Elastic waves in crystals under a bias

Abstract

The temperature and stress induced effects on the propagation of elastic waves in anisotropic solids have been described by equations for dynamic fields superposed on a static bias. These equations are derived from the rotationally invariant equations of nonlinear elasticity for small dynamic fields superposed on a linear (infinitesimal) bias. The salient features of such equations of motion written in the reference and intermediate configurations of solids have been reviewed. The definitions of effective elastic constants in the two formulations and their relations with some of the earlier linearly based descriptions have been outlined. It has been shown that a proper description of nonlinear temperature induced effects on wave propagation in terms of either fundamental or effective elastic constants requires temperature derivatives of higher order elastic constants of quartz which are presently not available. Although the existing phenomenological approach based on a linearly based formulation yields satisfactory results in many instances, the discrepancy in some cases can be significant depending upon the anisotropy involved. Among other things, a perturbation procedure for the computation of the fractional change in the resonant frequency of bulk wave resonators and travel time of a surface wave in delay lines has been outlined. Many results have been reported in the literature from this procedure for situations when the bias is either homogeneous or inhomogeneous in the propagating medium. A few illustrative examples from the propagation of elastic waves in quartz under a mechanical or thermal bias are given.