Dynamics of trains and train-like articulated systems travelling in confined fluid—Part 1: Modelling and basic dynamics

The dynamics and stability of a train of flexibly interconnected rigid cylinders travelling in a confined cylindrical “tunnel” subjected to fluid dynamic forces is studied theoretically. Each cylinder, which is coupled to other cylinders and supported by springs and dampers, has degrees of freedom in the lateral translational and rotational directions. The kinetic, dissipation, and potential energies of the system and the generalized forces associated with the fluid dynamic forces acting on the system, such as inviscid fluid dynamic forces, viscous frictional forces, and form drag, are obtained first. Then the equations of motion are derived in a Lagrangian framework. The principal aim of this study is to investigate the effect of the aerodynamic forces on the dynamics of a high-speed train running in a tunnel, or more generally of a train-like system travelling in a coaxial cylindrical tube. The results of this study show that the system loses stability by flutter and that viscous frictional drag has a considerable effect on stability of the system. In addition, the mechanism of instability of the system is clarified with the aid of a study of the modal shapes and energy considerations.