Study On The Design Of Wave-resistance Units Of Subway Track Elastic Pads Based On Phononic Crystal

With the large-scale construction and development of China's subway,the resulting environmental vibration problems increasingly affect people's production and life.At present,the most widely used vibration control in urban rail transit is to add a high elastic pad in the fastener system or to add a rubber vibration pad or steel spring in the track bed.Through vibration isolation measures to suppress vibration propagation,but for vibration can not be precisely controlled and attenuation is not ideal.Using periodic structure phonon crystal theory in solid physics,carries on the reasonable design from another aspect,this article provides a new way to further improve the low-frequency broadband damping effect of subway track elastic cushion.Based on the Bragg scattering and local resonant scattering mechanism,the structural design and material design of the elastic cushion is studied.Through the finite element analysis and theoretical analysis,the simplified calculation method of band gap is discussed,and the key parameters are studied.Combined with the response surface optimization method to give a reasonable engineering design,the final evaluation of the effectiveness of vibration and safety evaluation.The main research results and conclusions are as following:(1)The Bragg scattering mechanism is used to design the wave resistance unit,it discusses the feasibility of the design and the corresponding law.For three-tier cells,the middle layer of rubber grooving can increase the band gap,but will cause a decrease in stiffness;increasing the thickness of the intermediate rubber layer can reduce the starting frequency of the bandgap,which has no significant effect on the cutoff frequency but causes a decrease in stiffness;increasing the thickness of both sides of the steel band can increase the width of the bandgap,cut-off frequency will be significantly improved,the initial frequency will be slightly increased,almost no impact on the stiffness;increasing the elastic modulus of the intermediate rubber layer can improve the overall stiffness,but also increase the elastic wave velocity,resulting in the band gap decreases or even disappears.The elastic modulus of the rubber material is low,so the stiffness requirement of the cushion is difficult to meet.And the vertical dimension of the cushion is limited,so the band gap is more difficult to produce with the increase of the interface size.There is a long way to go for the elastic cushion to meet the requirements of stiffness and low band gap.(2)This article discuss the simplified method of calculating the bandgap and the calculation method of the cushion stiffness by using the local resonance scattering mechanism and analyze the influence of the key parameters on the bandgap.The bandgap frequency of the local resonant structure can be obtained by the natural frequency corresponding to the structural banding mode,which can simplify the calculation and improve the working efficiency.If the size of cell and scatterer is unchanged,the greater the thickness of the coating,the smaller the thickness of the matrix,and the band get lower,the band gap get narrower.If the size of cell and matrix is unchanged.the larger the size of the scatterer,the smaller the thickness of the cladding,and the starting frequency is gradually reduced,the band gap gradually widened.If the size of cell and cladding is unchanged,the smaller the size of the scatterer,the smaller the thickness of the matrix,and the band range get lower,the band gap get narrower.The density of the cladding and the scatterer,the elastic modulus of the cladding and the matrix are the main parameters of the bandgap control,whether it is a elastic pad in the fastener system or a rubber vibration pad in the track bed.With the increase of the elastic modulus of the matrix and cladding,the starting and ending frequency and the bandgap width gradually increases and the increase gradually slows down.The density of the matrix material mainly affects the ending frequency,the smaller the density of the matrix material,the easier it is to obtain a wider band gap and do not affect the initial low frequency.With the increase of the density of the scatterer material,the starting frequency is obviously reduced,the ending frequency is slightly reduced,the bandgap width gradually increases,and the larger the scatterer density is,the wider the band gap is.(3)The relationship between the band gap and the design parameters can be well analyzed by the response surface method.Based on the statistical analysis of the design sequence,the optimal design scheme is obtained according to the optimization target,what's more,proposing reasonable engineering design scheme according to the stiffness requirement.By comparing the results of the simplified algorithm with the dispersion curve,the rubber vibration pad in the track bed can be well matched,and the elastic pad in the fastener system has some error due to the absence of periodicity.The transmission loss of the frequency response function further validates the bandgap attenuation range.When considering the material damping,the transfer function curve is smoother,and the bandgap range is more obvious,but the attenuation value is reduced.With the increase of the elastic modulus of the matrix and the cladding,the bandgap attenuation is obviously decreased,so the stiffness and low frequency vibration isolation effect need to be weighed.For the rubber vibration pad in the track bed,the engineering scheme 1 attenuation is mainly in the range of 27.7Hz?121Hz,121Hz?146Hz,the maximum attenuation can reach 28.7dB and the stiffness is 17Mpa/m.The attenuation bandgap of engineering scheme 2 is mainly in the range of 28.64Hz?122.82Hz,112.82Hz?148.6Hz,the maximum attenuation can reach 28,88dB and the stiffness is 17Mpa/m.For elastic pad in the fastener system,engineering program 1 stiffness is 36.53 kN/mm,attenuation band gap is mainly located in 496.7Hz?1318Hz and the maximum attenuation value can reach 9.5dB.The stiffness of the engineering scheme 2 is 37.8kN/mm,the attenuation field is mainly located at 514Hz-1410Hz,and the maximum attenuation is about 9.4dB.