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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

Reflection of Plane Waves from Surface of a Generalized Thermo-viscoelastic Porous Solid Half-space with Impedance Boundary Conditions

Singh B.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 4

273--283

EN

A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in the 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 on the 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 the impedance parameter and the angle of incidence.

3

Circular crested waves in thermoelastic plates bordered with viscous liquid

Sharma J. N., Sharma P. K., Pathania S.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 2

513-534

EN

In this paper the propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting elastic plate bordered with layers (or half-spaces) of a viscous liquid on both sides is investigated in the context of non classical theories of thermoelasticity. Complex secular equations for symmetric and antisymmetric wave motion of the circular plate, in completely separate terms, are derived. The regions of the secular equation, waves of short and long wavelength are also discussed. Finally, in order to illustrate the analytical results, the numerical solution is carried out for a transversely isotropic plate of cobalt material bordered with water by using the functional iteration method. The results are deduced and compared with the existing ones in relevant publications available in the literature at various stages of this work.

4

Generalized thermoelastic plane harmonic waves in materials with voids

Sharma J. N., Kaur D.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 4

1019-1043

EN

The aim of the present paper is to give a detailed account of the plane harmonic generalized thermoelastic waves in solids containing vacuous voids based on the modified fourier law of heat conduction. The general characteristic equation being quartic suggests that there are four longitudinal waves, namely: quasi-elastic [...], quasi-thermal [...], volume fraction [...] and micro-thermal [...], in addition to transverse waves, which can propagate in such solids. The transverse waves get decoupled from the rest of the field quantities and hence remain unaffected due to temperature variation and porosity effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. The general complex characteristic equation has been solved by using descartes algorithm along with irreducible case of cardano's method with the help of demoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation. The propagation of waves in non-heat conducting solids has also been discussed. Finally, the numerical solution of the secular equation is carried out to compute phase velocities, attenuation coefficients and specific loss factors of thermoelastic waves which are presented graphically.

5

Generalized Rayleigh waves in thermoelastic solids under viscous fluid loading

Sharma J. N., Sharma R., Sharma Y. D.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 1

217-238

EN

The paper is aimed to study the propagation of Rayleigh surface waves in a homogeneous isotropic, thermally condueting, and elastic solid halfspace underlying a viscous liquid semi space in the context of generalized theories of thermoelasticity. The investigation is based on modelling the viscous liquid as a hypothetical solid in addition to conduction-convection condition of heat transfer at the interface. After developing the mathematical model, boundary conditions and formal solutions, the secular equations for a thermoelastic solid in closed form and isolated mathematical conditions for generalized Rayleigh waves (Stoneley waves), in complete forms are derived. The amplitude ratios of solid and liquid displacements and temperature change on the surface (interface) are obtained analytically. The surface particle motion has also been discussed and found to be elliptical. The semi-major and semi-minor axes, eccentricity and inclination of major axes with the wave normal are computed analytically and analyzed numerically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) underlying water, in the case of both light and heavy semi spaces. The dispersion curves, attenuation coefficient profiles and amplitude ratios of surface displacements, temperature change in the solid half space for generalized Rayleigh waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The present analysis is useful in electronics and navigation applications.

6

Forced vibrations due to mechanical loads in thermoviscoelastic halfspaces

Sharma J. N., Chand R., Chand D.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 1

105-121

EN

In the present article the Kelvin-Voigt model of linear viscoelasticity which describes the viscoelastic nature of a material is used to investigate the forced vibrations due to mechanical loads acting on the boundary of a thermoviscoelastic continuum. The Laplace and Hankel transform technique has been employed to solve the boundary value problem in the transform domain, in the context of various theories of generalized thermoelasticity. The inverse transform integrals are evaluated by using Romberg integration in order to obtain the results in the physical domain. The temperature and stresses so obtained in the physical domain are computed numerically and presented graphically in different situations for a copper material. The comparison of results for different theories of generalized thermoviscoelasticity is also presented at appropriate stages of this work.

7

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.

8

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.

9

Thermal radiation effects on free convection over a rotating axisymmetric body with application to a rotating hemisphere

Hossain M. A., Anghel M., Pop I.

Archives of Mechanics

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2002

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Vol. 54, nr 1

55-74

EN

This paper deals with the interaction of thermal radiation with free convection, laminar boundary-layer flow past a heated rotating axisymmetric round-nosed body of uniform surface temperature. The fluid considered is a gray, absorbing-emitting but nonscattering medium, and Rosseland approximation is used to describe the radiative heat flux. The difficulty of having a unified mathematical treatment of this problem is due to the nonsimilarity nature of the governing equations arising from the buoyant force-field and the transverse curvature of the body. The important parameters of this problem are the Planck number, Rd, the buoyancy parameter, ..., and the wall to free stream temperature ratio, .... Numerical solution of the boundary-layer equations are performed using the Keller-box method as well as the local nonsimilarity method. The theory is applied to a rotating hemisphere for a gas with Prandtl number of 0.72. The effects of the parameters ..., Rd and ... are shown on the velocity and temperature profiles, as well as on the local skin friction coefficient and local rate of heat transfer.

10

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.