The propagation of the energy of elastic waves in anisotropic media

The particular features of the propagation of the seismic energy of elastic waves in anisotropic media with four constants of elasticity, depending on the directions of motion of the waves and the ratios of the constants of elasticity for all practical media of the anisotropy class considered, are investigated. A direct connection is established between the formation of acute-angled edges on the fronts of quasi-transverse waves from point sources and the distinctive features of the propagation of the energy of the waves under certain conditions for the constants of elasticity.     

The propagation of shock waves in anisotropic materials

The propagation of shock waves in anisotropic materials (aluminium alloys), the state of which obeys a non-linear relation, which generalizes Grüneisen's equation for isotropic materials, is investigated. The concept of total generalized pressure and the pressure corresponding to the thermodynamic response is proposed. A modification of the anisotropic Hill criterion in the case of non-associated plastic flow, for which the yield surface is independent of the generalized hydrostatic stress, is considered.     

The propagation of elastic waves in a piezoelectric

Formulas of the ray method are developed in the case of the propagation of high-frequency waves in a piezoelectric. It follows from the equations of the paper that in first approximation the energy of the wave field propagates along rays.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 155–161, 1974.     

Stable elastic waves in anisotropic materials

Zusammenfassung Diese Arbeit befasst sich mit der Fortpflanzung von stabilen Wellen in einem anisotropen Medium infolge einer sich bewegenden Ladung an der Grenze des Materials. Wir behandeln besonders mobile Ladungen, deren Geschwindigkeit höher ist als diejenige der Wellen im Material. Das Problem wird als ebenes Spannungsproblem behandelt.

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This work was supported by the United States Atomic Energy Commission.     

The stability of quasi-transverse shock waves in anisotropic elastic media

The stability of weak quasi-transverrse shock waves in a weakly anistropic elastic medium with respect to arbitrarily oriented perturbations is investigated in the linear approximation. It is shown that fast quasi-transverse shock waves are stable.     

The propagation of elastic waves in a viscous-fluid-saturated porous medium

Elastic shock waves in a viscous-fluid-saturated porous medium are investigated. The porosity is only taken into account with respect to pores communicating with one another, and isolated pores are considered as elements of the elastic part of the porous skeleton. It is shown, using the theory of discontinuity, that in such a medium there are two types of vortex-free waves and one equivoluminal wave. Differential equations and their solution for determining the change in the wave-front intensity are obtained. The effect of the fluid viscosity and porosity on the propagation of spherical waves is demonstrated using an example.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Improved linear theory of elastic anisotropic multilayered shells. Part 1

The improved linear theory of elastic anistropic multilayered shells of an arbitrary shape has been confirmed, and hence the effect of the lateral displacement and normal lateral deformations is accounted for, for each layer.     

On the propagation of elastic waves in two-phase media

At the present time a number of papers has been already devoted to the dynamics of two-phase media. One may mention the papers by Frenkel' [1], Rakhmatulin [2], Biot [3,4], Zwikker and Kosten [5], and others. However, the basic problem of the setting up of the equations of motion in two-phase media still cannot be considered solved and requires additional study and experimental verification.

This paper is concerned with the study of the simplest case of motion, which is the propagation of elastic waves in a homogeneous isotropic medium consisting of a solid and a fluid phase. The problems of the reflection of plane waves and surface waves at the free boundary of the half-space are solved. It is shown that the stress-strain relations established by Frenkel' are equivalent to the analogous relations proposed by Biot and that the equations of motion of the latter are more general.     

On the growth of transverse waves in anisotropic elastic materials

Zusammenfassung Es wird gezeigt, dass die Amplituden ebener, transversaler Beschleunigungswellen, bei Fortpflanzung in einem anisotropischen und hyperelastischen Körper, entweder sich unendlich erweitern, oder bis auf Null abklingen können, je nach den Eigenschaften des Elastizitäts-Tensors zweiter Ordnung; auch wird weiterhin gezeigt, dass das Verhalten gewisser Komponenten der Unstetigkeits-Begleiterscheinungen dritter Ordnung tatsächlich verknüpft ist mit dem Verhalten der primären transversalen Wellen.     

The propagation of elastic waves in composite materials reinforced with piezoelectric fibres

The propagation of longitudinal elastic waves in composite materials, consisting of a polymer matrix reinforced by continuous fibres in one direction, is considered. The reinforcing fibres have piezoelectric properties and have a thin current-conducting coating (“shunted fibres”). The scattering of electric energy in such materials leads to dispersion of the velocity of the elastic waves and to their attenuation. The effective-field method is used to determine the macroscopic electroelastic constants of such composites. These constants enable one to obtain, in explicit form, the frequency dependence of the real and imaginary parts of the wave number of a longitudinal wave, propagating along the reinforcement direction, and also their dependenc on the physical and geometrical characteristics of the components.     

Reflection and transmission of elastic waves in the multilayered orthotropic couple-stressed plates sandwiched between two elastic half-spaces

In this paper, a high efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is provided to investigate the reflection and transmission of elastic waves in orthotropic couple-stress layered plates sandwiched between two elastic half-spaces. In this approach, the anisotropic couple-stress theory is introduced into the LOPM to calculate the reflection and transmission coefficients of the orthotropic interlayers. The stress components, couple-stress components, rotation vectors and governing equations are derived in terms of the Legendre orthogonal polynomial. The present method does not require calculations of the displacement solutions of each partial wave in anisotropic multilayered microstructures, but expands the displacement vector of each layer into a Legendre orthogonal polynomial series with the expansion coefficients to be calculated. The incident P wave and SH wave are calculated, respectively. The effects of length scale parameters in three different directions are studied. It is found that the reflection and transmission coefficients of the incident P wave are only related to the length scale parameter in the z direction. For incident SH wave, the influence of the length scale parameter along the thickness direction is much more significant than that of the length scale parameter in the y direction.     

On the dispersion of nonstationary surface waves in anisotropic elastic media

The whispering gallery modes propagating along the surface of an anisotropic elastic body are investigated with the use of space-time caustic expansions and space-time ray series. Each surface mode modulated in amplitude and frequency, is interpreted as a wave packet, with its amplitude’s maximum moving at a group velocity. On the boundary surface, asymptotic expressions for the group velocity (as a function of time and coordinates) are derived, which are in agreement with analogous formulas for Rayleigh waves of SV type in the isotropic case. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 299–312.     

On the speed of propagation of waves in a deformed elastic material

The secular equation is obtained for small amplitude waves propagated in an arbitrary direction in a body of incompressible isotropic elastic material subjected to a pure homogeneous deformation. Conditions are obtained that the wave speeds be real.

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Zusammenfassung Es wird die Säkulargleichung für Wellen kleiner Amplitude gewonnen, welche sich in beliebiger Richtung in einem inkompressiblen isotropen elastischen Material fortpflanzen, das einer reinen homogenen Deformation unterworfen ist. Es werden Bedingungen dafür aufgestellt, dass die Fortpflanzungsgeschwindigkeiten reell sind.