State space approach to generalized thermoelastic problem with thermomechanical shock (original) (raw)
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Three-dimensional thermal shock problem of generalized thermoelastic half-space
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The model of the two-dimensional equations of generalized thermo-viscoelasticity with two relaxation times is established. The state space formulation for two-dimensional problems is introduced. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. The Fourier transforms are inverted analytically. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered. Comparisons are made with the results predicted by the coupled theory. Ó
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International Journal of Engineering Science, 2002
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International Journal of Thermophysics, 2010
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Canadian Journal of Physics, 2003
We construct a model of the two-dimensional equations of generalized thermoelasticity with two relaxation times in an isotropic elastic medium with the modulus of elasticity being dependent on the reference temperature. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern theory, is applied to the nondimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate, varying exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature. PACS No.: 46.25.Hf
A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium
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A unified form of thermoelasticity theory that contains three familiar generalized thermoelasticity. The Lord–Shulman theory, Green–Lindsay theory, and the classical one can be outlined in this form. The field quantities of a rotating/non-rotating half-space with and without the effect of the decay parameter can be obtained due to the unified thermoelasticity theory. The present medium is subjected to a time-dependent thermal shock taking into account that the magnitude of the thermal shock wave is not totally fixed but decaying over time. A special case of a thermal shock waveform with constant magnitude may be considered. The field quantities such as temperature, displacements, and stresses of the present problem are analytically obtained. Some plots of these field variables are presented in two- and three-dimensional illustrations in the context of refined theories.
Two-dimensional thermal shock problem of fractional order generalized thermoelasticity
Acta Mechanica, 2012
In this study, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the fractional order generalized thermoelasticity theory. The medium is assumed initially quiescent. Laplace and Fourier transform techniques are used to obtain the general solution for any set of boundary conditions. The general solution is applied to a specific problem of a half-space subjected to thermal shock. The inverse Fourier transforms are obtained analytically, while the inverse Laplace transforms are computed numerically. Some comparisons have been shown in figures to estimate the effect of the fractional order on all the studied fields.
Numerical solution for a nonlinear, one-dimensional problem of thermoelasticity
Journal of Computational and Applied Mathematics, 1998
A numerical solution for a nonlinear, one-dimensional boundary-value problem of thermoelasticity for the elastic halfspace is presented. The resulting equations are discussed and the numerical method is investigated for stability. Comparison with other existing numerical schemes is carried out. The obtained results clearly indicate the process of shock formation. The presented ÿgures show the e ects of di erent nonlinear coupling constants on the distributions of the mechanical displacement and temperature in the medium. A special case is brie y discussed.