Dynamics of trains and train-like articulated systems travelling in confined fluid

The dynamical stability, wave propagation, response, and mode localization in a train of flexibly interconnected rigid cylinders travelling in a confined cylindrical "tunnel" subjected to fluid dynamic forces are studied theoretically. Each cylinder, which is coupled and supported by springs and dampers, has two degrees of freedom of translational and rotational motions. 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 by application of the Lagrange equation. The principal aim of this study is to investigate the effect of 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 (a) the system loses stability by flutter; (b) viscous frictional drag has a considerable effect on stability; (c) when the aerodynamic forces act on the train, the frequency bands of the dispersion relation of wave propagation shift, and thus no classical normal modes (standing wave solutions) exist in the system; (d) the wavelength of the travelling sinusoidal force controls phase differences among cylinders in the train: and (e) the imperfections in the supporting springs have a great influence on mode localization and considerably alter the stability of the system.