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1
Content available remote Fundamental Solutions in the Theory of Micromorphic Thermoelastic Diffusion Materials with Microtemperatures and Microconcentrations
Kansal Tarun
Computational Methods in Science and Technology
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2022
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Vol. 28, No. 1
11--25
EN
The main purpose of this paper is to construct the fundamental solutions of a system of equations of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations in case of steady oscillations in terms of elementary functions. In a particular case, the fundamental solutions of the system of equations of equilibrium theory of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations are also established.
2
Content available Generalized thermal microstretch elastic solid with harmonic wave for mode-I crack problem
Lotfy Khaled, El-Bary Alaa Abd, Allan Mohamed, Ahmed Marwa H.
Archives of Thermodynamics
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2020
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Vol. 41, no 2
147--168
EN
A general model of the equations of generalized thermo-microstretch for an infinite space weakened by a finite linear opening mode-I crack is solved. Considered material is the homogeneous isotropic elastic half space. The crack is subjected to a prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, using mathematical analysis with the purview of the Lord-Şhulman (involving one relaxation time) and Green-Lindsay (includes two relaxation times) theories with respect to the classical dynamical coupled theory (CD). The harmonic wave method has been used to obtain the exact expression for normal displacement, normal stress force, coupled stresses, microstress and temperature distribution. Variations of the considered fields with the horizontal distance are explained graphically. A comparison is also made between the three theories and for different depths for the case of copper crystal.
3
Content available remote Fundamental solution of plane waves in generalized thermo-microstretch elastic half-space
Othman M. I. A., Lotfy Kh., Farouk R. M.
International Journal of Applied Mechanics and Engineering
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2010
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Vol. 15, no 1
175-197
EN
A general model of equations of generalized thermo-microstretch for a homogeneous isotropic elastic half space is given. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of microstretch constants and between the three theories for two different times.
4
Content available remote Axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate
Kumar R., Partap G.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 1
211-237
EN
The propagation of axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of the conventional coupled thermoelasticity (CT) and Lord and Shulman (L-S) theories of thermoelasticity. The generalized theory of elasticity developed by Lord and Shulman is employed by assuming the mechanical behaviour as dynamic to study the problem. Mathematical modeling of the problem of obtaining dispersion curves for microstretch isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using the variable separable method to obtain the secular equations in isolated mathematical conditions for the plates with a stress free thermally insulated and isothermal boundary surface. The secular equations for both the symmetric and skew-symmetric wave mode propagation have been obtained. Thin plate results have also been deduced. These vibration modes are found to be dispersive and dissipated in character. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to the Rayleigh surface wave frequency equation. The dispersion curves, attenuation coefficients and amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically for the Lord and Shulman theory of elasticity. The theoretical and numerical computations are found to be in close aggrement.
5
Content available remote Propagatlon of Rayleigh-Lamb waves in thermomicrostretch elastic plates
Pathania D. S., Sharma J. N., Kumar R.
International Journal of Applied Mechanics and Engineering
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2007
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Vol. 12, no 4
1147-1163
EN
The propagation of waves in a thermo-microstretch elastic plate subjected to stress free isothermal and thermally insulated conditions is investigated in the context of the conventional coupled thermoelasticity (CT), Lord-Shulman (LS), and Green-Lindsay (GL) theories of thermoelasticity. The secular equations for the thermomicrostretch elastic plate in a closed form and isolated mathematical conditions for the symmetric and skewsymmetric wave mode propagation in completely separate terms are derived. The secular equations for the thermo-microstretch elastic plate, coupled thermoelastic, micropolar elastic, thermoelastic and elastic plates have been deduced as particular cases from the secular equations derived. At short wave length limits, the secular equations for the symmetric and skew symmetric waves in stresses free, thermally insulated and isothermal, thermo-microstretch elastic plate reduce to the Rayleigh surface wave's frequency equation. Finally, in order to illustrate the analytical development, the numerical solution is carried out for aluminum-epoxy composite material. The symmetric and skew symmetric wave modes are computed numerically and presented graphically. The theory and numerical computations are found to be in close agreement.
6
Content available remote Reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space
Kumar R., Partap G.
International Journal of Applied Mechanics and Engineering
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2005
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Vol. 10, no 2
253-266
EN
The present investigation is concerned with the reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space. The reflection coefficients of various reflected waves with the angle of incidence for Green-Lindsay theory for stress free and rigidly fixed boundaries have been obtained. The variations of various reflected waves showing thermal and stretch effects have been shown graphically. Special cases have been deduced.
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