Effect of imperfect contact on the cloaking of a circular elastic cylinder from antiplane elastic waves

The cloaking of an elastic circular cylinder embedded in a homogeneous, linear, isotropic, elastic medium from antiplane elastic waves, where the layered cloak has an imperfect interface, is investigated in this paper. The material properties of the cloak are determined using the transformation or change-of-variables method and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The location of the imperfect interface can be at the interface between the elastic cylinder and the cloak, or at any interface between the bi-material cells, or at the interface between the cloak and the surrounding medium. This problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices and the modified recursive procedure for a multilayered scatterer with an imperfect interface which is developed in this paper. Numerical results show that the effectiveness of the wave cloak depends on the location of the imperfect interface and the level of imperfect contact. The wave cloak is more effective when the imperfect interface is closer to the circular cylinder. In particular, when the imperfect interface is at the boundary of the circular cylinder, effective cloaking can be achieved independent of the level of imperfect contact. When the imperfect interface is located in the middle of the cloak, effective cloaking can only be achieved when the level of imperfect contact is very small, i.e., closer to a perfectly bonded interface.

Automated summary

This paper investigates the cloaking of an elastic circular cylinder embedded in an elastic medium from antiplane elastic waves. The multilayered cloak is constructed using the transformation method and the homogenization theory of composites. The effectiveness of the wave cloak depends on the location of the imperfect interface and the level of imperfect contact, with better performance when the imperfect interface is closer to the circular cylinder.