Symplectic Random Vibration Analysis of Vertically Coupled Vehicle-Track-Tunnel System Considering Frequency-dependent Stiffness of Rail Pads

In order to accurately predict the frequency-domain characteristics of random vibration of vehicle bogies, wheels, and the fundamental structure under wheels, a symplectic mathematics model of random vibration of a coupled vehicle-track-tunnel system is established using the pseudo excitation method (PEM) and the symplectic mathematics of infinite periodic substructures, with consideration of the low-frequency initial stiffness of rail pads and the frequency-dependent extent of stiffness. The model is used to analyze the influence of the frequency-dependent stiffness of rail pads on the random vibration of the coupled vehicle-track-tunnel system. Results show that the frequency-dependent stiffness of rail pads affects little the vertical random vibration of vehicle body, but it will increase vertical random vibration amplitudes of vehicle bogie at frequencies above 57 Hz and meanwhile significantly increase the peak power spectrum density (PSD) of the vertical random vibration of both wheelset and steel rail, as well as their 1st dominant frequencies. As the stiffness of rail pads increases with frequency, the natural frequency of the track structure shifts to a higher frequency range, and the energy of the wheel-rail resonance frequency band also transfers to a higher frequency region. As a result, the frequency domain of the wheel acceleration PSD distribution shifts upward by 8.6 Hz.