vehicle track. The fastener force results simulated in this scheme are slightly larger than those of the relevant existing technologies, which leads to the full-band noise radiation results presented in this section being slightly larger in the medium-high frequency band. The vehicle-track-bridge model in this scheme is a vertical model, which ignores the contribution of the lateral force between the wheel and rail to the vibration of the bridge, which will cause the simulation results to have a slightly smaller noise amplitude in the low-frequency band. These two main factors lead to an obvious mutation in the full-band noise radiation simulation results at 100Hz.

[0287] Effect of base slab concrete thickness on vibration: Fig.60 and Fig.61 The influence of different thickness of concrete poured in the bottom slab on the vertical displacement of the bottom slab in the middle of the span is given. It can be seen from the figure that when the thickness of the bottom slab concrete poured is 50mm, the peak value of the vertical deflection in the middle of the span is reduced from 3mm to 1mm compared with no concrete pouring. When the thickness of the concrete is increased from 50mm to 150mm, the time history curve of the vertical deflection in the middle of the span has almost no change in the peak deflection index. Fig.62 and Fig.63 The influence of different thickness of concrete poured on the bottom slab on the vertical vibration velocity at the mid-span of the bottom slab is given. It can be seen from the figure that when the bottom slab concrete thickness is poured with 50mm, the peak value of the vertical velocity at the mid-span and the effective value of the vertical velocity are significantly reduced compared with no concrete pouring. In the process of increasing the concrete thickness from 50mm to 150mm, the time history curve of the vertical velocity at the mid-span and the discounted index of the vertical velocity of the bottom slab change little. In this section, the peak value index of the velocity decreases slightly, while the effective value index of the velocity increases slightly.

[0288] Effect of bottom slab concrete thickness on noise: Fig.64 The results of the influence of different bottom slab concrete thickness on the fastener force spectrum are given. From the figure, the following conclusion can be drawn that as the concrete thickness increases from 0mm to 150mm, the peak value of the fastener force is almost unaffected. Therefore, when simulating the influence of bottom slab concrete thickness on medium and high frequency noise, the spectrum data of the external excitation force of the bridge deck does not change. Figure 65-Figure 70 The changes in structural noise radiation at the three points A, B, and C under different bottom slab concrete thicknesses are given. The following rules can be analyzed from the figure. In the low-frequency stage, that is, below 100Hz, the influence of the bottom slab concrete thickness on the noise radiation of the field point is not obvious, and the spectrum diagram is relatively messy; while in the medium and high frequency bands, that is, 100Hz to 1000Hz, the increase in the bottom slab concrete thickness has a more obvious effect on reducing noise radiation. Among them, the noise reduction effect of the bottom slab concrete pouring thickness of 50mm is the most obvious. The total sound pressure level of the three points is reduced by an average of 1dB, and the change in the bottom slab concrete thickness has the most obvious noise reduction effect on the B field point that is closer to the bottom slab.

[0289] In summary, the vibration and noise reduction of steel-concrete composite beams were analyzed through parameter analysis. When the train speed increased from 200km / h to 350km / h, the peak value of the mid-span vertical deflection of the bridge decreased from 3.5mm to around 3.0mm; the peak acceleration was 1m / s 2 Up to 2m / s 2 , and the effective value of the mid-span vertical acceleration also increased; the increase in train speed has the most obvious effect on the acceleration of the steel web and steel bottom plate. In terms of the influence of train speed on noise, the influence of train speed on the radiation enhancement of medium and high frequency noise is relatively obvious, which is caused by the increase in the peak value of the fastener force caused by the increase in train speed. On this basis, this chapter studies the influence of the change in the thickness of the bottom plate concrete on the vibration and noise radiation of the bridge structure. The results show that when the thickness of the bottom plate concrete is 50mm, the vibration reduction and noise reduction effect of the structure is the most obvious, among which the peak value of the vertical deflection of the bottom plate at the mid-span is reduced from 3.0mm to 0.9mm, and the effective value and peak value of the bottom plate velocity are reduced, showing the vibration reduction characteristics of the bottom plate concrete. The simulation of the bottom plate concrete in noise reduction shows that: the pouring of 50mm bottom plate concrete reduces the total sound pressure level of the three field points by an average of 1dB. However, if the thickness continues to increase on the basis of 50mm thickness, the effect on vibration reduction and noise reduction is not obvious.

[0290] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention 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 invention.

Claims

1. A vibration and noise analysis method for a combined box girder bridge with vehicle-bridge coupling, characterized in that: The steps include: S1. Establish a train-track-bridge coupled vibration model for high-speed railway steel-concrete composite box girder bridges, and compile 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 the low-frequency radiation noise of the bridge structure, and derive the low-frequency noise radiation law of the bridge structure; S3. Establish a prediction model for medium and high frequency noise of high-speed railway steel-concrete composite box girder bridges, conduct numerical simulation of medium and high frequency radiation noise of bridge structures, and derive the laws of medium and high frequency noise radiation of bridge structures; S4, combining the model established in steps S1-S3, analyzing the influencing parameters of the vibration noise of the high-speed railway steel-concrete composite box girder bridge, and obtaining the analysis results; Wherein, the step S1 is specifically as follows: S11, establishing a vehicle dynamics model, the train model includes 8 vehicle trains, each vehicle includes a car body, two bogies and 4 wheel pairs, and each car includes 10 degrees of freedom; S12, establishing a track dynamics model, the track model including self-compacting concrete layer, concrete track slab, concrete base slab, steel spring fasteners, rails and other components; S13, establishing a bridge finite element model, establishing the bridge model by using the Apdl finite element software, and numerically simulating the dynamic behavior of the bridge structure; S14, establish a wheel-rail interaction model, and calculate the vertical wheel-rail force through the Hertz nonlinear contact model; S15, taking track irregularity as an excitation source, and determining that the wavelength range of track irregularity is 0.04-85m; S16. Based on the bridge, vehicle and track models established in (1)-(3), the dynamic equations of the train-track-bridge coupling system are obtained; S17. Using computer simulation software and finite element software, compile a numerical simulation analysis program model for train-track-bridge coupling dynamics, solve it, and verify the results of the program operation; The dynamic equation of the train-track-bridge coupling system in step S17 is: Where 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 vibration and noise analysis method of a combined box girder bridge with vehicle-bridge coupling according to claim 1 is characterized by: In step (7), a 50-fold asynchronous long loading ratio is used to perform dynamic simulation calculations of the train-track-bridge system, that is, the simulation analysis step size of the train and track system is 0.1 ms, and the finite element transient response analysis step size of the bridge is 5 ms.

3. The vibration and noise analysis method of a combined box girder bridge with vehicle-bridge coupling according to claim 1 is characterized by: The equation of motion for a single-section vehicle is: Where M V is the mass matrix of a single vehicle; M V =diag(m w m w m w m w m t J t m t J t m c J c ) K V is the stiffness matrix of a single vehicle; Z V is the vertical displacement column matrix of a single vehicle; F V is the vertical wheel-rail force matrix of a single-section vehicle; F V =(2(F w1 -S) 2(F w2 -S) 2(F w3 -S) 2(F w4 -S) 0 0 0 0 0 0) Since the damping matrix and the stiffness matrix have similar content forms, we only need to replace the stiffness coefficient k with the damping coefficient c.

4. The vibration and noise analysis method of a combined box girder bridge with vehicle-bridge coupling according to claim 1 is characterized by: The equation of motion for the orbital dynamics model is: M R is the overall mass matrix; K R Overall stiffness matrix; Z R Track overall displacement matrix; C R The damping matrix of the track; In the formula, α 0,R , α 1,R is the damping coefficient, ξ R is the damping ratio, ω 1,R ,ω 2,R are the self-oscillating circular frequencies respectively.

5. The vibration and noise analysis method of a combined box girder bridge with vehicle-bridge coupling according to claim 1 is characterized by: When the track is not smooth, the wheel-rail force F W The expression is:

6. The vibration and noise analysis method of a combined box girder bridge with vehicle-bridge coupling according to claim 1 is characterized by: The step S2 specifically includes: (1) Establish the wave equation in an ideal fluid when the medium is stationary and uniform and the sound wave has a small amplitude; (2) Establish the Helmholtz equation for calculating the external noise radiation in the frequency domain, and derive the acoustic boundary conditions and the Green's function expression of the three-dimensional free sound field; (3) Using LMS Virtual.Lab Acoustics software, a simulation method for the low-frequency noise radiation model under train load excitation was obtained.

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

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

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