Noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA

Abstract

The present invention provides a noise prediction method for a steel box composite beam based on dynamic admittance and FEM-SEA, and relates to the technical field of bridge noise prediction. The method comprises the following steps: calculating the dynamic admittance of a floating plate in the frequency domain; calculating the vertical displacement of a rail and a floating plate; calculating the dynamic admittance of a rail at a driving wheel, and obtaining the vertical wheel-rail force between the rail and the driving wheel and the passive wheel in the frequency domain; taking each wheel as a driving wheel in turn, and obtaining the force transmitted to the bridge according to the vertical wheel-rail force between the rail and the driving wheel and the passive wheel in the frequency domain; treating components with low modal density in a bridge structure as deterministic components, and using finite element modeling to perform noise prediction by constructing a hybrid finite element-statistical energy analysis model. The present invention solves the problems of large number of degrees of freedom, high computational cost, long computational time, inaccurate noise prediction in a wide frequency range, and discontinuity caused by using different models for different frequency bands.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge noise prediction, and in particular relates to a noise prediction method for a steel box composite beam based on dynamic admittance and FEM-SEA. Background Art

[0002] With the full deployment of high-speed railway networks and the rapid development of high-speed railway bridges, people's transportation has been greatly facilitated, but the vibration and noise problems of bridge structures caused by trains crossing bridges have become increasingly prominent and have received more and more attention. Accurate calculation of the interaction force between wheels and rails is the key to studying the vibration and noise problems of track structures and bridge structures under the track. Previous studies have considered the degrees of freedom of the car body, bogie and wheels in all directions, which will lead to a large number of degrees of freedom, high calculation cost and long calculation time. For bridge structures, the dominant frequency band of noise on concrete bridge decks is generally lower than 250Hz. The modal density in this frequency range is low, so it is suitable for finite element modeling. The radiated noise of steel components can be as high as 1000Hz, and the modal density is sufficient to use statistical energy analysis methods. Floating slab track is a commonly used track structure in urban rail transit and high-speed railways. How to accurately and efficiently calculate the vertical wheel-rail force and predict vibration noise under the floating slab track structure is an urgent problem to be solved by technicians in this field. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a noise prediction method for steel box composite beams based on dynamic admittance and FEM-SEA, which solves the problem that the existing vertical wheel-rail force acquisition method takes into account the freedom of the car body, bogie and wheelset in all directions, resulting in a large number of degrees of freedom, high calculation cost and long calculation time. And by introducing the finite element-statistical energy analysis hybrid method to predict bridge structure noise, the problems of inaccurate noise prediction and long calculation time in a wide frequency range are solved, while avoiding the discontinuity problem caused by using different models for different frequency bands.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0005] This scheme provides a noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA, including the following steps:

[0006] S1. The floating plate is regarded as an Euler-Bernoulli beam with two free ends, and the dynamic admittance of the floating plate in the frequency domain is calculated according to the material parameters and cross-sectional parameters of the floating plate.

[0007] S2. Based on the dynamic admittance of the rail in the frequency domain, the dynamic admittance of the floating plate in the frequency domain and the superposition principle, the vertical displacement of the rail and the floating plate is obtained by constructing and solving a set of equations about the vertical displacement of the rail and the floating plate;

[0008] S3. Calculate the dynamic admittance of the rail at the driving wheel according to the vertical displacement of the rail and the floating plate, and obtain the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain according to the dynamic admittance of the wheel in the frequency domain and the wheel-rail contact dynamic admittance;

[0009] S4. Take each wheel as the driving wheel in turn, and obtain the vertical wheel-rail force of the floating slab structure in the frequency domain according to the vertical wheel-rail force between the rail and the driving wheel and the passive wheel in the frequency domain, and based on the superposition principle, obtain the force transmitted to the bridge;

[0010] S5. Components with low modal density in the bridge structure are regarded as deterministic components, and finite element modeling is used to construct a hybrid finite element-statistical energy analysis model FEM-SEA. The noise prediction is combined with the force transmitted on the bridge to complete the noise prediction of the steel box composite beam. Among them, the statistical components are represented by the statistical energy analysis subsystem.

[0011] The beneficial effects of the present invention are as follows: the present invention predicts bridge noise based on hybrid finite element-statistical energy analysis, solving the problem that the existing vertical wheel-rail force acquisition method considers the freedom of the vehicle body, bogie and wheelset in all directions, resulting in a large number of degrees of freedom, high calculation cost and long calculation time. And by introducing the hybrid finite element-statistical energy analysis method to predict bridge structure noise, the problems of inaccurate noise prediction and long calculation time in a wide frequency range are solved, thereby achieving a perfect balance between accuracy and calculation cost, while avoiding the discontinuity problem caused by using different models for different frequency bands.

[0012] Furthermore, the expression of the dynamic admittance of the floating plate in the frequency domain in step S1 is as follows:

[0013]

[0014] Among them, β s represents the dynamic admittance function of the floating plate in the frequency domain, n' represents the n'th order vibration mode, N represents the total number of modes, W n' (x1) represents the n'th order vibration mode function of the floating plate at x1, W n' (x2) represents the n'th order vibration mode function of the floating plate at x2, W n' represents the n'th order vibration mode function of the floating plate, ω represents the angular frequency, ω n' represents the n'th order natural frequency of the floating plate, i represents the imaginary unit, η s represents the floating plate loss coefficient;

[0015] The expressions of the n'th order natural frequency and normalized vibration mode function of the floating plate are as follows:

[0016]

[0017] Where W1(x) represents the first-order normalized vibration function of the floating plate, W2(x) represents the second-order normalized vibration function of the floating plate, and ρ s Indicates the density of the floating plate, A s represents the cross-sectional area of ​​the floating slab, L s represents the cross-sectional inertia moment of the floating plate, and x represents the coordinate of the floating plate along the axis direction, with a value range of 0 to L s , k n' and c n' Both represent vibration mode function parameters, E s Represents the elastic modulus of the floating slab.

[0018] The beneficial effect of the above further solution is that the present invention uses the vibration mode function to calculate the dynamic admittance of the floating plate, which provides a prerequisite for solving the vertical displacement of the rail and the floating plate.

[0019] Furthermore, the equation group of the vertical displacement of the rail and the floating plate in step S2 is as follows:

[0020]

[0021]

[0022] Among them, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, α r (x w,j ,0) represents the vertical displacement of the rail at the jth passive wheel when the rail is subjected to vertical unit harmonic excitation at the driving wheel, n represents the nth fastener, N f and N b Respectively represent the number of fasteners and floating plates, K f and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, u r (x f,n ) represents the vertical displacement of the rail at the nth fastener, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener, α r (x w,j ,x w,p ) represents the vertical displacement response of the rail at the jth passive wheel when a vertical unit harmonic excitation is applied at the position of the pth passive wheel of the rail, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,p ) represents the vertical displacement of the rail at the pth passive wheel position, α r (xw,j ,x f,n ) represents the vertical displacement of the rail at the jth passive wheel when a vertical unit excitation is applied to the rail at the nth fastener, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener, α r (x f,i ,0) represents the vertical displacement of the rail at the ith fastener when the rail is subjected to vertical unit harmonic excitation at the driving wheel, u r (x f,n ) represents the vertical displacement of the rail at the nth fastener position, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener position, α r (x f,i ,x f,n ) represents the vertical displacement of the rail at the ith fastener when a vertical unit excitation is applied to the rail at the nth fastener, α r (x f,i ,x w,p ) represents the vertical displacement of the rail at the i-th fastener when a vertical unit excitation is applied to the rail at the p-th passive wheel. Indicates that the floating plate is at the k+mN f The vertical displacement at each fastener, m represents the number of the floating plate, represents the complex stiffness of the fastener, u r (x f,n ) and u b (x f,n ) represent the displacements of the rail and the floating plate at the nth fastener, It means that when a vertical unit harmonic excitation is applied at the nth fastener position of the floating plate, the floating plate at the k+mN f Vertical displacement response at each fastener, N s Indicates the maximum value of the support spring number, Indicates the complex stiffness of the steel spring, K b and η b are the real part of the complex stiffness of the steel spring and the loss factor of the steel spring, u b (x s,n” ) represents the displacement of the floating plate at the n'th supporting spring, It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is f The vertical displacement response at each fastener is Indicates that the floating plate is at the l+mN s The displacement of the support spring, It means that when the vertical unit harmonic excitation is applied at the nth fastener of the floating plate, the floating plate sThe vertical displacement response at each support spring is: It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is l+mN s Vertical displacement response at each fastener.

[0023] The beneficial effect of the above further solution is that the present invention can obtain the vertical displacement of the rail and the floating plate by superimposing calculation by considering the influence of external excitation on fasteners at different positions.

[0024] Furthermore, step S3 includes the following steps:

[0025] S301, calculating the fastener force and the vertical force between the passive wheel j and the rail according to the vertical displacement of the rail and the floating plate;

[0026] S302, calculate the vertical force between the rail and the driving wheel j according to the fastener force and the vertical force between the passive wheel j and the rail * The dynamic admittance at

[0027] S303, according to the dynamic admittance of the wheel in the frequency domain and the wheel-rail contact dynamic admittance, obtain the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain.

[0028] Furthermore, the rail is on the driving wheel * The expression of the dynamic admittance at is as follows:

[0029]

[0030] F f,i =-K f (1+iη f )[u r (x f,i )-u b (x f,i )]

[0031] F w,j =-Z cw u r (x w,j )

[0032] in, Indicates that the rail is on the driving wheel j * The dynamic admittance at r (0,0) represents the vertical displacement of the rail at the driving wheel position when the rail is subjected to unit harmonic excitation at the driving wheel position, N f Indicates the number of fasteners, F f,i represents the fastener force, α r (0,x f,i) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the i-th fastener position, F w,j represents the vertical force between the passive wheel j and the rail, α r (0,x w,j ) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the jth passive wheel position, K f and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, i represents the imaginary unit, u b (x f,i ) represents the vertical displacement of the floating plate at the i-th fastener position, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener.

[0033] Furthermore, the expression of the vertical wheel-rail force in step S4 is as follows:

[0034]

[0035]

[0036]

[0037] Among them, F w-r,j' represents the vertical wheel-rail force between the rail and the j'th wheel, F aw-r,j* Indicates the jth * When a wheel is used as a driving wheel, the vertical force between it and the rail is F (pw-r,j'),j* Indicates that the j'th wheel is a passive wheel, and the jth * When the wheel j' is used as the driving wheel, the vertical force between the wheel j' and the rail, R(ω) represents the track irregularity spectrum, α w , α c and They represent the dynamic admittance of the wheel in the frequency domain, the dynamic admittance of the wheel-rail contact, and the dynamic admittance of the rail at the driving wheel j*, respectively. w represents the dynamic stiffness of the wheel in the frequency domain, u r (x w,j ) represents the vertical displacement of the rail at the driving wheel j, R0 represents the reference value of track irregularity, and λ represents the wavelength of track irregularity.

[0038] The beneficial effect of the above further scheme is that the present invention uses the superposition principle to superimpose the wheel-rail force results when each wheel is used as a driving wheel, so as to obtain the force transmitted to the bridge, thereby providing a load effect for the subsequent solution of the acoustic response of the bridge structure.

[0039] Furthermore, step S5 includes the following steps:

[0040] S501, treating components with low modal density in the bridge structure as deterministic components, and using a statistical energy analysis subsystem to represent the statistical components;

[0041] S502. The concrete bridge deck is modeled using the finite element method, and the steel box composite beam and the fully enclosed noise barrier are simulated using the statistical energy analysis subsystem. The connection between the finite element method and the statistical energy analysis subsystem is achieved through the built-in hybrid point connection and hybrid line connection of the software to complete the construction of the hybrid finite element-statistical energy analysis model FEM-SEA.

[0042] S503. Based on the force transmitted to the bridge, noise prediction is performed using a hybrid finite element-statistical energy analysis model FEM-SEA to complete the noise prediction of the steel box composite beam.

[0043] The beneficial effect of the above further scheme is: the present invention effectively solves the problem of large degrees of freedom and large amount of calculation through the above simplified method of solving wheel-rail forces, converts the solution of external loads of the structure into the solution of dynamic admittance of the track component, and predicts the bridge structure noise by introducing a finite element-statistical energy analysis hybrid method, solves the problems of inaccurate noise prediction and long calculation time in a wide frequency range, thereby achieving a perfect balance between accuracy and calculation cost, and avoiding the discontinuity problem caused by using different models for different frequency bands. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The present invention is a flow chart of the method.

[0045] Figure 2 It is a schematic diagram of the full bridge dimensions of a large-span cable-stayed bridge for urban rail transit in this embodiment.

[0046] Figure 3 This is a diagram of the finite element-statistical energy analysis hybrid model established in this embodiment.

[0047] Figure 4 Schematic diagram of the noise measurement point arrangement in this embodiment.

[0048] Figure 5 It is a comparison chart of the actual measurement results and the predicted results of the field points in steps S1 to S4 in this embodiment. DETAILED DESCRIPTION

[0049] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0050] Example

[0051] like Figure 1 As shown, the present invention provides a noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA, and its implementation method is as follows:

[0052] S1. Consider the floating plate as an Euler-Bernoulli beam with both ends free, and calculate the dynamic admittance of the floating plate in the frequency domain based on the material parameters and cross-sectional parameters of the floating plate:

[0053]

[0054] Among them, β s represents the dynamic admittance function of the floating plate in the frequency domain, n' represents the n'th order vibration mode, N represents the total number of modes, W n' (x1) represents the n'th order vibration mode function of the floating plate at x1, W n' (x2) represents the n'th order vibration mode function of the floating plate at x2, W n' represents the n'th order vibration mode function of the floating plate, ω represents the angular frequency, ω n' represents the n'th order natural frequency of the floating plate, i represents the imaginary unit, η s represents the floating plate loss coefficient;

[0055] The expressions of the n'th order natural frequency and normalized vibration mode function of the floating plate are as follows:

[0056]

[0057] Where W1(x) represents the first-order normalized vibration function of the floating plate, W2(x) represents the second-order normalized vibration function of the floating plate, and ρ s Indicates the density of the floating plate, A s represents the cross-sectional area of ​​the floating slab, L s represents the cross-sectional inertia moment of the floating plate, and x represents the coordinate of the floating plate along the axis direction, with a value range of 0 to L s , k n' and c n' Both represent vibration mode function parameters, E s Represents the elastic modulus of the floating slab.

[0058] In this embodiment, as shown in Table 1, Table 1 is a vibration mode function parameter table.

[0059] Table 1

[0060] nth mode 3 4 5 ≥6 <![CDATA[k n L s ]]> 4.730 7.853 10.996 (2n-3)π / 2

[0061] S2. Based on the dynamic admittance of the rail in the frequency domain, the dynamic admittance of the floating plate in the frequency domain and the superposition principle, the vertical displacement of the rail and the floating plate is obtained by constructing and solving a set of equations about the vertical displacement of the rail and the floating plate;

[0062] In this embodiment, the equations for the vertical displacement of the rail and the floating plate are as follows:

[0063]

[0064] Among them, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, α r (x w,j ,0) represents the vertical displacement of the rail at the jth passive wheel when the rail is subjected to vertical unit harmonic excitation at the driving wheel, n represents the nth fastener, N f and N b Respectively represent the number of fasteners and floating plates, K f and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, u r (x f,n ) represents the vertical displacement of the rail at the nth fastener, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener, α r (x w,j ,x w,p ) represents the vertical displacement response of the rail at the jth passive wheel when a vertical unit harmonic excitation is applied at the position of the pth passive wheel of the rail, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,p ) represents the vertical displacement of the rail at the pth passive wheel position, α r (x w,j ,x f,n ) represents the vertical displacement of the rail at the jth passive wheel when a vertical unit excitation is applied to the rail at the nth fastener, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener, α r (x f,i ,0) represents the vertical displacement of the rail at the ith fastener when the rail is subjected to vertical unit harmonic excitation at the driving wheel, ur (x f,n ) represents the vertical displacement of the rail at the nth fastener position, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener position, α r (x f,i ,x f,n ) represents the vertical displacement of the rail at the ith fastener when a vertical unit excitation is applied to the rail at the nth fastener, α r (x f,i ,x w,p ) represents the vertical displacement of the rail at the i-th fastener when a vertical unit excitation is applied to the rail at the p-th passive wheel. Indicates that the floating plate is at the k+mN f The vertical displacement at each fastener, m represents the number of the floating plate, represents the complex stiffness of the fastener, u r (x f,n ) and u b (x f,n ) represent the displacements of the rail and the floating plate at the nth fastener, It means that when a vertical unit harmonic excitation is applied at the nth fastener position of the floating plate, the floating plate at the k+mN f Vertical displacement response at each fastener, N s Indicates the maximum value of the support spring number, Indicates the complex stiffness of the steel spring, K b and η b are the real part of the complex stiffness of the steel spring and the loss factor of the steel spring, u b (x s,n” ) represents the displacement of the floating plate at the n'th supporting spring, It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is f The vertical displacement response at each fastener is represents the displacement of the floating plate at the l+mNsth supporting spring, It means that when the vertical unit harmonic excitation is applied at the nth fastener of the floating plate, the floating plate s The vertical displacement response at each support spring is: It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is l+mN s The vertical displacement response at each fastener. i=1,2,...,N f ×N b is the number of the rail fastener, m = 0, 1, 2, ..., N b -1 is the number of the floating plate, k=1,2,...,Nf and l=1,2,...,N s Number the fasteners and support springs connected to each floating plate separately.

[0065] S3. According to the vertical displacement of the rail and the floating plate, the dynamic admittance of the rail at the driving wheel is calculated, and according to the dynamic admittance of the wheel in the frequency domain and the wheel-rail contact dynamic admittance, the vertical wheel-rail force between the rail and the driving wheel and the driven wheel in the frequency domain is obtained. The implementation method is as follows:

[0066] S301. Calculate the fastener force and the vertical force between the passive wheel j and the rail according to the vertical displacement of the rail and the floating plate:

[0067] F f,i =-K f (1+iη f )[u r (x f,i )-u b (x f,i )]

[0068] F w,j =-Z cw u r (x w,j )

[0069] S302, calculate the vertical force between the rail and the driving wheel j according to the fastener force and the vertical force between the passive wheel j and the rail * The dynamic admittance at

[0070] S303, according to the dynamic admittance of the wheel in the frequency domain and the dynamic admittance of the wheel-rail contact, the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain are obtained:

[0071]

[0072] in, Indicates that the rail is on the driving wheel j * The dynamic admittance at r (0,0) represents the vertical displacement of the rail at the driving wheel position when the rail is subjected to unit harmonic excitation at the driving wheel position, N f Indicates the number of fasteners, F f,i represents the fastener force, α r (0,x f,i ) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the i-th fastener position, F w,j represents the vertical force between the passive wheel j and the rail, α r (0,x w,j ) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the jth passive wheel position, Kf and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, i represents the imaginary unit, u b (x f,i ) represents the vertical displacement of the floating plate at the i-th fastener position, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener;

[0073] S4. Take each wheel as the driving wheel in turn, and obtain the vertical wheel-rail force of the floating slab structure in the frequency domain according to the vertical wheel-rail force between the rail and the driving wheel and the passive wheel in the frequency domain, and based on the superposition principle, obtain the force transmitted to the bridge;

[0074] In this embodiment, the calculation expressions of the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain are:

[0075]

[0076]

[0077] R(ω) represents the track irregularity spectrum, and its calculation expression is:

[0078]

[0079] The calculation expression of the vertical wheel-rail force of the floating slab structure in the frequency domain based on the superposition principle is:

[0080]

[0081] Among them, F w-r,j' represents the vertical wheel-rail force between the rail and the j'th wheel, F aw-r,j' represents the vertical force between the j'th wheel and the rail when it is used as the driving wheel, Indicates that the j'th wheel is a passive wheel, and the jth * When the wheel j' is used as the driving wheel, the vertical force between the wheel j' and the rail, R(ω) represents the track irregularity spectrum, α w , α c and They represent the dynamic admittance of the wheel in the frequency domain, the dynamic admittance of the wheel-rail contact, and the dynamic admittance of the rail at the driving wheel j*, respectively. w represents the dynamic stiffness of the wheel in the frequency domain, u r (x w,j) represents the vertical displacement of the rail at the driving wheel j, R0 represents the reference value of track irregularity, and λ represents the wavelength of track irregularity.

[0082] In this embodiment, the four situations (F w-r,j is the vertical wheel-rail force between the rail and the jth wheel; F aw-r,j is the vertical force between the jth wheel and the rail when it is used as the driving wheel; The jth wheel is used as a passive wheel, and the jth * When each wheel is used as the driving wheel, the calculation results of the vertical force between wheel j and the rail are superimposed to obtain the final result of the bridge force.

[0083] In this embodiment, in the specific implementation process, when the distance between the wheel-rail contact point and the inspection point exceeds 10m, the influence of the wheel-rail interaction on the inspection point can be ignored. Figure 2 As shown in FIG. 1 , for urban rail transit trains, the vehicle spacing is 12.6 m and the bogie wheelbase is 2.2 m. Therefore, according to the influence range of the wheel-rail force and the characteristic dimensions of the vehicle, the present invention only considers the interaction between the four wheels under the adjacent bogies of the front and rear carriages. Figure 3 As shown, the present invention takes 1 / 2 track structure, 1 / 4 bogie and a single wheel as research objects according to the symmetry of the vehicle, track structure and wheelset.

[0084] In this embodiment, the subway vehicle parameters are shown in Table 2, and the calculation parameters of the steel spring floating plate track structure are shown in Table 3. The train speed is 60km / h, that is, v = 16.7m / s. The wheel-rail contact dynamic admittance is taken as a according to Table 2 c =7.55×10 - 10 m / N. According to the steps of the present invention, the vertical wheel-rail force of the steel spring floating plate structure can be calculated. Table 3 is a parameter table of the steel spring floating plate track structure.

[0085] Table 2

[0086]

[0087] Table 3

[0088]

[0089]

[0090] S5. Components with low modal density in the bridge structure are regarded as deterministic components, and finite element modeling is used to build a hybrid finite element-statistical energy analysis model FEM-SEA. In combination with the force transmitted on the bridge, noise prediction is performed to complete the noise prediction of the steel box composite beam. Among them, the statistical component is represented by the statistical energy analysis subsystem, and its implementation method is as follows:

[0091] S501, treating components with low modal density in the bridge structure as deterministic components, and using a statistical energy analysis subsystem to represent the statistical components;

[0092] S502. The concrete bridge deck is modeled using the finite element method, and the steel box composite beam and the fully enclosed noise barrier are simulated using the statistical energy analysis subsystem. The connection between the finite element method and the statistical energy analysis subsystem is achieved through the built-in hybrid point connection and hybrid line connection of the software to complete the construction of the hybrid finite element-statistical energy analysis model FEM-SEA.

[0093] S503. Based on the force transmitted to the bridge, noise prediction is performed using a hybrid finite element-statistical energy analysis model FEM-SEA to complete the noise prediction of the steel box composite beam.

[0094] In this embodiment, the components with lower modal density in the bridge structure are regarded as deterministic components and modeled using finite elements, while the statistical components are represented by the statistical energy analysis subsystem. A hybrid finite element-statistical energy analysis model FEM-SEA is established in the vibroacoustic software, and the noise is calculated in combination with the force transmitted to the bridge:

[0095] The concrete bridge deck was modeled using the finite element method, while the steel box composite beam and the fully enclosed noise barrier were simulated using the statistical energy analysis subsystem. The connection between the finite element method and the statistical energy analysis subsystem is achieved through the software's built-in "mixed point connection" and "mixed line connection" functions. In order to ensure the accuracy of the finite element calculation, there should be at least 4 units in each bending wavelength of the concrete bridge deck. In order to meet the accuracy requirements, the principle that the mode of each subsystem in the frequency band is not less than 1 is also required in the statistical energy analysis.

[0096] In this embodiment, the selected bridge is a large-span cable-stayed bridge of a certain urban rail transit, with a main span of 480m, a steel box composite beam, a full width of 20.08m, and a height of 3.5m. The schematic diagram of the bridge dimensions is shown in FIG. Figure 2 As shown in the figure, the transverse beams are arranged every 3.5m along the longitudinal direction of the bridge, the steel box beams are Q345qE, and the concrete bridge deck strength grade is C55. In the area close to residential buildings, the bridge is equipped with a fully enclosed sound barrier (fully enclosed sound barrier) composed of metal plates filled with glass wool. This sound barrier has a good isolation effect on sharp wheel-rail noise, but the suppression effect on bridge deck noise is not obvious. Table 4 lists the thickness of each plate-like component and fully enclosed sound barrier of the bridge.

[0097] Table 4(a) Concrete bridge deck and steel box girder parts

[0098] Concrete slab Side plate Inclined belly plate Middle Grid Base Plate Diaphragm 260 30 16 20 16 16

[0099] (b) Sound barrier

[0100] Outer galvanized steel sheet Glass wool Galvanized steel sheet inside 2 80 1.5

[0101] The cutoff frequency of the present invention is 1000Hz, corresponding to the 1.41m bending wavelength of the 260mm thick concrete bridge deck. Therefore, in order to meet the accuracy requirements, the finite element size is set to 0.35m. According to the principle that the mode of each subsystem in the frequency band is not less than 1, the steel box composite beam and the fully enclosed sound barrier are divided into statistical energy analysis subsystems to meet the prerequisites for using statistical energy analysis. Since the total length of the As-type subway with 6 carriages is about 120m, the bridge unit is only set on the south side of the south tower. The established finite element-statistical energy analysis hybrid model is as follows Figure 3 As shown in Figure 1, there are 54,624 shell elements and 1,536 statistical energy analysis subsystems in the hybrid model. The calculation process is completed in the vibroacoustic software.

[0102] In this embodiment, the calculation results of step S4 and step S5 are compared with the simulated values ​​and the measured values ​​to verify the reliability and accuracy of the prediction method and the prediction model, and then the method is used according to the actual engineering background to achieve the purpose of predicting noise.

[0103] In this embodiment, four noise measuring points are set for the bridge, and the measuring points are arranged as follows: Figure 4 As shown, Figure 5 A comparison chart of the measured results and the predicted results of each measuring point is given. The deviations of the measuring points in steps S1 to S4 are 0.75dB, 0.71dB, 0.74dB and 0.86dB respectively. The deviation between the noise measurement result and the predicted result is allowed to be within the error range, which verifies the rationality of the present invention.

[0104] In summary, the present invention solves the problem that the existing vertical wheel-rail force acquisition method takes into account the degrees of freedom of the car body, bogie and wheelset in all directions, resulting in a large number of degrees of freedom, high calculation cost and long calculation time. And by introducing the finite element-statistical energy analysis hybrid method to predict bridge structure noise, the problems of inaccurate noise prediction and long calculation time in a wide frequency range are solved, thereby achieving a perfect balance between accuracy and calculation cost, while avoiding the discontinuity problem caused by using different models for different frequency bands. The present invention can provide technical support for predicting the vibration noise of urban rail transit and high-speed railway floating plate track structures and sub-track bridge structures.

Claims

1. A noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA, characterized in that: The following steps are involved: S1. The floating plate is regarded as an Euler-Bernoulli beam with both ends free, and the dynamic admittance of the floating plate in the frequency domain is calculated according to the material parameters and cross-sectional parameters of the floating plate. S2. Based on the dynamic admittance of the rail in the frequency domain, the dynamic admittance of the floating plate in the frequency domain and the superposition principle, the vertical displacement of the rail and the floating plate is obtained by constructing and solving a set of equations about the vertical displacement of the rail and the floating plate; S3. Calculate the dynamic admittance of the rail at the driving wheel according to the vertical displacement of the rail and the floating plate, and obtain the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain according to the dynamic admittance of the wheel in the frequency domain and the wheel-rail contact dynamic admittance; S4. Take each wheel as the driving wheel in turn, and obtain the vertical wheel-rail force of the floating slab structure in the frequency domain according to the vertical wheel-rail force between the rail and the driving wheel and the passive wheel in the frequency domain, and based on the superposition principle, obtain the force transmitted to the bridge; S5. Consider the components with low modal density in the bridge structure as deterministic components, and use finite element modeling to build a hybrid finite element-statistical energy analysis model FEM-SEA. Combined with the force transmitted on the bridge, noise prediction is performed to complete the noise prediction of the steel box composite beam. Among them, the statistical components are represented by the statistical energy analysis subsystem. The expression of the dynamic admittance of the floating plate in the frequency domain in step S1 is as follows: Among them, β s represents the dynamic admittance function of the floating plate in the frequency domain, n' represents the n'th order vibration mode, N represents the total number of modes, W n' (x1) represents the n'th order vibration mode function of the floating plate at x1, W n' (x2) represents the n'th order vibration mode function of the floating plate at x2, W n' represents the n'th order vibration mode function of the floating plate, ω represents the angular frequency, ω n' represents the n'th order natural frequency of the floating plate, i represents the imaginary unit, η s represents the floating plate loss coefficient; The expressions of the n'th order natural frequency and normalized vibration mode function of the floating plate are as follows: Where W1(x) represents the first-order normalized vibration function of the floating plate, W2(x) represents the second-order normalized vibration function of the floating plate, and ρ s Indicates the density of the floating plate, A s represents the cross-sectional area of ​​the floating slab, L s represents the cross-sectional inertia moment of the floating plate, and x represents the coordinate of the floating plate along the axis direction, with a value range of 0 to L s , k n' and c n' Both represent vibration mode function parameters, E s Represents the elastic modulus of the floating slab.

2. The noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA according to claim 1 is characterized in that: The equations for the vertical displacement of the rail and the floating plate in step S2 are as follows: Among them, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, α r (x w,j ,0) represents the vertical displacement of the rail at the jth passive wheel when the rail is subjected to vertical unit harmonic excitation at the driving wheel, n represents the nth fastener, N f and N b Respectively represent the number of fasteners and floating plates, K f and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, u r (x f,n ) represents the vertical displacement of the rail at the nth fastener, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener, α r (x w,j ,x w,p ) represents the vertical displacement response of the rail at the jth passive wheel when a vertical unit harmonic excitation is applied at the position of the pth passive wheel of the rail, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,p ) represents the vertical displacement of the rail at the pth passive wheel position, α r (x w,j ,x f,n ) represents the vertical displacement of the rail at the jth passive wheel when a vertical unit excitation is applied to the rail at the nth fastener, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener, α r (x f,i ,0) represents the vertical displacement of the rail at the ith fastener when the rail is subjected to vertical unit harmonic excitation at the driving wheel, u r (x f,n ) represents the vertical displacement of the rail at the nth fastener position, u b (x f,n ) represents the vertical displacement of the floating plate at the nth fastener position, α r (x f,i ,x f,n ) represents the vertical displacement of the rail at the ith fastener when a vertical unit excitation is applied to the rail at the nth fastener, α r (x f,i ,x w,p ) represents the vertical displacement of the rail at the i-th fastener when a vertical unit excitation is applied to the rail at the p-th passive wheel. Indicates that the floating plate is at the k+mN f The vertical displacement at each fastener, m represents the number of the floating plate, represents the complex stiffness of the fastener, u r (x f,n ) and u b (x f,n ) represent the displacements of the rail and the floating plate at the nth fastener, It means that when a vertical unit harmonic excitation is applied at the nth fastener position of the floating plate, the floating plate at the k+mN f Vertical displacement response at each fastener, N s Indicates the maximum value of the support spring number, Indicates the complex stiffness of the steel spring, K b and η b are the real part of the complex stiffness of the steel spring and the loss factor of the steel spring, u b (x s,n” ) represents the displacement of the floating plate at the n'th supporting spring, It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is f The vertical displacement response at each fastener is Indicates that the floating plate is at the l+mN s The displacement of the support spring, It means that when the vertical unit harmonic excitation is applied at the nth fastener of the floating plate, the floating plate is s The vertical displacement response at each support spring is: It means that when the floating plate is subjected to vertical unit harmonic excitation at the position of the nth supporting spring, the floating plate is l+mN s Vertical displacement response at each fastener.

3. The noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA according to claim 1 is characterized in that: The step S3 comprises the following steps: S301, calculating the fastener force and the vertical force between the passive wheel j and the rail according to the vertical displacement of the rail and the floating plate; S302, calculate the vertical force between the rail and the driving wheel j according to the fastener force and the vertical force between the passive wheel j and the rail * The dynamic admittance at S303, according to the dynamic admittance of the wheel in the frequency domain and the wheel-rail contact dynamic admittance, obtain the vertical wheel-rail forces between the rail and the driving wheel and the driven wheel in the frequency domain.

4. The noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA according to claim 3 is characterized in that: The rail is on the driving wheel * The expression of the dynamic admittance at is as follows: F f,i =-K f (1+iη f )[you r (X f,i )-you b (X f,i )] F w,j =-Z cw u r (x w,j ) in, Indicates that the rail is on the driving wheel j * The dynamic admittance at r (0,0) represents the vertical displacement of the rail at the driving wheel position when the rail is subjected to unit harmonic excitation at the driving wheel position, N f Indicates the number of fasteners, F f,i represents the fastener force, α r (0,x f,i ) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the i-th fastener position, F w,j represents the vertical force between the passive wheel j and the rail, α r (0,x w,j ) represents the displacement of the rail at the driving wheel when the rail is subjected to unit harmonic excitation at the jth passive wheel position, K f and η f They represent the real part of the complex stiffness of the fastener and the loss factor of the fastener, i represents the imaginary unit, u b (x f,i ) represents the vertical displacement of the floating plate at the i-th fastener position, Z cw represents the series dynamic admittance of the wheel-rail contact dynamic admittance and the wheel dynamic admittance, u r (x w,j ) represents the vertical displacement of the rail at the jth passive wheel, u r (x f,i ) represents the vertical displacement of the rail at the i-th fastener.

5. The noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA according to claim 1 is characterized in that: The expression of the vertical wheel-rail force in step S4 is as follows: Among them, F w-r,j' represents the vertical wheel-rail force between the rail and the j'th wheel, Indicates the jth * When a wheel is used as a driving wheel, the vertical force between it and the rail is Indicates that the j'th wheel is a passive wheel, and the jth * When the wheel j' is used as the driving wheel, the vertical force between the wheel j' and the rail, R(ω) represents the track irregularity spectrum, α w , α c and They represent the dynamic admittance of the wheel in the frequency domain, the dynamic admittance of the wheel-rail contact, and the dynamic admittance of the rail at the driving wheel j*, respectively. w represents the dynamic stiffness of the wheel in the frequency domain, u r (x w,j ) represents the vertical displacement of the rail at the driving wheel j, R0 represents the reference value of track irregularity, and λ represents the wavelength of track irregularity.

6. The noise prediction method for steel box composite beam based on dynamic admittance and FEM-SEA according to claim 1 is characterized in that: The step S5 comprises the following steps: S501, treating components with low modal density in the bridge structure as deterministic components, and using a statistical energy analysis subsystem to represent the statistical components; S502. The concrete bridge deck is modeled using the finite element method, and the steel box composite beam and the fully enclosed noise barrier are simulated using the statistical energy analysis subsystem. The connection between the finite element method and the statistical energy analysis subsystem is achieved through the built-in hybrid point connection and hybrid line connection of the software to complete the construction of the hybrid finite element-statistical energy analysis model FEM-SEA. S503. Based on the force transmitted to the bridge, noise prediction is performed using a hybrid finite element-statistical energy analysis model FEM-SEA to complete the noise prediction of the steel box composite beam.

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