Analysis of thermoelastic response in functionally graded hollow sphere without load

Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids

“…|, from Sharma and Mishra [51] for thermoelastic models. Here, themoelastic damping 𝑄 −1 has been denoted as 𝐷 𝐹 .…”

“…If nonlocal parameter, phase lag relaxation time parameters and voids constants have been ignored, that is, $${\zeta _0} = 0$$, $$\alpha = b = M = {\xi _1} = {\xi _2} = 0$$ and $${t_p} = {t_q} = 0$$, and system is in thermal equilibrium then the analysis of free vibrations is reduced to the coupled magneto‐thermoelastic hollow sphere. Further if nonlocal, voids, magneto parameters, the phase‐lags of temperature gradient relaxation time parameter are ignored, that is, $${\zeta _0} = 0$$, $$\alpha = b = M = {\xi _1} = {\xi _2} = \phi = 0$$, $${\mu _e}\, = {H_0} = 0$$, $${t_p} = 0$$ and the value of heat flux is considered as $${t_q} = {t_0}\,,\,\,t_q^2 = 0$$, also the functionally graded parameter $$\alpha = 0$$ has been taken in Sharma and Mishra [51], then the governing equations in present paper and Sharma and Mishra [51] have been reduced to …”

“…Keles and Tutuncu [50] investigated the vibration analysis of the elastic cylinder/sphere using Laplace transform technique. Sharma and Mishra [51] studied the vibration analysis of non-homogeneous thermoelastic sphere with traction free boundary conditions. Lots of work for free and forced vibrations in the reference of homogeneous and inhomogeneous materials were done by some researchers and authors such as Sharma et al [52], Abbas [53], Sharma and Mittal [54], Wang et al [55], Sharma et al [56], etc.…”

A control volume finite element method for the thermoelastic problem in functional graded material with one relaxation time

“…In the reported studies about the FGM thermoelastic problems in the context of L-S theory, to simplify the numerical solution process, the effects of T1 in equation (12) are also neglected. 12–15,20 However, the authors find that T1 has a great effect on the temperature distributions for the thermal shock problems in inhomogeneous material or FGM. To illustrate this point, the second example also demonstrates the effects of T1 on temperature.…”

“…Thermoelasticity in cylindrical shells with L-S theory was compared with that obtained from the G-L theory, and the effects of linear and non-linear temperature field across the shell thickness were examined. Sharma 15 used the Laplace transform technique to study the free vibration of spherically symmetric, thermoelastic, and FGM hollow sphere in the context of L-S theory, and analyzed the effects of grading index parameter and thermal relaxation time on strength and quality of signals. Xue 16 solved a two-dimensional multilayered structure considering thermal resistance based on the L–S theory.…”