Wave-induced motion of rigid bodies: beads, boats and buildings

Abstract

The determination of rigid-body motion caused by incident waves is a familiar problem in mechanics. Good examples are the motion of a ship in the presence of water waves and the motion of a rigid structure in the presence of seismic waves. The basic goals are to determine the motion of the rigid body and the effects of the motion on the wave field, assuming linear theory is adequate. Although the underlying mathematical problems are similar, several solution methods have evolved, depending on the physical problems of interest. For ship motions, the standard approach is to decompose the problem into seven subproblems, one for each of the six rigid-body modes and one to take account of the incident wave. This approach is reviewed and then adapted to problems in acoustics and to problems in elastodynamics, such as those that arise in simple examples of soil–structure interaction. It is argued that the resulting approach for elastodynamic problems has clear advantages over those currently in use.