Active cloaking of inclusions for flexural waves in thin elastic plates

We present a new method to create an active cloak for a single clamped inclusion in a Kirchhoff plate in the presence of flexural waves. In order to cloak this inclusion, we place control sources in the exterior of the scatterer and choose their intensities to eliminate propagating components of the scattered wave, thus reconstructing the incident wave. Our initial discussion is on the canonical problem of active cloaking of a clamped circular cylinder for which a closed form analytic solution is derived, and exemplified in a number of illustrative cases. We then consider a clamped scatterer of arbitrary shape with a smooth boundary and describe a method for solving the active cloaking problem.