Scattering Theory of Gravity-Flexural Waves of Floating Plates on Water

We combine the theories of scattering for linearized water waves and flexural waves in thin plates to achieve control and characterization of water waves by floating plates. This requires manipulating a sixth-order partial differential equation with appropriate boundary conditions in terms of the velocity potential. Making use of multipole expansions, we reduce the scattering problem to certain linear algebraic system. The response of a floating plate simplifies in the quasistatic limit, with a different behavior for water waves and flexural waves. We then proceed with cloaking via scattering cancellation techniques. Unlike for similar studies in electromagnetics and acoustics, scattering is dominated by zeroth-order and this results in non-vanishing scattering cross-section in the zero frequency limit.