Broadband cloaking for flexural waves

TL;DR

This paper introduces a novel broadband cloaking method for flexural waves in elastic plates using nonlinear transformation and equation matching, achieving high efficiency across a wide frequency range.

Contribution

It presents the first perfect broadband cloak for flexural waves by matching transformed and original equations, and offers an approximate practical implementation.

Findings

High cloaking efficiency over broad frequency range

Successful simulation demonstrating effective wave steering

Method applicable to other systems with non form-invariant equations

Abstract

The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the use of a nonlinear transformation, and by matching term-by-term the original and transformed equations. For a readily achievable flexural cloak in a physical setting, we further present an approximate adoption of our perfect cloak under more restrictive physical constraints. Through direct simulation of the governing equations, we show that this cloak, as well, maintains a consistently high cloaking efficiency over a broad range of frequencies. The methodology developed here may be used for steering waves and designing cloaks in other physical systems with non form-invariant governing equations.