Special inhomogeneous plane waves in cubic elastic materials

Abstract

The purpose of this paper is to present new special explicit inhomogeneous plane wave solutions of the linearized equations of motion for elastic cubic crystals. It is based upon the "directional-ellipse" method which leads to an eigenvalue problem for the complex symmetric acoustical tensor. The solutions are obtained by considering a special case for which the determination of the three complex eigenvalues of this tensor reduces to finding the three complex cubic roots of a real positive number. Explicit simple expressions are presented for the slowness and amplitude bivectors.

Mechanical/Thermal Sources in a Micropolar Thermoelastic Medium Possessing Cubic Symmetry without Energy Dissipation

“…Steeds [10] gave a complete discussion on the displacements, stresses, and energy factors of the dislocations for twodimensional anisotropic materials. Boulanger and Hayes [11] investigated inhomogeneous plane waves in cubic elastic materials. Bertram et al [12] discussed generation of discrete isotropic orientation distributions for linear elastic cubic crystals.…”

Deformation in micropolar cubic crystal due to various sources

“…Steeds (1973) gave a complete discussion on the displacements, stresses and energy factors of the dislocations for two-dimensional anisotropic materials. Boulanger and Hayes (2000) investigated inhomogeneous plane waves in cubic elastic materials. Bertram et al (2000) discussed generation of discrete isotropic orientation distributions for linear elastic cubic crystals.…”

The history and properties of ultrasonic inhomogeneous waves

“…Further findings of the interaction of inhomogeneous waves with anisotropic materials can be found in Deschamps and Assouline [76], Rogé [80], and Boulanger and Hayes [81]. In addition, the propagation of inhomogeneous waves in piezoelectric media has been considered by the first author of the current paper [108].…”