On the propagation of plane waves in type–III thermoelastic media

Abstract

The propagation of plane waves in infinite, three-dimensional, type-III thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low-and high-frequency asymptotic expressions are given, small-coupling limit results are derived, and special/limiting cases, including those corresponding to thermoelastic media of types II and I, are noted. Computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters. Of the findings presented, the following are most significant: (i) the determination of critical values of the physical parameters and their impact on the wavefields; (ii) ascertaining that type-III media behave, essentially, like type-II (respectively, type-I) media with respect to low-(respectively, high-) frequency plane waves; (iii) establishing the Whitham stability of plane waves in type-III media; and (iv) the determination of the dispersion characteristics of type-III media.

Regular global attractors of type III thermoelastic extensible beams

“…We recall results concerning uniqueness of solutions (see [21,23]) and their spatial behavior (see [20]), as well as several kind of wave propagation phenomena (see [19,24]). But, probably, the main efforts have been directed towards the asymptotic analysis of the related models (see [15-18, 22, 26, 29, 30]).…”

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

“…Moreover, the heat flux vector is determined by the same potential function that determines the stress. The Green-Naghdi theory has been studied in various papers (see, e.g., Chandrasekharaiah 1998;Hetnarski and Ignazack 1999;Quintanilla andStraughan 2000, 2004;Quintanilla 2003;Puri and Jordan 2004;Ieşan and Quintanilla 2009;Bargmann 2012 and references therein). The gradient theories of thermomechanics have been studied in various papers (see, e.g., Ahmadi and Firoozbakhsh, 1975;Ieşan, 1983Ieşan, , 2004Ieşan and Quintanilla, 1992;Ciarletta and Ieşan, 1993;Martinez and Quintanilla, 1998;Forest et al, 2000Forest et al, , 2002Forest and Amestoy, 2008;Forest and Aifantis, 2010).…”

Strong ellipticity and progressive waves in elastic materials with voids

“…The use of acceleration waves and related analysis has proved extremely useful in the recent investigations of wave motion in various dispersive and random media, in a variety of thermodynamic states, e.g. Ostoja-Starzewski & Trebicki (1999), Puri & Jordan (2004), Quintanilla & Straughan (2004), , , Jordan & Puri (2005) and Christov et al (2006).…”