On the motion of a catamaran-type wave energy converter under periodic external forcing

Abstract Wave energy is one of the most promising renewable energy sources, and the catamaran-type point-absorption wave energy converter (PAWEC) is a widely studied prototype because of its compact size and its ability to absorb wave energy from all directions. The dynamics of such a device, however, are described by a system of high-dimensional nonlinear non-autonomous vibration equations under $T$-periodic excitation, and whether the system possesses a stable periodic response has not been rigorously established in general. In this paper, the radiation damping is represented by an equivalent constant-coefficient linear damping model commonly used in engineering practice, and the PTO system is modeled as a linear spring acting in parallel with a nonlinear damper whose damping coefficient is proportional to a power of the relative velocity. Using the coincidence degree theory of Mawhin, we prove that the resulting system admits a unique $T$-periodic solution, and we further prove that the solution of the Cauchy problem with arbitrary initial values converges asymptotically to this periodic solution. Numerical simulations for a catamaran-type PAWEC confirm the theoretical results and illustrate the global attractivity of the periodic response.