Steady state and stability of a beam on a damped tensionless foundation under a moving load

In the first part of this paper we study the effect of damping on the multiple steady state deformations of an infinite beam resting on a tensionless foundation and under a point load moving with a sub-critical speed. Due to the non-linear characteristics of the problem, a guess on the deformed shape has to be made before a numerical search can be initiated. It is found that when the damping is present, all the steady state solutions are asymmetric. As the damping approaches zero, some of the steady state solutions become symmetric, while some others remain asymmetric. In the second part of the paper we propose to test the stability of these steady state deformations by a transient analysis on a long finite beam. Our numerical experiment indicates that among all these multiple steady state solutions only one of them is stable. This stable steady state deformation reduces to a symmetric solution when the damping approaches zero. Furthermore, it is found that this stable solution is also the one among all steady state solutions closest in shape to the linear solution based on a bilateral foundation model.