Classifications of surface waves in anisotropic elastic materials

Abstract

Surface waves in an anisotropic elastic material can be classified according to the number of distinct eigenvalues and the number of independent eigenvectors of the 6 × 6 real matrix N( υ). There are six groups under this classification. Surface waves can also be classified according to the number of partial waves in the solution and the form of each partial wave. There are again six groups according to this classification. The classifications encompass both subsonic and supersonic surface waves. The relationships between the two different classifications and the existence or non-existence of a surface wave in each group are discussed. We show how one can obtain a set of orthogonal and normalized eigenvectors and generalized eigenvectors for the matrix N( υ). The eigenvectors and generalized eigenvectors that appear in the surface wave solutions belong to a set of orthogonal eigenvectors with few exceptions, although orthonormalization is not required for surface wave construction.