The effect of initial stresses on main characteristics of elastic waves in anisotropic media

Abstract

For a model of a hyperelastic anisotropic material, dynamic equations of acoustic wave propagation, written with respect to the velocity field associated with the passage of the wave are obtained. The propagation of a plane monochromatic wave in a medium with homogeneous preliminary finite strains and initial stresses is considered. It is assumed that during the propagation of sound waves, the gradients of displacements and velocities are small, and the field
of initial stresses is homogeneous. Using these assumptions, the equations of motion, linearized
in the vicinity of the initial stress-strained state are written.
Within the framework of the constructed model, the Christoffel equation, the expression for the radial velocity vector, and the equation of the refraction surface are generalized for the case of a hypoelastic medium. These equations make it possible to analyze the effect of initial stresses on the main characteristics of elastic waves.
The radial velocity vectors describing the energy transfer during the passage of acoustic waves are determined. An expression for the angle that characterizes the deviation of the direction of energy transfer from the direction of wave propagation is obtained. The effect of initial stresses and account of nonlinearity on the deviation of the radial velocity vector from the phase velocity vector compared with the classical solution is considered.
The problem of reflection of a plane elastic wave from a rigid barrier is solved. The influence of initial stresses on the change in the angle of reflection of quasi-longitudinal and quasi-transverse waves from a rigid barrier is considered.
For an anisotropic material with symmetry of properties inherent in cubic crystals, the influence of prestresses on wave propagation characteristics such as phase velocities, directions of polarization vectors, radial velocity vectors and refraction vectors is estimated.