Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach
Youssef Hamdy M. 1, El-Bassiouny Ahmed Habib 2
1Faculty of Engineering, Umm Al-Qura University, PO. Box 5555, Makkah, Saudi Arabia
e-mail: yousefanne@yahoo.com
2King Saud University, Faculty of Science, Department of Mathematics P.O.Box 83, 11942 Al-Kharj, Saudi Arabia
e-mail: essambassiouny@hotmail.com
Received:
Received: 25 April 2007; revised: 8 February 2008; accepted: 21 February 2008; published online: 7 April 2008
DOI: 10.12921/cmst.2008.14.01.55-64
OAI: oai:lib.psnc.pl:646
Abstract:
The theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one dimensional piezoelectric half-space with heating its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using state-space approach of the modern control theory. The general solution obtained is applied to a specific problems of a half-space subjected to three types of heating; the thermal shock type, the ramp type and the harmonic type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress and the strain distributions are shown graphically with some comparisons
Key words:
generalized thermoelasticity, piezoelectric material, state space, two-temperature
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