Abstract:
A linearized equation for the propagation of acoustic waves in bodies with preliminary finite deformations and initial stresses is obtained for hypoelastic materials. The equation is written in terms of the velocity field, which leads to perturbations of the initial configuration of the medium. The formula for a symmetric acoustic tensor is written for plane monochromatic waves.
It is shown that if a plane wave propagates along one of the anisotropy axes in cubic material, then the normal stresses in the plane of the wave front affect the phase propagation velocities of both longitudinal and transverse waves. The normal stresses acting perpendicular to the wave normal vector affect only the magnitude of the phase velocity of the transverse wave polarized along the stress direction. The shear stresses acting in the plane of the wave front have an effect on the propagation velocities of quasi-longitudinal and quasi-transverse waves. The shear stresses acting in the plane perpendicular to the wave front affect only the phase velocities of transverse waves. Analysis of the effect of initial stress on wave propagation in an isotropic material allowed revealing the occurrence of anisotropy in the acoustic properties of the medium and to describe shear wave splitting.
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