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Thermo-Mechanical Responses of an Annular Cylinder with Temperature Dependent Material Properties under Thermoelasticity without Energy Dissipation

Kumar A., Kumari B., Mukhopadhyay S.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 4

317--329

EN

The present work is concerned with thermoelasticity without the energy dissipation theory for a problem of an infinitely long and isotropic annular cylinder of temperature dependent physical properties.We employ the thermoelasticity theory of GN-II and derive the basic governing equations with variable material properties. The formulation is then applied to solve a boundary value problem of an annular cylinder with its inner boundary assuming to be stress free and subjected to exponential decay in temperature and sinusoidal temperature distribution. The outer boundary is also assumed to be stress free and is maintained at reference temperature in both cases. We solve the non-linear coupled differential equations by applying the finite difference approach efficiently. We analyze the numerical results in a detailed way with the help of different graphs. The effects of temperature dependency of material properties on the thermo-mechanical responses for two different time dependent temperature distributions applied at the inner boundary are highlighted.

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Spherically symmetric thermo-elastic wave propagation without energy dissipation in an unbounded medium with a spherical cavity

Bandyopadhyay N., Roychoudhuri S. K.

International Journal of Applied Mechanics and Engineering

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2010

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Vol. 15, no 4

993-1007

EN

The present paper is concerned with spherically symmetric thermo-elastic wave propagation without energy dissipation in an unbounded elastic medium with a spherical cavity. The inner boundary of the cavity is subjected to a unit step in stress and a zero temperature change. Short-time approximations of the solutions for displacement, temperature and stresses are given. The Laplace Transform is applied as a mathematical tool. It is observed that the solutions consist of two types of waves-modified thermal wave, traveling with speed […] and modified elastic wave, traveling with speed […]. Waves propagate without attenuation which is not the case in the Lord-Shulman theory (LST), Green-Lindsay theory (GLT) and Conventional Coupled theory (CCT). It is observed that the displacement is continuous at both the wave fronts while the temperature and stresses suffer jump discontinuities at these locations and that the jumps vary inversely with the radial distance from the center of the cavity in contrast to the case of LST, GLT, CCT where the jumps decay exponentially with distance from the centre of the cavity. The radial displacement, temperature, radial and circumferential stresses are numerically computed for different values of the radial distance from the centre of the cavity and their graphical representation is made.

3

Thermoelastic interactions without energy dissipation due to various sources

Kumar R., Rani L.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 2

431-446

EN

The linear theory of thermoelasticity without energy dissipation is employed to investigate the disturbance due to mechanical (horizontal or vertical) and thermal source in a homogeneous, thermoelasic half-space. Laplace-Fourier transforms are applied to the basic equations to form a vector matrix differential equation, which is then solved by using the eigenvalue approach. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and ilIustrated graphically for a magnesium-like material for an insulated boundary and temperature gradient boundary, respectively.

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Propagation of micropolar thermoelastic waves in plate

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 3

655-675

EN

The propagation of waves in a homogeneous isotropic micropolar thermoelastic plate subjected to stress free and rigidly fixed boundary conditions is investigated. The theory of micropolar thermoelasticity without energy dissipation has been taken to study the problem The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in the case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.

5

Reflection and refraction of thermoelastic plane waves at an interface between two thermoelastic media without energy dissipation

Kumar R., Sarthi P.

Archives of Mechanics

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2006

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Vol. 58, nr 2

155-185

EN

The reflection and refraction of thermoelastic plane waves at an imperfect interface between two dissimilar thermoelastic solid half-spaces has been investigated. The thermoelastic theory without energy dissipation developed by Green Naghdi [18] has been used to study the problem. The amplitude ratios of various reflected and refracted waves are obtained for an imperfect boundary. Particular cases of normal stiffness, transverse stiffness, slip and welded boundaries are discussed. The amplitude ratios are also deduced at the interface of two semi-infinite media (I) Elastic/Thermoelastic without energy dissipation, (II) Thermal Conducting Liquid/Thermoelastic without energy dissipation, (III) Non-viscous Fluid/Thermoelastic without energy dissipation, (IV) Thermal Conducting Liquid/Thermal Conducting Liquid and (V) Elastic/Elastic. It is found that the amplitude ratios of various reflected and refracted waves are affected by the stiffness and thermal properties of the media. The amplitude ratios of reflected waves are also deduced for a special case of stress-free boundary.

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Reflection of plane waves from the boundaries of a micropolar thermoelastic half-space without energy dissipation

Kumar R., Sharma J. N.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 4

631-645

EN

The present study is concerned with the reflection of plane waves in a micropolar thermoelastic half-space without energy dissipation. The reflection coefficients of various reflected waves with angle of incidence for thermaIly insulated and isothermal boundaries have been obtained. Thermal and micropolarity effects on these reflection coefficients have been shown graphicaIly. Some special cases have been deduced.