Interaction of a Beam and Supporting Continuum under a Moving Periodic Load

摘要

Paper deals with the problem of critical velocities of a time variable vertical load moving along the horizontal axis of a track resting on a deformable subsoil. Provided the operating speed of the load oversteps a critical velocity, the system response increases beyond acceptable limits concerning the moving as well as stable parts of this dynamic system. Therefore critical velocities of various types should be carefully investigated. From the practical viewpoint, the load operating speed must not approach the lowest critical velocity in order to avoid any danger of the derailment. The track itself is considered as an infinitely long beam, supported by a visco-elastic 2D layer of a constant thickness with uniformly distributed mass resting on a hard bedrock. Velocity of the moving load is taken to be constant. The load history is supposed as harmonically variable in time. Critical velocities are investigated using mathematical model representing an interaction of two subsystems: (i) Timoshenko type prismatic beam and (ii) visco-elastic layer modelling the subsoil. Influence of the most parameters on the system response and mainly on critical velocity levels are investigated. It comes to light that conventional models neglecting the mass of the subsoil omit the most important critical velocities which are decisive from the viewpoint of the system applicability.