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 time-harmonic and of small amplitude near equilibrium, the linear setting reduces to a spectral problem with the radian frequency as the spectral parameter. It occurs that the total energy is finite provided the radiation condition holds; moreover, 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 of a symmetric cylinder with two immersed parts, symmetric and antisymmetric modes are considered separately. © 2023, Springer Nature Switzerland AG.