An approximate method for controlling solid elastic waves by transformation media

TL;DR

This paper introduces an approximate transformation method to control solid elastic waves using specially designed media, enabling advanced manipulation of elastic waves for various practical applications.

Contribution

It develops an approximate approach based on local affine mappings to derive transformed elastic parameters compatible with classical elasticity theory.

Findings

The method produces symmetric elastic moduli suitable for wave control.

Numerical simulations show effectiveness at high frequencies or small material gradients.

Potential applications include nondestructive testing and seismic wave management.

Abstract

By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration and seismology.