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Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
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. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
MAGNETOVISCOELASTIC PLANE WAVES IN ROTATING MEDIA IN THE GENERALIZED THERMOELASTICITY II
, 2004
"... A study is made of the propagation of timeharmonic magnetothermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of KelvinVoigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The gene ..."
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A study is made of the propagation of timeharmonic magnetothermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of KelvinVoigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The generalized thermoelasticity theory of type II (Green and Naghdi model) is used to study the propagation of waves. A more general dispersion equation for coupled waves is derived to ascertain the effects of rotation, finite thermal wave speed of GN theory, viscoelastic parameters and the external magnetic field on the phase velocity, the attenuation coefficient, and the specific energy loss of the waves. Limiting cases for low and high frequencies are also studied. In absence of rotation, external magnetic field, and viscoelasticity, the general dispersion equation reduces to the dispersion equation for coupled thermal dilatational waves in generalized thermoelasticity II (GN model), not considered before. It reveals that the coupled thermal dilatational waves in generalized thermoelasticity II are unattenuated and nondispersive in contrast to the thermoelastic waves in classical coupled thermoelasticity (Chadwick (1960)) which suffer both attenuation and dispersion. 1.
THERMOELASTIC WAVE PROPAGATION IN A ROTATING ELASTIC MEDIUM WITHOUT ENERGY DISSIPATION
, 2003
"... A study is made of the propagation of timeharmonic plane thermoelastic waves of assigned frequency in an infinite rotating medium using GreenNaghdi model (1993) of linear thermoelasticity without energy dissipation. A more general dispersion equation is derived to examine the effect of rotation on ..."
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A study is made of the propagation of timeharmonic plane thermoelastic waves of assigned frequency in an infinite rotating medium using GreenNaghdi model (1993) of linear thermoelasticity without energy dissipation. A more general dispersion equation is derived to examine the effect of rotation on the phase velocity of the modified coupled thermal dilatational shear waves. It is observed that in thermoelasticity theory of type II (GreenNaghdi model), the modified coupled dilatational thermal waves propagate unattenuated in contrast to the classical thermoelasticity theory, where the thermoelastic waves undergo attenuation (Parkus, Chadwick, and Sneddon). The solutions of the more general dispersion equation are obtained for small thermoelastic coupling by perturbation technique. Cases of high and low frequencies are also analyzed. The rotation of the medium affects both quasielastic dilatational and shear wave speeds to the first order in ω for low frequency, while the quasithermal wave speed is affected by rotation up to the second power in ω. However, for large frequency, rotation influences both the quasidilatational and shear wave speeds to first order in ω and the quasithermal wave speed to the second order in 1/ω. 1.
Speed of Thermoelastic Rayleigh Wave in a Transversely Isotropic Heatconducting Elastic Material 1
"... Abstract: Thermal effects on Rayleigh wave speed in transversely isotropic medium are studied. A formula for the speed is derived first time in the said material. The speed of waves in some model transversely isotropic materials is calculated and is compared with the speed of the waves which propaga ..."
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Abstract: Thermal effects on Rayleigh wave speed in transversely isotropic medium are studied. A formula for the speed is derived first time in the said material. The speed of waves in some model transversely isotropic materials is calculated and is compared with the speed of the waves which propagate without thermal effects. It is observed that two Rayleigh waves propagate in the material under thermal effect. One wave propagates with the speed of the wave which propagates without thermal effect and the other one propagates with some higher speed. Key words: Rayleigh waves • transversely isotropic • orthotropic • strain energy