State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading |
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Authors: | Hamdy M Youssef Amnah H Al-Harby |
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Institution: | (1) Mathematical Department, Faculty of Education, Alexandria University, Alexandria, Egypt;(2) Faculty of Engineering, Umm Al-Qurah University, P. O. 5555 Makkah, Saudi Arabia;(3) Scientific Departments, Faculty of Education, Jeddah, Saudi Arabia |
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Abstract: | In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing
equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech
26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state
space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained
is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and
ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques.
Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters. |
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Keywords: | Generalized thermoelasticity Two-temperature State-space approach |
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