State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

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.

State-space approach to vibration of gold nano-beam induced by ramp type heating

“…Youssef with many authors investigated many applications in which the ramp-type heating is used [15][16][17][18][19][20][21].…”

Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids

“…Various investigators Youssef [12] , Puri and Jordan [13], Youssef and Al-Lehaibi [14], Youssef and Al-Harby [15], Magana and Quintanilla [16], Mukhopadhyay and Kumar [17], Roushan and Santwana [18], Kaushal et al [19], Kaushal et al [20], Ezzat and Awad [21] and Ezzat et al [22] studied different problems in thermoelastic medias with two temperature.…”

Two-Temperature Generalized Thermoelasticity without Energy Dissipation of Infinite Medium with Spherical Cavity Thermally Excited by Time Exponentially Decaying Laser Pulse

“…For this purpose, copper is taken as the thermoelastic material for which we take the following values of the different physical constants [11]: 1 3 386 kg m K s K Figures 1-5 represent the conductive temperature distribution, the thermodynamic temperature distribution, the strain distribution, the displacement distribution, and the stress distribution respectively, in the context of one-temperature type (solid lines) and two-temperature type (dashed lines). We can notice that the two-temperature parameter has significant effects on all distribution.…”