Active exterior cloaking of an inclusion with evanescent multipole devices for flexural waves in thin plates

Abstract

We present an active exterior cloak for flexural waves propagating in a Kirchhoff plate of infinite extent. The evanescent multipole devices are characterized by Macdonald functions K n of the required order, which, assuming time-harmonic vibrations, are solutions of the fourth-order biharmonic equation. It is shown that in the region of interfering waves, which emanate from the devices, a field is recreated which cancels the incident wave to yield a region of ‘stillness’. An inclusion is then positioned in this region for further investigation, with additional attention given to the boundary condition. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.