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1

Reflection of plane waves from surface of a generalized thermo-viscoelastic porous solid half-space with impedance boundary conditions

Singh B.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

1483--1496

EN

A phenomenon of reflction of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

2

The Thermal Relaxation Effect on 2-D Problems of the Generalized Linear Thermo-Viscoelasticity

Othman M. I. A.

Mechanics and Mechanical Engineering

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2009

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Vol. 13, nr 1

45-62

EN

In this paper we introduced the normal mode analysis for two-dimensional problems of the generalized linear thermo-viscoelasticity with one relaxation time. The exact expressions for the temperature distribution, the displacement components and the stress are obtained. The resulting formulation is applied to three different concrete problems. The first deals with a thick plate subjected to a time-dependent heat source on each face. The second concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-viscoelastic half-space subjected to appropriate boundary conditions and the third problem deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory.

3

Generalized Thermoelasticity Plane Waves in Rotating Media with Thermal Relaxation under the Temperature Dependent Properties

Othman M. I. A.

Mechanics and Mechanical Engineering

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2005

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Vol. 9, nr 2

89--110

EN

A two-dimensional coupled problem in generalized thermoelasticity for rotating media under the temperature dependent properties is studied. The problem is in the context of the Lord-Shulman's theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the temperature distribution, displacement components and thermal stresses. The resulting formulation is applied to two different problems. The first concerns the case of a heat punch moving across the surface of a semi-infinite thermoelastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subject to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. Comparisons are made with the results obtained predicted by the two theories in case of absence of rotation.

4

Effect of Rotation in Case of 2-D Problems of the Generalized Thermoelasticity with Thermal Relaxation

Othman M. I. A.

Mechanics and Mechanical Engineering

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2005

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Vol. 9, nr 2

115--130

EN

The mode of two-dimensional equations of generalized thermo-elasticity with one relaxation time under the effect of rotation is studied using the theory of thermo-elasticity recently proposed by Lord-Shulman. The normal mode analysis is used to obtain the exact expressions for the temperature distributions, the displacement components and thermal stresses. The resulting formulation is applied to two different concrete problems. The first concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-elastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subjected to a time-dependent heat source on each face. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with one relaxation time in the absence of rotation.

5

A domain of influence theorem in linear thermo-elasticity with thermal relaxation and internal variable

Cimmelli V. A., Rogolino P.

Archives of Mechanics

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2002

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Vol. 54, nr 1

15-33

EN

A domain of influence theorem is proved for a linear thermoelastic solid with a Cattaneo's type heat conduction law and a scalar internal variable. The obtained result is applied to prove the hyperbolicity of a semiempirical heat conduction theory, describing the propagation of thermal waves in crystals at low temperatures.