Study On Dynamic Response And Sound Radiation Prediction Of The Track Based On The Green’s Functions Method

The construction of urban rail transit is an important link to promote the process of regional integration.With the continuous development of subway systems and suburban rapid railway systems,the resulting vibration and noise problems have also attracted more and more attention.The track noise is one of the main sound sources of urban rail transit,and conducting an in-depth study of it is of great significance to reduce the vibration and noise of the track system.Appropriate theoretical models are the basis for the study on the track vibration and noise.The thesis aims to analyze the track dynamic response and predict the track sound radiation.The track system mechanics models and the time-domain wheel-rail dynamic coupled models are established based on the Green’s functions method,which realizes the rapid calculation of the track dynamic response.Adopting the FEM-BEM to establish the prediction and analysis model for the sound radiation characteristics of the track system,the results obtained by the Green’s functions method are further used to predict the track sound radiation.Thus,a complete calculation method of the track vibration and noise is formed.The main research contents of this thesis are as follows:(1)For the typical ballasted track and ballast-less slab track,the corresponding mechanics models are established.The frequency-domain and time-domain Green’s functions of the track system are obtained by using the Fourier method and the wave propagation method.Correlate frequency-domain analysis with time-domain analysis through Fourier transform,and the influence of the supporting stiffness in the track system on the track Green’s functions is also investigated.According to the numerical calculation results,the Fourier method and the wave propagation method have the different solving processes but the same essence.The former is faster but needs to meet conditions of mutual independence of the under-rail supports,while the latter has a wider range of applications without such limitation.The supporting stiffness in the track system has different effects on the amplitude,resonance frequency and attenuation of the track Green’s functions.In the slab track,the Green’s functions of the slab are much smaller than that of the rail.Different slab models and the changes of the supporting stiffness under the slab have little effect on the rail Green’s functions.(2)Based on the Green’s functions method and Hertz’s theory,the time-domain wheelrail dynamic coupled models are established,and the wheel-rail interaction is solved to obtain the dynamic response of the wheel and rail.The results show that the Green’s functions method can efficiently solve the wheel-rail dynamic response based on the known track Green’s functions.When the wheel moves at a constant speed,the wheel-rail interaction includes the transient and steady-state processes.The transient behavior occurs at the initial moment of movement and quickly decays into the steady state.Ideally,within the considered speed range,the wheel-rail force amplitude is the largest when the frequency of the wheel passing through the rail pads approaches the natural frequency of the wheel-rail system.Typical wheel-rail geometric irregularities,including the wheel flat,the rail corrugation and rail welded joints,can aggravate the wheel-rail interaction and may cause the wheel-rail impact.The increase in speed would amplify the influence of irregularities on the wheel-rail interaction,and parameters of the irregularities itself are also closely related to the dynamic response.(3)Applying the FEM-BEM,the prediction and analysis model for the sound radiation characteristics of the track system is established,and the wheel-rail forces obtained through the Green’s functions method are further used for the track sound radiation calculation,so as to study the changing laws of the track sound radiation.The simulation results show that the track sound radiation caused only by the parameter excitation would increase with the increase of the speed.Typical wheel-rail geometric irregularities,such as the wheel flat,the rail corrugation and rail welded joints have different effects on the amplitude and significant frequency bands of track sound radiation,and increasing speed would also amplify the influence of irregularities on the track sound radiation.The thesis mainly explores the dynamic response and sound radiation characteristics of the track,and forms a complete set of calculation method for the track vibration and noise based on the Green’s functions method and the FEM-BEM,which takes into account the accuracy and speed of calculation at the same time and provides a new idea for the vibration and noise prediction of the track system.