Study On The Theoretical Model Of Coupled Vehicle&Track And The Characteristics Of Vibration Sources In A Curved Track

The rapid development of underground railways can effectively solve the problem of traffic congestion,but it will also induce environmental vibration.In order to satisfy the layout requirements of the city's topography,geology,and passenger flow distribution on the route of subway line,it is often necessary to set a large number of curved track when designing urban subway lines.For example,the curved track account for 30%-50%of the total mileage of different lines in Beijing subway based on incomplete statistics.The train-induced environmental vibration in the curved track is different from the straight line.The field test show that the ground vibration caused by the subway train passing through the curved track is larger than that of the straight line,and the lateral vibration intensity is 2-4 times larger than vertical.The research on its mechanism is still insufficient at present.In addition,about 50%of the curve track is subjected to dynamic load generated by the train operating with accelerating or decelerating velocity in parts of the subway lines.The wheel-rail dynamic interaction is very complicated as the train running through the curved track with variable speed,which may increase the train-induced environmental vibration.However,no scholars have conducted research on this issue so far.As an important factor affecting the train-induced environmental vibration.intensity,the vibration source generated during the subway train passing through the curve track has not been studied so far.The current rail transit environment vibration prediction and evaluation method is not accurate enough to consider the vertical vibration source characteristics of the curved track by the correction item,and it lacks the method for predicting and evaluating the lateral vibration.The vibration source in curved track will also influence the accuracy of the vibration prediction results and the reliability of the prediction method.In order to obtain the characteristics of the vibration source in the curved track,a theoretical model of coupled vehicle&curved track(TMCVCT)is established in the frequency domain in this dissertation under the supported of the National Natural Science Foundation of China named "Study on Prediction Model and Mitigation Laws of Environmental Vibrations Induced by Variable-speed Metro Trains in Curved Tunnels"(51378001)and "Study of Prediction Accuracy and Reliability of Train-induced Vibration and Its Environmental Influence"(No.51778049).The spectral and amplitude features of vehicle-track vibration sources in a curved subway track are obtained by analysis the amplitude and frequency distribution characteristics of the support reaction force.The main research contents and results of this dissertation are as follows.(1)The theoretical model of the dynamic response of a curved track is established in the frequency domain.The curved track supported by discrete fasteners can be treated as periodic structure.The vertical,lateral,longitudinal and torsional vibrations of the basic curved beam element are expressed by the mathematical mode superposition method,which is proposed based on the property of periodic structure in the frequency domain.The in-plane and out-of-plane dynamic response of the curved beam can be solved in the frequency domain.Dynamic responses of the curved track simulated by Euler-Bernoulli and Timoshenko beam are also obtained.(2)The theoretical model of the dynamic response of a curved track subjected to moving load with variable speeds is established in the frequency domain based on the superposition method of the steady-state dynamic response.(3)The theoretical model of coupled vehicle&curved track(TMCVCT)is established in the frequency domain.The flexibility matrix of curved rail and wheels which considering various movement states of vehicle operating on the curved track are derived using the moving loads excitation type according to Fourier integral transformation and coordinate transformation methods.The theoretical coupling of the dynamic equations of the vehicle system and the track system is realised according to the contact relationship between wheel-rail contact force and displacement in the frequency domain.The model of coupled curved track and accelerating/decelerating moving vehicle is also established.The models have clear concept of physics and mechanics,high computational efficiency,and no truncation error.(4)The dynamic load property of vibration source in the curved track are analyzed according to the theoretical model of coupled vehicle&curved track(TMCVCT),and both the train operating with a constant speed and a uniform acceleration speed are considered.And finally,the spectral and amplitude features of vibration sources in a curved subway track are obtained.