A method and system for directional control of environmental vibration in rail transit using a wedge-shaped tree array

Abstract

The present invention provides a method and system for directional control of environmental vibration in rail transit using a wedge-shaped tree array. The present invention calculates the vertical vibration of the ground surface caused by the passing of a train beside a ballast track by constructing a semi-analytical three-dimensional dynamic response model. By coupling the wedge-shaped tree array into the model, the simulation of the effect of the tree vibration reduction measures is realized. By adjusting the parameters of the wedge-shaped tree array, a wedge-shaped tree array with the desired vibration reduction effect is obtained, and then the design parameters of the wedge-shaped tree array vibration reduction measures are obtained. The wedge-shaped tree array is arranged between the track structure and the target vibration control area, and the selection of tree characteristics such as tree species, tree height, and tree diameter and the arrangement method can be optimized according to the target vibration reduction frequency band and the desired vibration reduction effect. The present invention overcomes the limitations of existing traditional vibration isolation technologies in terms of cost and implementation, provides a wedge-shaped tree array vibration reduction measure with low cost, easy layout and meeting environmental protection requirements, and has good potential for popularization and application.

Description

Technical Field

[0001] The present invention relates to a design method for vibration reduction measures in the field of rail transit vibration and noise, and specifically, to a rail transit environmental vibration directional control method and system using a wedge-shaped tree array. Background Art

[0002] When rail transit is running, the wheel-rail interaction force is transmitted in the form of vibration waves along the track structure, tunnels and soil to nearby buildings, thereby reducing the indoor living comfort of residents along the line, interfering with the normal functions of vibration-sensitive targets such as precision instruments, high-end equipment and ancient buildings, and affecting the safe service of infrastructure such as track structures.

[0003] At present, existing research and existing technologies have shown that vibration isolation screens such as open trenches, filled trenches and wave blocking blocks can be set up in the propagation path to alleviate the environmental vibration caused by subway vehicles; however, traditional vibration isolation screens can only block elastic waves with a wavelength comparable to their size, and have a good control effect on medium and high frequency vibrations, but require a large size to achieve low-frequency vibration control, which is too costly.

[0004] Compared with the above-mentioned traditional vibration isolation screens, due to the local resonance mechanism, the smaller-sized metamaterial barrier can control low-frequency vibrations with wavelengths much larger than its size. Currently, various meter-scale local resonance metamaterials have been designed to be embedded in the soil or arranged on the surface to control the vibrations generated by seismic waves or elastic waves. Summary of the invention

[0005] To achieve the above object, the solution of the present invention is:

[0006] A method for directional control of rail transit environment vibration using a wedge-shaped tree array, comprising the steps of:

[0007] S1. Obtain the track structure and stratigraphic profile parameters within the target vibration control area based on geological survey data;

[0008] And count the distribution of vehicles passing over the track to obtain representative vehicle parameters;

[0009] and obtaining track structure parameters according to the structural design;

[0010] and preliminarily determining characteristic parameters of a wedge-shaped tree array; the wedge-shaped tree array is disposed between the track structure and the target vibration control area;

[0011] S2. Based on the stratigraphic profile parameters, representative vehicle parameters, and track structure parameters obtained in S1, a vehicle-track-stratum coupling semi-analytical dynamic calculation model (abbreviated as “Model 1”) is constructed;

[0012] S3. Based on the “Model 1” constructed in S2, calculate the vibration condition of the target vibration control area caused by the operation of adjacent rail transit trains, and determine the target vibration reduction frequency band and the expected vibration reduction effect;

[0013] S4. Based on the characteristic parameters of the wedge-shaped tree array initially planned and on the basis of the “Model 1” constructed in S2, the wedge-shaped tree array is regarded as a resonator array composed of vertical vibrating rods. Through the displacement continuity and stress balance conditions of the contact surface between the ground and the trees, a semi-analytical dynamic calculation model of vehicle-track-stratum-tree coupling (abbreviated as “Model 2”) can be established;

[0014] S5. Based on the target vibration reduction frequency band and expected vibration reduction effect determined in S3, the "Model 2" established in S4 is used to calculate the insertion gain / loss peak frequency band and amplitude of the target vibration control area amplitude when considering different wedge-shaped tree array characteristic parameters, and a series of laws of how the vibration reduction characteristics of the wedge-shaped tree array change with the characteristic parameters of the wedge-shaped tree array are obtained. Based on this law, the characteristic parameters and arrangement of the wedge-shaped tree array are strategically adjusted to guide the layout of the wedge-shaped tree array to achieve effective directional vibration reduction control.

[0015] Preferably, in S1, the wedge-shaped tree array:

[0016] A measure to achieve directional control of rail transit environmental vibration using a wedge-shaped tree array. The wedge-shaped tree array is set between the track structure and the target vibration control area and arranged in an inverted wedge shape. The selection and arrangement of the tree characteristics of the tree species, tree height, and tree diameter can be optimized according to the target vibration reduction frequency band and the expected vibration reduction effect.

[0017] Preferably, in S1, the tree species, tree height, and tree diameter characteristics of the wedge-shaped tree array should comply with the "Railway Safety Management Regulations" and local municipal or greening requirements. The initially determined wedge-shaped tree array parameters include: longitudinal tree spacing a jx , horizontal tree spacing a jy , the number of vertical trees is N x , the number of horizontal trees is N y , tree height h, tree diameter d, tree Young's modulus E t , Poisson's ratio ν t , damping ratio ξ t , density ρ t .

[0018] Preferably, in S1, the wedge-shaped tree array is arranged in order of tree height in the direction perpendicular to the track, and the closer the tree is to the track, the higher the tree is. The horizontal distance between the wedge-shaped tree array and the track and the target vibration control area is expressed as D t , D s .

[0019] Preferably, in S1, the formation parameters of the track structure and the target vibration control area are obtained according to the geological survey data, including: the shear wave velocity C of each soil layer within 10m below the ground surface; s1 ,...,C sn , longitudinal wave velocity C p1 ,...,C pn , damping ratio ξ s1 ,...,ξ sn , and the corresponding density ρ s1 ,...,ρ sn , n represents the type of soil layer within 10m below the surface.

[0020] Preferably, in S1, the track structure parameters obtained according to the structural design include: rail bending stiffness EI, mass per unit length m R , rail pad compression stiffness k P , rail pad damping ratio, sleeper unit length mass m S , the contact width between the ballast and the ground surface is 2b, and the mass per unit length of the ballast is m B , ballast compression stiffness k B .

[0021] Preferably, in S1, the representative vehicle parameters obtained according to the statistical vehicle distribution include: the distance w between adjacent wheelsets under the same bogie a , the distance between adjacent wheelsets under two bogies is w b , vehicle length l k .

[0022] Preferably, in S2, the construction process of "Model 1" (implemented by writing code in MATLAB):

[0023] For the vehicle-track part in "Model 1", the traditional wheel-rail coupling model is used. The vehicle is simulated by multiple simple harmonic point loads acting on the wheelset on the wheel and rail. The track adopts a double-layer beam model, the rails and sleepers are simulated by infinitely long Euler beams, and the rail pads and ballast are simulated by mass springs.

[0024] The track structure and the stratum are coupled through the stress-strain equilibrium condition at the contact surface.

[0025] For the stratum part in "Model 1", the wave equation (1.1) is solved by the three-dimensional thin layer method, and a three-dimensional semi-analytical dynamic calculation model of the stratum is constructed based on this:

[0026]

[0027]

[0028] In formula (1.1), L is the differential operator, as shown in formula (1.2), D is the stiffness matrix, and the shear wave velocity C of the soil layer can be obtained from S1 s1 ,...,C sn , longitudinal wave velocity C p1 ,...,C pn , and the corresponding density ρ s1 ,...,ρ sn to determine, b is the external load vector, and u is the surface displacement vector to be solved.

[0029] Based on equation (1.1), the discrete wave equation (1.3) of the thin layer can be constructed by double Fourier transform:

[0030]

[0031] in is the external load vector and the surface displacement vector to be solved, A xx , A xy , A yy , B x , B y , G, M can be obtained by transforming D and L in formula (1.1), k x , k y are the vertical and horizontal wave number coordinates, and i is an imaginary number.

[0032] Based on formula (1.3), the vertical displacement of any point on the ground surface under any load frequency can be solved by writing code in MATLAB and combining it with the eigenvalue method. As shown in formula (1.4):

[0033]

[0034] in represents the second kind Bessel function, k j , Represents the jth eigenvalue and the corresponding eigenvector, which can be calculated by formula (1.3). The thickness of each thin layer in the thin layer method should be less than 1 / 6 times the maximum wavelength corresponding to the load frequency. A single thin layer is simulated by a four-node finite element. Considering a semi-infinite layered foundation, several perfectly matched layers are set below the finite thin layer to simulate the underlying semi-infinite space.

[0035] Preferably, in S4, according to the characteristic parameters of the wedge-shaped tree array preliminarily planned, on the basis of "Model 1" constructed in S2, the trees in the wedge-shaped tree array are simplified into vertical vibrating rods, and the wedge-shaped tree array is coupled with the stratum through the force and displacement balance conditions of the contact between the bottom of the trees and the ground, so as to construct "Model 2".

[0036] The "Model 2" still realizes the calculation and solution through MATLAB code:

[0037] S4.1 Abstract processing of each tree, i.e., a single tree:

[0038] The vertical vibration characteristics of a single tree are represented by the vertical vibration control equation of the rod (Equation (1.5)):

[0039]

[0040] where the parameter E of the tree t , ρ t was determined in S1, is the vertical displacement of the j-th tree to be solved, ω is the load frequency, and the general solution of this equation can be obtained through theoretical derivation as:

[0041]

[0042] In the formula, C 1 j and C 2 j are undetermined coefficients, ξ = ω(ρ t / E t ), 1 / 2 Let z = 0, and the vertical displacement at the contact point between the tree and the formation can be obtained, as shown in Equation (1.7):

[0043]

[0044] where is the vertical force at the contact point, and h is the height of the tree.

[0045] S4.2 Model 2 includes:

[0046] By the displacement continuity and force balance conditions in the vertical direction at the contact point between each tree and the ground surface, the vertical displacement vector U t at the contact point between each tree and the formation is solved, as shown in Equation (1.8):

[0047] U t =(I + H dd K t ) -1 H ds F ex (1.8)

[0048] In the formula, F ex where is the external load vector, K t is the vertical vibration displacement vector of the tree, calculated from Equation (1.6), I is the identity matrix; H dd , H ds is the fundamental solution matrix and vector of the ground surface, as shown in Equation (1.9):

[0049]

[0050] The subscripts x and y in the figure represent the tree numbers. Calculated by formula (1.4), the vertical displacement U of each tree contact point with the ground is obtained by formula (1.8): t After that, the vertical displacement vector U of the formation at any position s It can be calculated by formula (1.10):

[0051] U s =H ps F ex -H pd K t U t (1.10)

[0052] Where H ps ,H pd Specifically, as shown in formula (1.11), Also calculated by formula (1.4):

[0053]

[0054] Preferably, in S5, the vertical displacement of the ground surface in the target vibration control area is used as the vibration directional control index, and the vertical and horizontal boundary coordinates of the target vibration control area are expressed as x l ,x u ,y l ,y u It indicates that when the "Model 2" constructed in step S4 calculates the insertion gain / loss peak frequency band and amplitude of the amplitude of the target vibration control area with or without the wedge-shaped tree array considering the characteristic parameters of different wedge-shaped tree arrays, the characteristic parameters and arrangement of the wedge-shaped tree array are optimized and adjusted, and the layout of the wedge-shaped tree array is guided to achieve effective directional vibration reduction control.

[0055] In S5, the specific calculation scheme is:

[0056] a) Calculate the vertical displacement amplitude u of the ground surface in the target vibration control area with or without the wedge-shaped tree array at different load frequencies through "Model 2" with ,u without , and insert the profit and loss IL ave , as shown in formula (1.12):

[0057]

[0058] b) Combine the target vibration reduction frequency band and the expected vibration reduction effect, and compare the insertion gain / loss peak value, peak position, and frequency band width in the above calculation results;

[0059] c) Adjust the following wedge-shaped tree array arrangement parameters, including: the longitudinal tree spacing is a jx , the horizontal tree spacing is a jy , the number of vertical trees is N x , the number of horizontal trees is N y ; and adjust tree characteristic parameters, including tree height h, tree diameter d, and tree Young's modulus E t , Poisson's ratio ν t , damping ratio ξ t , density ρ t ;

[0060] Until the target vibration reduction frequency band and the expected vibration reduction effect are obtained.

[0061] A rail transit environment vibration directional control system using a wedge-shaped tree array is designed based on the above control method, including a track structure, a stratum within a target vibration control area, and a vehicle traveling on the track structure.

[0062] Also included are arrays of wedge-shaped trees;

[0063] The wedge-shaped tree array is disposed between the track structure and the target vibration control area;

[0064] The above-mentioned vehicles, track structure, strata, and wedge-shaped tree array are used to establish a vehicle-track-strata-tree coupling semi-analytical dynamic calculation model (abbreviated as "Model 2");

[0065] And in order to achieve effective directional vibration reduction control, the wedge-shaped tree array is arranged as follows:

[0066] Based on the obtained stratigraphic profile parameters, representative vehicle parameters, and track structure parameters, a vehicle-track-stratum coupling semi-analytical dynamic calculation model (abbreviated as "Model 1") is constructed; based on the constructed "Model 1", the vibration conditions of the target vibration control area caused by the operation of adjacent rail transit trains are calculated to determine the target vibration reduction frequency band and the expected vibration reduction effect;

[0067] According to the characteristic parameters of the wedge-shaped tree array initially planned, on the basis of the constructed "Model 1", the wedge-shaped tree array is regarded as a resonator array composed of vertical vibrating rods, and the displacement continuity and stress balance conditions of the contact surface between the ground and the trees are used to establish a semi-analytical dynamic calculation model of vehicle-track-stratum-tree coupling (abbreviated as "Model 2");

[0068] According to the determined target vibration reduction frequency band and the expected vibration reduction effect, "Model 2" is used to calculate the insertion gain and loss peak frequency band and amplitude of the target vibration control area amplitude when considering different wedge-shaped tree array characteristic parameters, and a series of laws of the vibration reduction characteristics of the wedge-shaped tree array changing with the characteristic parameters of the wedge-shaped tree array are obtained. Based on this law, the characteristic parameters and arrangement of the wedge-shaped tree array are strategically adjusted.

[0069] Compared with the prior art, the present invention has the following advantages:

[0070] 1. Based on the semi-analytical dynamic calculation model, a set of directional vibration reduction measures and design methods for rail transit wedge-shaped tree arrays that can be used in engineering practice are formed. The operation is simple, the calculation is efficient and has a theoretical basis. Compared with engineering experience judgment and complex numerical simulation calculations, it is more efficient.

[0071] 2. The directional vibration reduction measures and design method for the wedge-shaped tree array around the rail transit obtained by the present invention have a highly targeted vibration reduction effect, meet the needs of the project, and can achieve the purpose of saving subsequent construction costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present application, but do not constitute an improper limitation of the present invention. In the drawings:

[0073] Figure 1 The figure is a schematic diagram of the steps of the method of the present invention.

[0074] Figure 2 It is a schematic diagram of the vehicle-track-stratum-tree coupling semi-analytical dynamic calculation model in the present invention.

[0075] Figure 3 Schematic diagram of the double-layer beam model of the track structure in Example S2.

[0076] Figure 4 Schematic diagram of the vehicle model in Example S2.

[0077] Figure 5 Schematic diagram of calculation results of the vertical amplitude of the ground surface in the frequency domain under the wedge-less tree array when a train passes by in the embodiment.

[0078] Figure 6 It is a schematic diagram of the calculation results of the insertion gain and loss of the vertical amplitude of the ground surface in the frequency domain when there is a train passing under the wedge-shaped tree array when the target vibration control area under the wedge-shaped tree array is preliminarily prepared in the embodiment.

[0079] Figure 7 It is a schematic diagram of the calculation results in the frequency domain of the vertical amplitude insertion gain and loss of the surface under the wedge-shaped tree array in the target vibration control area under the wedge-shaped tree array after the directional adjustment of the parameters in the embodiment. DETAILED DESCRIPTION

[0080] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0081] Example:

[0082] This method constructs a semi-analytical three-dimensional dynamic response model to calculate the vertical vibration of the ground surface caused by the passage of a train beside a ballasted track. By coupling the wedge-shaped tree array 1 into the model, the effect of the tree vibration reduction measure is simulated. By adjusting the parameters of the wedge-shaped tree array 1, the wedge-shaped tree array 1 with the desired vibration reduction effect is obtained, and then the design parameters of the vibration reduction measure of the wedge-shaped tree array 1 are obtained. For details, see Figure 1 and Figure 2 , including the following steps:

[0083] S1 specifically includes the following steps:

[0084] (S1.1) The profile parameters of the stratum 4 of the track and target vibration control area 3 are obtained based on the geological survey data: In this case, the stratum 4 is regarded as a single-phase layered semi-infinite space soil, which is mainly composed of three layers of homogeneous strata 4 and the underlying semi-infinite space 5. Its soil layer parameters are: the shear wave velocity C of the first layer of soil s1 is 100m / s, longitudinal wave velocity C p1 is 200m / s, damping ratio ξ s1 is 0.01, density ρ s1 1800kg / m 3 ; The second layer of soil shear wave velocity C s2 is 100m / s, longitudinal wave velocity C p2 is 200m / s, damping ratio ξ s2 is 0.01, density ρ s2 1800kg / m 3 ; The shear wave velocity of the third layer of soil C s3 is 100m / s, longitudinal wave velocity C p3 is 200m / s, damping ratio ξ s3 is 0.01, density ρ s3 1800kg / m 3 There are no important buildings on the ground except the track structure 2, and since the groundwater level is low, the impact of groundwater does not need to be considered.

[0085] (S1.2) According to the construction design, the track structure 2 parameters are obtained: the rail bending stiffness EI is 1.26×10 7 GPa, mass per unit length m R is 120kg / m, and the unit length compression stiffness k of the rail pad P 3.50×10 8 GPa, rail pad damping ratio ξ t=0.15, sleeper unit length mass m S is 490kg / m, the contact width b between the ballast and the ground surface is 2.70m, and the mass per unit length of the ballast is m B is 1200kg / m, ballast compression stiffness k B 3.15×10 8 GPa.

[0086] (S1.3) According to the distribution of passing vehicles, obtain representative vehicle parameters: Consider the axle weight of the two carriages as the applied load, the distance w between adjacent wheels under the same bogie a is 2.5m, and the distance w between adjacent wheels under two bogies b is 14.875m, the vehicle length is l k It is 24.5m.

[0087] (S1.4) According to the Railway Safety Management Regulations and the preliminary selection of the municipal greening requirements, the design parameters of the wedge-shaped tree array 1 are proposed: the horizontal distance D between the wedge-shaped tree array 1 and the track and the target vibration control area 3 respectively t , D s 15m and 20m respectively; the number of vertical trees N x =15, number of horizontal trees N y =15, the spacing of trees in the horizontal and vertical directions a jx with a jy The tree diameter d is 0.5m, and the tree Young's modulus E t is 1.67GPa, Poisson's ratio ν t is 0.30, the damping ratio ξ t is 0.01, density ρ t 700kg / m 3 The trees are arranged in an inverted wedge shape. The closer to the track, the taller the trees are. The height difference between trees is in three levels: 0.5, 1.0 and 2.4m. There are 5 trees in each level. The height range of trees in each level is 0.5-3m, 3-8m and 8-20m.

[0088] S2 specifically includes the following steps:

[0089] (S2.1) Since the groundwater level in this case is low, the influence of groundwater is not considered. The foundation is simulated as an underlying semi-infinite space 5, and a three-dimensional semi-analytical dynamic calculation model of the stratum is constructed by the thin layer method: the thickness of the soil layer of interest is taken as 10m, the target vibration frequency is 1-80Hz, 60Hz is taken as the key frequency of interest, the thickness of the thin layer is taken as 0.33m, and the total number of thin layers is taken as 30; the underlying semi-infinite space 5 is simulated by a perfect matching layer (PML), and thin layer units are also used for division. The above thin layers are all simulated by four-node finite elements, and the schematic diagram can be seen in Figure 2Based on this, the dynamic response of any point in the stratum 4 when a unit simple harmonic load acts on any position on the surface can be calculated.

[0090] (S2.2) Establishing a track structure 2 model: This embodiment uses a double-layer beam model to simulate the ballasted track. Figure 3 The rails are used as the first layer of beams, and the sleepers are used as the second layer of beams. The vibration control equation of the Euler beam is used to describe the vibration characteristics of the above two layers of beams. The rail pads and ballast are simulated by uniformly distributed springs. The above-mentioned tracks and rail pads, rail pads and sleepers, and sleepers and ballast are coupled using the equilibrium conditions of stress and displacement.

[0091] (S2.3) Coupling track structure and stratum: The track structure is coupled with the stratum through the displacement continuity and stress balance conditions of the contact surface (see the following formula), thereby constructing a track-stratum coupling semi-analytical dynamic calculation model:

[0092] u g (x,y=0,z=0,t)=u sw (x,t)

[0093]

[0094] Where u g and p z is the ground vertical displacement and normal stress, u sw and F sw is the vertical displacement and normal stress of the roadbed at the interface between the roadbed and the stratum. Based on this model, the dynamic response of any point in the stratum under any load on the rail can be calculated.

[0095] (S2.4) Coupling track structure and vehicle: Since the vehicle load in this case only considers two carriages, each carriage contains two bogies and four wheelsets, see Figure 4 Without considering the unevenness of wheel-rail contact, the vehicle load in this case can be regarded as a series of moving point loads, that is, the superposition of unit loads at the positions of 8 sets of wheels, that is, P 1 ~P 8 The center line of the track structure is the x-axis, and the origin of the coordinate is located at the midpoint of the train longitudinal direction, that is, P 4 ,P 5 The midpoint of the vehicle-track-stratum coupling semi-analytical dynamic calculation model of this case is constructed.

[0096] In S3, the target vibration reduction frequency band and expected vibration reduction effect should comply with the "Urban Area Environmental Vibration Standard GB 10070-88" and the "Environmental Vibration Control Specification for Sensitive Buildings Constructed Around Metro Main Lines DB11 / T 1735-2020".

[0097] The specific contents of S3 are as follows:

[0098] Based on the vehicle-track-stratum coupling semi-analytical dynamic calculation model constructed in S2, the average vertical vibration displacement amplitude of the target vibration control area 3 within the load frequency range of 1-80Hz is calculated The target vibration control area 3 boundary is defined as: x l =-15m,x u =15m,y l =60m,y u =80m. Calculation results refer to Figure 5 The sensitive frequency range of the target vibration body is 70-75Hz in the medium and high frequency band. According to the national standard "Urban Area Environmental Vibration Standard GB 10070-88" and the local standard "Environmental Vibration Control Specification for Sensitive Buildings Constructed around Metro Main Lines DB11 / T 1735-2020", the target vibration reduction frequency band is determined to be 60-80Hz, and the expected vibration reduction effect is 10dB.

[0099] The specific contents of S4 are as follows:

[0100] According to the geometric characteristics and vertical vibration characteristics of trees, a single tree can be cleverly regarded as a vertically vibrating rod. The vibration characteristics of the wedge-shaped tree array 1 are described by the vertical vibration control equation of the rod, see Figure 1 The wedge-shaped tree array 1 is coupled with the vehicle-track-stratum model in S2 through the displacement continuity and stress balance conditions at the contact position between the bottom of each tree and the ground, so that the dynamic response of any point in the stratum 4 when the train passes by considering the wedge-shaped tree array 1 in this case can be obtained.

[0101] The specific calculation scheme of S5 is:

[0102] a) Calculate the vertical displacement amplitude u of the ground surface in the target vibration control area 3 with or without the wedge-shaped tree array 1 at different load frequencies through "Model 2" with ,u without , and insert the profit and loss IL ave , as shown in formula (1.12):

[0103]

[0104] b) Combine the target vibration reduction frequency band and the expected vibration reduction effect, and compare the insertion gain / loss peak value, peak position, and frequency band width in the above calculation results;

[0105] c) Adjust the following wedge-shaped tree array 1 arrangement parameters, including: the longitudinal tree spacing is a jx , the horizontal tree spacing is a jy , the number of vertical trees is N x , the number of horizontal trees is Ny ; and adjust tree characteristic parameters, including tree height h, tree diameter d, and tree Young's modulus E t , Poisson's ratio ν t , damping ratio ξ t , density ρ t ;

[0106] Until the target vibration reduction frequency band and the expected vibration reduction effect are obtained.

[0107] The embodiment specifically comprises the following steps:

[0108] S5.1 Evaluate the vibration reduction effect of the preliminarily designed wedge-shaped tree array 1: When the train passes through the target vibration control area 3 in the longitudinal direction, the vertical vibration displacement amplitude of the ground surface without considering the wedge-shaped tree array 1 is recorded as u without , the vertical vibration displacement amplitude of the ground surface when considering the wedge-shaped tree array 1 is recorded as u with , the dynamic response insertion loss is obtained through formula (1.12) to evaluate the vibration reduction effect of the wedge-shaped tree array 1.

[0109] S5.2 Figure 6 The insertion gain and loss of vibration amplitude in the range of 1-80Hz under the preliminary designed wedge-shaped tree array 1 are shown. It can be found that the vibration reduction frequency band of the existing scheme only includes 60-68Hz, which cannot cover the target vibration reduction frequency band (60-80Hz), and the maximum vibration reduction effect in the above section is only 8dB. It is necessary to further adjust the design parameters of the wedge-shaped tree array 1 to achieve the ideal vibration reduction target.

[0110] S5.3 Based on the parameter study of the model, the law of vibration reduction characteristics of the series of wedge-shaped tree array 1 is obtained:

[0111] ① Increasing the number of longitudinal trees or the number of transverse trees can significantly enhance the vibration isolation effect of the wedge-shaped tree array 1;

[0112] ② Larger horizontal tree spacing will produce additional attenuation bands in lower frequency bands;

[0113] ③ Reducing the longitudinal tree spacing will appropriately increase the bandwidth of the attenuation zone;

[0114] ④ The greater the height and diameter of a single tree, the higher the vibration reduction zone frequency of the target vibration control area 3. Based on this, the design parameters of the wedge-shaped tree array 1 are strategically adjusted to achieve the directional vibration reduction target. The specific steps are as follows:

[0115] a) According to the proposed vibration reduction target, the performance that needs to be improved is: widening the vibration reduction frequency band around 65Hz, and taking measures to reduce the longitudinal tree spacing to achieve bandwidth effect, and reduce the height and tree diameter of a single tree to achieve a higher frequency resonance effect. Updated longitudinal tree spacing a jxThe height of the tree is 1.5m and the tree diameter d is 0.4m.

[0116] b) According to the proposed vibration reduction target, the performance that needs to be improved is: increase the vibration reduction effect within the target vibration reduction frequency band (60-80Hz), and take measures to increase the number of horizontal and vertical trees and reduce the horizontal tree spacing to increase the vibration reduction effect. Updated horizontal tree spacing a jy is 1.5m, and the number of trees in the vertical and horizontal directions is N x =21,N y =21. The horizontal tree height arrangement is as follows: the trees are arranged in an inverted wedge shape, the closer the trees are to the track, the taller they are. The height difference between trees is in three levels: 0.4, 0.8 and 2.0m, with 7 trees in each level. The height range of trees in each level is 0.2-3m, 3-8.6m and 8.6-22.6m.

[0117] In this case, trees are selected as natural metamaterials with advantages such as low cost and green environmental protection. The local resonance between their vertical vibration and the surface waves will lead to vibration attenuation, which provides a new idea for low-frequency vibration control in rail transit. In addition, compared with traditional vibration reduction measures, the wedge-shaped tree array 1 can adjust the spacing, height and other parameters to achieve directional vibration reduction according to the needs of engineering design. Compared with the normal tree array of equal height, the wedge-shaped tree array 1 with a height arranged in a wedge shape can further convert the surface waves into shear waves and transmit them to the deep foundation, thereby generating a wider vibration attenuation zone frequency band.

[0118] c) Calculate the insertion gain or loss of the dynamic response in the frequency domain of the adjusted target vibration control area 3: Figure 7 As shown, it can be found that the overall vibration reduction effect is greatly improved due to the increase in the vertical and horizontal trees; due to the reduction in the vertical tree spacing, each vibration reduction frequency band achieves a bandwidth effect; in addition, due to the reduction in the horizontal wedge-shaped tree array 1 spacing, the Bragg scattering effect is more obvious, and additional vibration reduction frequency bands appear near 25Hz, 48Hz, and 73Hz.

[0119] In summary, in this case, by deploying the wedge-shaped tree array 1, the vibration in the 60-80 Hz frequency band of the target vibration control area 3 is reduced by more than 10 dB when a train passes by, which has a good directional vibration reduction effect.

[0120] In this case, only one parameter adjustment of the wedge-shaped tree array 1 is performed for simple illustration. In actual engineering, the comprehensive vibration reduction objectives and costs will be adjusted multiple times to obtain the optimal design parameters, thereby achieving the directional vibration reduction objectives more reasonably.

Claims

1. A method for directional control of vibration in rail transit environment using a wedge-shaped tree array, characterized in that: Includes steps: S1. Obtaining profile parameters of the track structure (2) and the stratum (4) within the target vibration control area (3) based on geological survey data; And count the distribution of vehicles passing over the track to obtain representative vehicle parameters; and obtaining track structure (2) parameters according to the structural design; and preliminarily determining characteristic parameters of a wedge-shaped tree array (1); the wedge-shaped tree array (1) is arranged between the track structure (2) and the target vibration control area (3); S2. Based on the stratigraphic (4) profile parameters, representative vehicle parameters, and track structure (2) parameters obtained in S1, a vehicle-track-stratum coupling semi-analytical dynamic calculation model is constructed, referred to as "Model 1"; S3. Based on the "Model 1" constructed in S2, calculate the vibration condition of the target vibration control area (3) caused by the operation of adjacent rail transit trains, determine the target vibration reduction frequency band and the expected vibration reduction effect; S4. Based on the characteristic parameters of the wedge-shaped tree array (1) preliminarily planned and on the basis of the "Model 1" constructed in S2, the wedge-shaped tree array (1) is regarded as a resonator array composed of vertical vibrating rods, and through the displacement continuity and stress balance conditions of the contact surface between the ground and the trees, a vehicle-track-ground-tree coupling semi-analytical dynamic calculation model is established, referred to as "Model 2"; S5. Based on the target vibration reduction frequency band and the expected vibration reduction effect determined in S3, the "Model 2" established in S4 is used to calculate the insertion gain / loss peak frequency band and amplitude of the amplitude of the target vibration control area (3) when considering different characteristic parameters of the wedge-shaped tree array (1), and obtain a series of laws of changes in the vibration reduction characteristics of the wedge-shaped tree array (1) as the characteristic parameters of the wedge-shaped tree array (1) change. Based on this law, the characteristic parameters and arrangement of the wedge-shaped tree array (1) are strategically adjusted to guide the layout of the wedge-shaped tree array (1) to achieve effective directional vibration reduction control.

2. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 1, characterized in that: In S1, the wedge-shaped trees array (1): The wedge-shaped tree array (1) is arranged in an inverted wedge shape, and the characteristic parameters and arrangement of the wedge-shaped tree array (1) are optimized and designed according to the target vibration reduction frequency band and the expected vibration reduction effect; The characteristic parameters of the wedge-shaped tree array (1) initially determined include: longitudinal tree spacing a jx , horizontal tree spacing a jy , the number of vertical trees is N x , the number of horizontal trees is N y , Tree height h , Tree Path d , Young's modulus of trees E t , Poisson's ratio ν t , Damping ratio ξ t ,density ρ t .

3. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 1, characterized in that: In S1, the wedge-shaped tree array (1) is arranged in order of tree height in the direction perpendicular to the track. The closer the tree is to the track, the taller it is. The horizontal distance between the wedge-shaped tree array (1) and the track and the target vibration control area (3) is expressed as: D t , D s .

4. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 2, characterized in that: In S1, the geological survey data are used to obtain the track structure (2) and the formation parameters of the target vibration control area (3), including: the shear wave velocity of each soil layer within 10 m below the surface of the formation (4); , longitudinal wave velocity , damping ratio , and the corresponding density , n Indicates the type of soil layer within 10m below the surface.

5. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 1, characterized in that: In S1, the track structure (2) parameters obtained according to the structural design include: rail bending stiffness EI , mass per unit length m R , rail pad compression stiffness k P , rail pad damping ratio, sleeper mass per unit length m S , the contact width between the ballast and the ground (4) surface is 2 b , ballast mass per unit length m B , ballast compression stiffness k B .

6. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 1, characterized in that: In S1, representative vehicle parameters obtained based on the statistical vehicle distribution include: distance between adjacent wheelsets under the same bogie , the distance between adjacent wheelsets under two bogies , vehicle length .

7. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 4, characterized in that: In S2, the construction process of "Model 1" is implemented by writing code in MATLAB: For the vehicle-track part in "Model 1", the traditional wheel-rail coupling model is used. The vehicle is simulated by multiple simple harmonic point loads acting on the wheelset on the wheel and rail. The track adopts a double-layer beam model, the rails and sleepers are simulated by infinitely long Euler beams, and the rail pads and ballast are simulated by mass springs. The track structure (2) and the stratum (4) are coupled via a stress-strain equilibrium condition at the contact surface; For the stratum part in "Model 1", the wave equation (1.1) is solved by the three-dimensional thin layer method, and a three-dimensional semi-analytical dynamic calculation model of the stratum is constructed based on this: （1.1） （1.2） In its formula (1.1) is a differential operator, as shown in formula (1.2), is the stiffness matrix, and the shear wave velocity of the soil layer obtained from S1 is , longitudinal wave velocity , and the corresponding density To confirm, is the external load vector, is the surface displacement vector to be solved; Based on equation (1.1), the discrete wave equation of the thin layer (1.3) is constructed by double Fourier transform: （1.3） in are the external load vector and the surface displacement vector to be solved, From (1.1) and Transformed to get, is the vertical and horizontal wave number coordinate, i is an imaginary number; Based on formula (1.3), the vertical displacement of any point on the ground surface under any load frequency is obtained by writing a code in MATLAB and solving it with the eigenvalue method. , as shown in formula (1.4): （1.4） in represents the Bessel function of the second kind, Indicates j The eigenvalues ​​and corresponding eigenvectors are calculated by formula (1.3). The thickness of each thin layer in the thin layer method should be less than 1 / 6 of the maximum wavelength corresponding to the load frequency. A single thin layer is simulated by a four-node finite element. Considering a semi-infinite layered foundation, several perfectly matched layers are set below the finite thin layer to simulate the underlying semi-infinite space (5).

8. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 7, characterized in that: In S4, according to the characteristic parameters of the wedge-shaped tree array (1) preliminarily planned, on the basis of the "model one" constructed in S2, the trees in the wedge-shaped tree array (1) are simplified into vertical vibrating rods, and the wedge-shaped tree array (1) and the stratum (4) are coupled through the force and displacement balance condition of the contact between the bottom of the tree and the ground surface, that is, "model two" is constructed; The "Model 2" is still calculated and solved by MATLAB code: S4.1 Abstract processing of each tree, that is, a single tree: The vertical vibration characteristics of a single tree are expressed by the vertical vibration control equation (1.5) of the rod: （1.5） The parameters of the trees is determined in S1, For the next j The vertical displacement of trees, is the load frequency, and the general solution of the equation is obtained by theoretical derivation: （1.6） In the formula C 1j and C 2j is the coefficient to be determined, ,make z = 0, and the vertical displacement of the contact point between the tree and the stratum is obtained, as shown in formula (1.7): （1.7） in is the vertical force at the contact point, h is the tree height; S4.2 "Model 2" includes: Through the displacement continuity and force balance conditions at the contact point between each tree and the ground, the vertical displacement vector at the contact point between each tree and the ground is solved. , as shown in formula (1.8): （1.8） In the formula where is the external load vector, is the vertical vibration displacement vector of the tree, calculated by formula (1.6), is the identity matrix; is the basic solution matrix and vector of the surface, as shown in formula (1.9): （1.9） middle The subscripts represent the tree numbers. Calculated by formula (1.4), the vertical displacement of each tree contact point with the ground is obtained by formula (1.8): After that, the vertical displacement vector of the formation at any position Calculated by formula (1.10): （1.10） In the formula Specifically, as shown in formula (1.11), Also calculated by formula (1.4): （1.11）。 9. A method for directional control of rail transit environment vibration using a wedge-shaped tree array as claimed in claim 1, characterized in that: In S5, the vertical displacement of the ground surface in the target vibration control area (3) is used as the vibration directional control index, and the vertical and horizontal boundary coordinates of the target vibration control area (3) are Indicates; the "model 2" constructed by step S4 calculates the insertion gain / loss peak frequency band and amplitude of the amplitude of the target vibration control area (3) with or without the wedge-shaped tree array (1) when considering different characteristic parameters of the wedge-shaped tree array (1), thereby optimizing and adjusting the characteristic parameters and arrangement of the wedge-shaped tree array (1), guiding the layout of the wedge-shaped tree array (1), and realizing effective directional vibration reduction control; In S5, the specific calculation scheme is: a) Calculation of the vertical displacement amplitude of the ground surface in the target vibration control area (3) with and without the wedge-shaped tree array (1) at different load frequencies using "Model 2" , , and insert profit and loss , as shown in formula (1.12): （1.12） b) Combine the target vibration reduction frequency band and the expected vibration reduction effect, and compare the insertion gain / loss peak value, peak position, and frequency band width in the above calculation results; c) Adjust the following wedge-shaped tree array (1) arrangement parameters, including: longitudinal tree spacing is a jx , the horizontal tree spacing is a jy , the number of vertical trees is N x , the number of horizontal trees is N y ; and adjust tree characteristic parameters, including tree height h , Tree Path d , Young's modulus of trees E t , Poisson's ratio ν t , Damping ratio ξ t ,density ρ t ; Until the target vibration reduction frequency band and the expected vibration reduction effect are obtained.

10. A rail transit environment vibration directional control system using a wedge-shaped tree array designed based on the rail transit environment vibration directional control method using a wedge-shaped tree array as described in any one of claims 1 to 9, comprising a rail structure (2), a stratum (4) within a target vibration control area (3), and a vehicle traveling on the rail structure (2). It is characterized in that Also included is an array of wedge-shaped trees (1); The wedge-shaped tree array (1) is arranged between the track structure (2) and the target vibration control area (3); The above-mentioned vehicle, track structure (2), ground layer (4), and wedge-shaped tree array (1) are used to establish a vehicle-track-ground layer-tree coupling semi-analytical dynamic calculation model, referred to as "Model 2"; And in order to achieve effective directional vibration reduction control, the wedge-shaped tree array (1) is arranged as follows: Based on the obtained stratum (4) profile parameters, representative vehicle parameters, and track structure (2) parameters, a vehicle-track-stratum coupling semi-analytical dynamic calculation model, referred to as "Model 1", is constructed; based on the constructed "Model 1", the vibration conditions of the target vibration control area (3) caused by the operation of adjacent rail transit trains are calculated to determine the target vibration reduction frequency band and the expected vibration reduction effect; According to the characteristic parameters of the wedge-shaped tree array (1) preliminarily planned, on the basis of the constructed "Model 1", the wedge-shaped tree array (1) is regarded as a resonator array composed of vertical vibrating rods, and through the displacement continuity and stress balance conditions of the contact surface between the ground surface and the trees, a vehicle-track-ground-tree coupling semi-analytical dynamic calculation model is established, referred to as "Model 2"; According to the determined target vibration reduction frequency band and the expected vibration reduction effect, "Model 2" is used to calculate the insertion gain / loss peak frequency band and amplitude of the target vibration control area (3) when considering different characteristic parameters of the wedge-shaped tree array (1), and a series of laws of the vibration reduction characteristics of the wedge-shaped tree array (1) changing with the characteristic parameters of the wedge-shaped tree array (1) are obtained. Based on this law, the characteristic parameters and arrangement of the wedge-shaped tree array (1) are strategically adjusted.

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