On the Problem of Time-harmonic Water Waves in the Presence of a Freely Floating Structure

The two-dimensional problem of time-harmonic water waves in the presence of a freely floating structure (it consists of a finite number of infinitely long surface-piercing cylinders connected above the water surface) is considered. The coupled spectral boundary value problem modeling the small-amplitude motion of this mechanical system involves the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations governing the structure’s motion. It is proved that any value of the frequency turns out to be an eigenvalue of the problem for a particular structure obtained with the help of the so-called inverse procedure.