The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

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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.

The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids.The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design.The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.

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The traditional problems of the thick walled spherical and circular cylindrical shells under internal and external pressure are solved in the context of the theory of linear elastic materials with voids. The solutions are quasi-static. The stress distributions are those predicted by isotropic linear elasticity. The displacement and solid volume fraction charge fields exhibit a volumetric viscoelasticity induced by a rate dependence of the volume fraction change.

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