Work

Transformation-based cloaking for flexural–gravity waves in an anisotropic plate floating on shallow water

Year: 2025

Type: article

Abstract: The principle of cloaking has been developed and applied to different types of waves. We consider the application in the context of flexural–gravity waves on shallow water in order to reduce the wave force on an object. The parameters of the plate used to create a cloak in the vicinity of the object are found applying a space transformation method to the wave-propagation equation. The governing equation of a Kirchhoff–Love plate is generally not shape invariant, which traditionally induces error terms in the (thus approximate) use of the space transformation method. First deriving the equations of motion for the shallow-water–fully anisotropic plate system by a variational principle, we extend the transformation method to anisotropic plates and show that for every change of coordinates there exists a class of anisotropic plates such that the equation of motion is shape invariant. Furthermore, we consider examples in which the wave force on and the scattering by a rigid bottom-mounted vertical cylinder is reduced when surrounded by a floating plate with a cloaking region having material parameters computed by the presented method and we illustrate an approximate case by simulations.

Source: Wave Motion

DOI: 10.1016/j.wavemoti.2025.103642

Authors: Sophie Thery, Malte A. Peter, Luke G. Bennetts, Sébastien Guenneau