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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). ...
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
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.
Dual Phase Lag Heat Conduction and Thermoelastic Properties of a SemiInfinite Medium Induced by Ultrashort Pulsed Laser
"... In this work the uncopled thermoelastic model based on the Dual Phase Lag (DPL) heat conduction equation is used to investigate the thermoelastic properties of a semiinfinite medium induced by a homogeneously illuminating ultrashort pulsed laser heating. The exact solution for the temperature, the ..."
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In this work the uncopled thermoelastic model based on the Dual Phase Lag (DPL) heat conduction equation is used to investigate the thermoelastic properties of a semiinfinite medium induced by a homogeneously illuminating ultrashort pulsed laser heating. The exact solution for the temperature, the displacement and the stresses distributions obtained analytically using the separation of variables method (SVM) hybrid with the source term structure. The results are tested numerically for Cu as a target and presented graphically. The obtained results indicate that at very small time duration disturbance by the pulsed laser the behavior of the temperature, stress and the displacement distribution have wave like behaviour with finite speed. 1
MaxwellCattaneo Heat Convection and Thermal Stresses Responses of a Semiinfinite Medium due to High Speed Laser Heating
"... Based on MaxwellCattaneo convection equation, the thermoelasticity problem is investigated in this paper. The analytic solution of a boundary value problem for a semiinfinite medium with traction free surface heated by a highspeed laserpulses have Dirac temporal profile is solved. The temperatu ..."
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Based on MaxwellCattaneo convection equation, the thermoelasticity problem is investigated in this paper. The analytic solution of a boundary value problem for a semiinfinite medium with traction free surface heated by a highspeed laserpulses have Dirac temporal profile is solved. The temperature, the displacement and the stresses distributions are obtained analytically using the Laplace transformation, and discussed at small time duration of the laser pulses. A numerical study for Cu as a target is performed. The results are presented graphically. The obtained results indicate that the small time duration of the laser pulses has no effect on the finite velocity of the heat conductivity, but the behavior of the stress and the displacement distribution are affected due to the pulsed heating process and due to the structure of the governing equations. 1
© Hindawi Publishing Corp. THE REFLECTION PHENOMENA OF SVWAVES IN A GENERALIZED THERMOELASTIC MEDIUM
, 1998
"... Abstract. We discuss the reflection of thermoelastic plane waves at a solid halfspace nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic wave ..."
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Abstract. We discuss the reflection of thermoelastic plane waves at a solid halfspace nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.
© Hindawi Publishing Corp. MAGNETOELASTIC PLANE WAVES IN ROTATING MEDIA IN THERMOELASTICITY OF TYPE II (GN MODEL)
, 2004
"... A study is made of the propagation of timeharmonic plane waves in an infinite, conducting, thermoelastic solid permeated by a uniform primary external magnetic field when the entire medium is rotating with a uniform angular velocity. The thermoelasticity theory of type II (GN model) (1993) is used ..."
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A study is made of the propagation of timeharmonic plane waves in an infinite, conducting, thermoelastic solid permeated by a uniform primary external magnetic field when the entire medium is rotating with a uniform angular velocity. The thermoelasticity theory of type II (GN model) (1993) is used to study the propagation of waves. A more general dispersion equation is derived to determine the effects of rotation, thermal parameters, characteristic of the medium, and the external magnetic field. If the primary magnetic field has a transverse component, it is observed that the longitudinal and transverse motions are linked together. For low frequency (χ 1, χ being the ratio of the wave frequency to some standard frequency ω∗), the rotation and the thermal field have no effect on the phase velocity to the first order of χ and then this corresponds to only one slow wave influenced by the electromagnetic field only. But to the second order of χ, the phase velocity, attenuation coefficient, and the specific energy loss are affected by rotation and depend on the thermal parameters cT, cT being the nondimensional thermal wave speed of GN theory, and the thermoelastic coupling T, the electromagnetic parameters H, and the transverse magnetic field RH. Also for large frequency, rotation and thermal field have no effect on the phase velocity, which is independent of primary magnetic field to the first order of (1/χ) (χ 1), and the specific energy loss is a constant, independent of any field parameter. However, to the second order of (1/χ), rotation does exert influence on both the phase velocity and the attenuation factor, and the specific energy loss is affected by rotation and depends on the thermal parameters cT and T, electromagnetic parameter H, and the transverse magnetic field RH, whereas the specific energy loss is independent of any field parameters to the first order of (1/χ). 2000 Mathematics Subject Classification: 74F05. 1. Introduction. The
ON THE FLEXURAL AND EXTENSIONAL THERMOELASTIC WAVES IN ORTHOTROPIC PLATES WITH TWO THERMAL RELAXATION TIMES
, 2003
"... Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and fl ..."
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Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases. 1.
Director
, 2005
"... This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Doctor of Philosophy. ..."
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This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Doctor of Philosophy.