Acoustic Waves in Axial Crystals and Quasicrystals with Preliminary Finite Strains

The dynamic problem of acoustic wave propagation in elastic bodies with preliminary finite deformations is formulated. Several types of anisotropic elastic materials are considered: hexagonal crystals of class [Formula: see text], transversally isotropic materials and axial quasicrystals with an arbitrary order of the rotary axis. A variant of nonlinear hypoelasticity relations is constructed for these materials. In the constitutive relations, the tensor connecting the rate of change of the stress tensor and the strain rate tensor is a function of deformations. The propagation of acoustic waves in a hypoelastic material with preliminary finite deformations and stresses is described as a process of weak perturbations superimposed on finite strains. The characteristic features of elastic wave propagation in hexagonal crystals and axial quasicrystals are revealed. Within the framework of the constructed models, the most significant differences are found in the phase velocities of a transverse wave with a polarization vector located in the crystallographic plane (110). Unlike hexagonal crystals, in axial quasicrystals, there are such directions of acoustic wave propagation for which the phase velocities of transverse waves are insensitive to the degree of preliminary deformations. Based on the solution of the problem of elastic wave propagation, a program of dynamic experiments with macrosamples, which allows to distinguish axial quasicrystals from hexagonal crystals by the peculiarities of acoustic wave propagation, is proposed.