Uniformly bounded input gives ultimately bounded outpulon the dynamics of a piecewise linear beam system

A periodically excited piecewise linear beam system is studied. The beam system consists of a supported multi-degree-of-freedom beam with one-sided spring. This system is proved to have a 1-periodic solution to any uniformly bounded periodic force applied along the beam. The existence of a 1-periodic solution will be shown numerically and experimentally for both a harmonic force and a block-wave force.