The time-honored method of studying the dynamics of fluid-solid interaction problems has been to either fix the solid or to prescribe its motion, for example, a steady translation or a regular oscillation. Investigations then focus primarily on the dynamics of the fluid flow and the study of the various features that develop, such as, for example, boundary layers, vortices, shock waves, and turbulence. An equally important focus, especially in engineering applications, is on computing the fluid dynamic loads exerted on the solid with a view to designing it to withstand these loads as it executes the prescribed motions—some familiar engineering examples being the aerodynamic loads on an aircraft and the hydrodynamic loads on a submarine. The dynamics of solids—rigid and deformable, in the absence of any ambient fluid—is also a well-researched topic. In each of these two principle branches of mechanics, many fundamental results have been obtained and many fundamental principles elucidated, starting from the very birth of the subject of theoretical mechanics.

Relatively far less attention has been paid to the dynamics of fluid-solid interaction problems where the solid is not constrained to stay put or move in a prescribed manner, and is free to move in response to the instantaneous fluid stress field on its surface. The focus in such a setting is as much on the dynamics of the solid as on the dynamics of the fluid. Moreover, the motion of the solid in turn influences the flow of the fluid around it, thereby intricately coupling the fluid and the solid dynamics. This is the definition of the dynamically coupled setting, and the topic, in the author’s opinion, merits consideration as an independent branch of theoretical mechanics.