Active elastodynamic cloaking

TL;DR

This paper introduces an active elastodynamic cloaking method that uses multiple sources to cancel incident elastic waves within a region, with explicit source amplitude predictions and analysis of cloaking accuracy.

Contribution

It provides a new explicit method to determine source amplitudes for active elastodynamic cloaking in two dimensions, including analysis of truncation effects.

Findings

Active cloaking effectively cancels elastic waves within a finite region.

The method explicitly predicts source amplitudes using Bessel function coefficients.

Cloaking accuracy depends on the truncation of infinite summations.

Abstract

An active elastodynamic cloak destructively interferes with an incident time harmonic in-plane (coupled compressional/shear) elastic wave to produce zero total elastic field over a finite spatial region. A method is described which explicitly predicts the source amplitudes of the active field. For a given number of sources and their positions in two dimensions it is shown that the multipole amplitudes can be expressed as infinite sums of the coefficients of the incident wave decomposed into regular Bessel functions. Importantly, the active field generated by the sources vanishes in the far-field. In practice the infinite summations are clearly required to be truncated and the accuracy of cloaking is studied when the truncation parameter is modified.