Water wave diffraction by a bottom-mounted circular cylinder clamped to an elastic plate floating on a two-layer fluid

Abstract

The wave diffraction by a bottom-mounted circular cylinder, which is clamped to the center of a floating circular thin elastic plate, in the two-layer fluid of finite depth is investigated for the time-harmonic incident waves of the surface and interfacial wave modes. Each fluid layer is inviscid, incompressible and of constant density. The flexural–gravity waves are composed of the propagating, decaying propagating and evanescent wave modes. Within the framework of the linear potential flow theory, a closed system of simultaneous linear equations is derived to solve the undetermined expansion coefficients with the methods of the angular eigenfunction expansion and the inner product. Explicit numerical computations are employed to test the convergence of the two series for the angular expansions and the evanescent wave modes. The horizontal forces and the moments exerted on the circular cylinder due to different wave modes are discussed in the case of the incident waves of either the surface or interfacial wave mode. It is obtained that the evanescent wave modes are appreciable parts for a high frequency.