Transient motion of an anisotropic elastic half-space due to a buried line source

A method to deal with the two-dimensional transient problem of a line force or dislocation in an anisotropic elastic half-space is developed. The proposed formulation is similar to Stroh’s formalism for anisotropic elastostatics in that the two-dimensional anisotropic elastodynamic problem is cast into a six-dimensional eigenvalue problem and the solution is expressed in terms of the eigenvalues and eigenvectors. An analytic solution is obtained without performing integral transforms. Numerical examples are presented for a silicon half-space subjected to a line force or dislocation.