Elastodynamic cloaking for earthquake protection - The importance of the inner boundary condition

Paper in proceeding, 2014

A decade ago transformational cloaking was discovered by Greenleaf, Lassas, and Uhlmann. Soon to follow were extensions of the approach to electrodynamics, elastodynamics, and acoustics. Early on, it was suggested that cloaking could be utilized to protect structures against seismic surface waves, by placing a suitable cloaking layer around the structure. Apart from the graded properties of the cloaking layer, the boundary conditions between cloak and surrounding soil, and the boundary condition between cloak and the structure are of importance for the performance of such a cloak. This is not surprising, as already the ancient Greeks discovered that, by arranging the interface between important structures and the underlying ground, it was possible to achieve some protection against earthquake waves, that might otherwise damage the structures. In the present paper we explore theoretically and numerically, how the inner boundary condition between cloak and the protected structure may affect the performance of some suggested modern elastodynamic cloaks.