Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media

Abstract

A large variety of degeneracy exist in both static and dynamic regimes in anisotropic elastic media. Extraordinary degeneracies occur mostly in the static regime and they are of great importance in understanding the existence of the so-called space of degeneracy in the dynamic regime. This paper deals with the interconnection between degeneracies in the static and dynamic regimes. Both the modified Lekhnitskii formalism and the Stroh formalism are employed in exploring the degeneracies in the transversely isotropic media. It is demonstrated that the space of degeneracy can be regarded as an extension of the static degeneracy, and the development of the static extraordinary degeneracy into the dynamic regime is via a number of spaces of degeneracy of various types. The static degeneracy can also span a space of degeneracy.