Symplectic Analysis Of Random Vibration Of Vertical Vehicle-Track-Tunnel Coupled System With Consideration Of The Frequency-Dependent Stiffness Of Rail Pads

Combined with symplectic method and pseudo-excitation method(PEM), the random vibration of vehicle-track-tunnel vertical coupling system based on fixed-vehicle and moved-vehicle models is established. This model can calculate the influence of the frequency-dependent stiffness of rail pads on the frequency-domain random vibration of vehicle-track-tunnel vertical coupling system. The main research can be summarized as follows:(1) Based on symplectic method and PEM of random vibration, the more accurate and more efficient symplectic(fixed-vehicle) and generalized symplectic(moved-vehicle) model of vehicle-track-tunnel vertical coupling system were established. A comparative analysis of the stationary and non-stationary random response of vehicle-track-tunnel vertical coupling system was investigated.(2) By taking the typical sleeper-buried ballastless track structure in subway shield tunnel as the object, and based on the model of vehicle-track-tunnel vertical coupling system by the method of PEM and symplectic, the influence of the frequency-dependent stiffness of rail pads on the random vibration of vehicle body, vehicle bogie, vehicle wheelset, rail and tunnel was investigated.(3) The conclusions show that the frequency-dependent stiffness of rail pads has little effect on the random vibration of vehicle body, and yet alters the middle- and high-frequency random vibration amplitudes of vehicle bogie, meanwhile significantly increases the power peak and the 1 st dominant frequency of the random vibration response PSD of vehicle wheelset; the variation of the power peak and the 1st dominant frequency of wheelset’random vibration with the low-frequency initial stiffness of rail pads or the frequency-dependent extent of their stiffness respectively appears the wavy gradual and the stepped increasing trend. In the range of stiffness of the commonly-used rail pads, the power peak of wheelset’ random vibration response PSD has the maximal increase of 33.63 times, and its 1st dominant frequency also has the biggest increment of 46.9 Hz. Thus, in order to accurately predict the frequency-domain characteristics of random vibration of the structure under vehicle wheels, it is necessary to comprehensively consider the low-frequency initial stiffness of rail pads and the variation of their stiffness with middle and high frequencies.