Surface waves in a rotating anisotropic elastic half-space

Abstract

The Stroh formalism for surface waves in an anisotropic elastic half-space is extended to the case when the half-space rotates about an axis with a constant rotation rate. The sextic equation for the Stroh eigenvalues, the eigenvectors, the orthogonality and closure relations are obtained. The Barnett–Lothe tensors are no longer real, but two of them are Hermitian. Taziev’s equation is generalized and used to derive the polarization vector and the secular equation without computing the Stroh eigenvalues and eigenvectors. An alternative derivation using the method of first integrals by Mozhaev and Destrade yields new invariants that relate the displacement and stress and are independent of the depth from the free surface. Explicit expression of the polarization vector and the secular equation for monoclinic materials with the symmetry plane at x 3 = 0 with the rotation about the x 3-axis obtained by Destrade is re-examined, and new results are presented. Also presented is the one-component surface wave in the rotating half-space.