Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals

TLDR: In this paper, it was shown that a proper surface wave may always occur in a stable linear anisotropic half space provided that a certain real symmetric 3*3 matrix B is not positive definite for all velocities less than a limiting velocity nu L, the velocity at which bulk wave solutions first appear.

Abstract: From a previous analysis it is known that a proper surface wave may always occur in a stable linear anisotropic half space provided that a certain real symmetric 3*3 matrix B is not positive definite for all velocities less than a limiting velocity nu L, the velocity at which bulk wave solutions first appear. B is also the lagrangian factor matrix for a particular straight dislocation moving uniformly in an infinite medium which is elastically identical to the half space. By examining the behaviour of the dislocation lagrangian and the eigenvalues of B at nu L, it is proved that proper surface waves may always occur except in cetain special cases. In each special case there always exists at least one bulk wave solution which satisfies the free surface condition on the half space boundary. Thus, there exist no forbidden directions for steady state propagation satisfying the free surface condition, i.e. either a proper (attenuated) surface wave and/or an unattenuated 'bulk surface wave' solution is possible. One simple numerical integration suffices to determine if a given propagation direction admits a proper surface solution.