On a cylinder floating freely in oblique waves

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study the so-called oblique waves. Under the assumption that the motion is of small amplitude near equilibrium and describes time-harmonic oscillations, the phenomenon's linear setting reduces to a spectral problem with the radian frequency as the spectral parameter. If the radiation condition holds, then the total energy is finite and the equipartition of kinetic and potential energy holds for the whole system. On this basis, it is proved that no wave modes are trapped under some restrictions on their frequencies; in the case when a symmetric cylinder has two immersed parts restrictions are imposed on the type of mode as well.