Wave power absorption by floating plates with application to piezoelectric or other bending-based absorption

Abstract

The wave scattering, motion, and energy absorption for a floating elastic plate that has an imaginary part to the bending rigidity in the frequency domain is found using an expansion in modes and a Green’s function. This imaginary part appears when energy is extracted from bending and arises in particular when the piezoelectric effect is used to absorb wave energy. However, it can also appear in other flexible wave-energy converters. The solution for a single plate is extended to multiple plates and various boundary conditions are investigated. A general energy identity is found showing that the energy absorption must be proportional to an integral over the plate of the imaginary part of the bending stiffness multiplied by the second derivative of the displacement squared. Various results investigating the absorption of energy are given, and simulations are presented in the time domain.