BOUNDS ON ELASTIC-WAVE SPEEDS IN CRYSTALS - THEORY AND APPLICATIONS

The propagation of plane waves is considered in the context of the lin earized theory of elastic crystals (or anisotropic materials) which ex hibit orthorhombic, tetragonal, hexagonal, or cubic symmetry ('RTHC cr ystals'). Although not explicitly considered, the analysis is valid al so for waves of infinitesimal amplitude superposed on finite static ho mogeneous deformations of isotropic elastic bodies. An extremely simpl e procedure is presented for finding a lower bound and an upper bound on the speeds of propagation of all possible plane waves which may pro pagate in a given crystal of these classes. There is a drawback, howev er, in that the procedure may fail to give a meaningful lower bound (n egative lower bound for the squared wave speeds). Also, the bounds are not always attained, but the procedure immediately shows in which cas es they are attained. Even so, because of its simplicity the procedure may be of value particularly when searching for crystals with desirab le properties. The procedure is then applied in turn to each of the RT HC crystal systems. Numerical values of the bounds are presented for s everal specific crystals, illustrating the various possibilities arisi ng in the theory.