State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources |
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Authors: | M I A Othman |
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Institution: | 1.Zagazig University,Zagazig,Egypt |
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Abstract: | A two-dimensional equation of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with the
elastic modulus dependent on temperature and with an internal heat source is established using a Laplace transform in time
and a Fourier transform in the space variable. The problem for the transforms is solved in the space of states. The problem
of heating of the upper and the lower surface of a plate of great thickness by an exponential time law is considered. Expressions
for displacements, temperature, and stresses are obtained in the transform domain. The inverse transform is obtained using
a numerical method. Results of solving the problem are presented in graphical form. Comparisons are made with the results
predicted by the coupled theory and with the case of temperature independence of the elastic modulus. |
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Keywords: | |
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