Reciprocity and Energy Theorems Associated with Motions of a Floating Body in Waves

Abstract

There exists various mechanical relations associated with motions of a floating body in waves, and these relations have great value, because they help us to understand water wave phenomena. In this paper, reciprocity and energy relations between diffraction and radiation of a wave by a floating body are discussed from a new and systematic point of view. As an example, there exists the Haskind theorem, which relates the amplitude of the wave excitation force to that of the radiated wave (⇾eq. (14)). When the body is freely floating in a wave, the similar theorem can be derived by considering the equation of the motion of the body as well as the equation of the fluid motion. In this case, the amplitude of the displacement of the body is proportional to that of the radiated wave (⇾eq. (19)). The external damping does not affect the reciprocity relations, but energy relations for freely floating body must include a term, which represents the energy dissipation due to the external damping. The further results such as the Bessho theorem between diffraction and radiation potentials will be presented in near future.