Instability of vibration of high-speed train-and-rail system

The instability of vibration of train-and-rail coupling system is an important issue, in particular for high-speed trains. Till now, most of the research reports in this topic are based on simplified model. Some modeled the train as an infinitely long chain of evenly spaced oscillators, while some modeled the train just as a single moving mass or a moving vehicle having a single axle. This paper present a more sophisticated but realistic model. Each wagon comprising four axles is modeled as a coupling vibration system that has ten degrees of freedom. The railway track is modeled as an infinitely long Euler beam, which is subjected to an axial compressive force and rests on a visco-elastic foundation. In the formulation, the derivation of the governing differential equations for the integrated system is based on the Lagrangian approach. The Fourier and Laplace transforms are then employed to solve these differential equations. Through inverse Fourier transform and contour integration, a general instability equation is finally obtained and solved. Parametric studies are then carried out.