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 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 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.     

Thermo-poroacoustic acceleration waves in elastic materials with voids

A model for coupled elasto-acoustic waves, thermal waves, and waves associated with the voids, in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment such models for thermo-poroacoustic waves are of much interest to the building industry. Analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to industry and medicine. We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal wave. The thermodynamics is based on an entropy inequality of A.E. Green, F.R.S. and N. Laws and is presented for a modification of the theory of elastic materials with voids due to J.W. Nunziato and S.C. Cowin. A fully nonlinear acceleration wave analysis is initiated.     

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.     

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.     

Thermo-mechanic shock waves in elastic materials and viscous fluids

Sunto Si studiano onde d'urto termo-elastiehe, precisamente T--onde d'urto, propagantisi in corpi che o sono elastici, o appartengono a una certa classe K di fluidi Stokesiani, includenti propriamente quelli di Navier-Stokes. Inoltre si propongono dei problemi unidimensionali di evoluzione tnvolgenti T--onde d'urto, posti in una forma linearizzata. La teoria delle onde termo-meccaniche di accelerazione, o T--onde di accelerazione, per corpi elastici e fluidi di Navier-Stokes, è estesa brevemente alla classe K; inoltre si mostra che essa concorda con la presente per onde d'urto. Ciò ha luogo qualitativamente in ogni caso, e quantitativamente in molti casi importanti, includenti tutti quelli di T--onde (d'urto o di accelerazione) propagantisi in corpi elastici (o fluidi non-viscosi). Si intende che sia che esplicitino ed estendano un certo diffuso procedimento per studiare la propagazione delle onde in un certo corpo reale schematizzato soddisfacentemente da un corpo C capace di conduzione termica, il quale sia elastico o sia un fluido viscoso. Secondo questo procedimento (i) si considera un certo corpo puramente meccanico, (ii)si studiano le onde di accelerasione o d'urto in esso, e (iii)si attribuiscono i risultati di questo studio a C. Come è posto in evidenza in [1], sia che la parte di connessa eon onde di accelerazione, sono non-ortodossi, ossia incompatibili con la validità incondizionata di tutte le leggi fisiche. Inveee, come la corrispondente parte di, è ortodossa. Per il suddetto accordo tra e, questo fatto fornisce una spiegagione del successo sperimeniale di. Sia che sono teorie termo-meccaniche di discontinuità iterate in quanto in esse è necessario porre qualche postulato aggiuntivo, come analogo della scelta di in o rispettivamente.

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This work has been performed within the sphere of activity of the research group n. 3 of the C.N.R. (Consiglio Nazionale delle Ricerche) for mathematical physics, in the academic year 1978–79.     

Ultrasonic method of determining the elastic characteristics of anisotropic materials

An ultrasonic method of determining the elastic characteristics, developed for isotropic materials and based on the measurement of the angles of total internal reflection of ultrasound at a liquid-solid interface, is applied to an anisotropic Compreg of the DSPA type. The results obtained for the shear modulus using the ultrasonic method at 2.5 MHz and an independent method based on measuring the frequency of the damped torsional vibrations of a prismatic bar at 10–30 Hz are compared. It is shown that the shear modulus varies only slightly (10–12%) on the frequency interval investigated.Leningrad Kirov Forest Engineering Academy. Translated from Mekhanika Polimerov, No. 4, pp. 728–731, July–August, 1969.     

Propagation of quasielastic Rayleigh waves in an inhomogeneous,anisotropic, elastic medium

The propagation of modulated oscillations along the smooth surface free from normal stresses of an inhomogeneous, anisotropic, elastic body with parameters which vary little over a characteristic wavelength is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 234–245, 1979.The author thanks the participants of the seminar on the propagation and diffraction of waves of the Leningrad Branch of the Mathematics Institute (LOMI), in particular, V. S. Buldyrev and V. M. Babich, for fruitful discussions and their attention to the work.     

On nonstationary love waves near the surface of an anisotropic elastic body

Space-time (ST) ray expansions in the presence of a caustic are used for the construction of an asymptotics of surface waves similar to the SH Love waves. Certain conditions which ensure the existence of surface waves with SH polarization are deduced. Some special cases of anisotropic media are indiceted where these conditions are satisfied. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 166–172. Translated by Z. A. Yason.