Forced Transient Motion of a Rigid Body Bonded to a Deformable Continuum

The dynamic response of a rigid mass supported by a deformable continuum is investigated, for the case that the mass is subjected to a load of arbitrary time-dependence. The motion of the mass generates waves in the supporting continuum. The accompanying radiation of energy provides a damping mechanism for the motion of the mass. In this paper two-dimensional problems are investigated for which the wave motion in the supporting continuum is governed by a single wave equation. Two examples to which the results apply are (a) normal motions of a rigid line element which is supported by a stretched membrane, and (b) antiplane motions of a rigid strip which is bonded to an elastic half space. The traction between the rigid body and the supporting continuum is determined in subsequent intervals of time, and the velocity and displacement of the mass are computed. Numerical results are presented for the case that the applied load is a step function with time.