Complex dispersion analysis and elastic wave control of periodic steel spring floating slab track structures in urban railways

Urban railways represent another significant national strategy in China following high-speed railways. To mitigate environmental vibrations induced during the operation of suburban railways, steel spring floating slab tracks are installed in vibration-sensitive sections. This type of track exhibits distinct periodicity along the line direction, and this characteristics of the track structure have a filtering effect on the propagation of internal vibration waves. Unlike conventional metro lines, suburban railways operate at higher speeds. Therefore, investigating the propagation and attenuation mechanisms of elastic waves in periodic SSFSTs is of paramount importance for achieving refined vibration reduction in track structures. This study focuses on periodic SSFSTs, modeling the suburban SSFST as a Timoshenko beam-Mindlin plate system. Floquet-Bloch periodic boundary conditions are established based on the null-space method, and the complex frequency dispersion characteristics of the suburban SSFST are derived using the variational principle of the energy functional. The vibration transmissibility is analyzed through a finite-length track harmonic response model. Utilizing this approach, the influence of structural damping on the complex frequency dispersion of the track structure is thoroughly examined. Finally, a quasi-zero-stiffness (QZS) isolator is introduced to control low-frequency vibrations of the suburban SSFST, and its isolation effectiveness is verified through a three-dimensional vehicle-track coupling model. The research findings indicate that the suburban SSFST demonstrates superior vibration reduction capabilities compared to conventional SSFSTs. Moreover, structural damping significantly impacts the attenuation zones and attenuation rates of vibrations in the suburban SSFST structure. The QZS isolator reduces the dynamic stiffness of floating slab, resulting in a decrease in the first-order vertical resonance frequency of the floating slab track structure from 16 Hz to 8 Hz. This leads to a substantial attenuation in the vertical displacement response amplitude of the rail within the low-frequency range, thereby proving the excellent low-frequency vibration isolation performance of the QZS isolator.