Shock Loading of Heteromodular Elastic Materials under Plane-Strain Condition

The paper discusses the results of mathematical modeling the two-dimensional nonlinear dynamics of heteromodular elastic materials. The resistance of these materials under tension and compression is various. The deformation properties of the heteromodular medium are described within the framework of the isotropic elasticity theory with stress-dependent elastic moduli. In the plane strain case, it is shown that only two types of the nonlinear deformation waves can appear in the heteromodular elastic materials: a plane-polarized quasi-longitudinal wave and a plane-polarized quasi-transverse wave. Basing on obtained properties of the plane shock waves, two plane self-similar boundary value problems are formulated and solved.

Analysis of plane waves in anisotropic piezothermoelastic diffusive medium

Purpose – The purpose of this paper is to study the propagation of harmonic plane waves in a homogeneous anisotropic piezothermoelastic diffusive medium. Design/methodology/approach – After developing the mathematical model and theoretical analysis of the problem, computational work has been performed to study the different characteristics of the plane harmonic waves. Findings – The existence of waves namely, quasi-longitudinal wave (QP), quasi-thermal wave and quasi-mass diffusion wave have been found which propagates in an anisotropic piezothermoelastic diffusive medium. The different characteristics of waves like phase velocity and attenuation quality factor are computed numerically and presented graphically to show the piezoelectric effect. Originality/value – A significant piezoelectric effects have been observed on the different characteristics of the waves in an anisotropic piezothermoelastic diffusive medium.

ELASTIC WAVES IN TRIGONAL CRYSTALS

In non-isotropic single crystals the normals to the wavefronts of elastic waves are not colinear with the vectors representing either the energy flow or the particle displacement. Calculations have been carried out on the propagation characteristics of sound waves in two particular trigonal crystals, α-quartz and sapphire.The development of the eigenvalue equation for the velocity and the formulae for the components of the displacement and energy-flow vectors are summarized. The assumption that the wave has a plane wavefront normal to a given direction leads to three solutions, one representing a quasi-longitudinal wave and the other two representing quasi-transverse waves. The velocities of propagation, directions of displacement, and directions of energy flow for the three waves have been calculated for many orientations of the wave normal. Detailed results for propagation near one of the pure-mode axes are presented.