A GDQ approach to thermally nonlinear generalized thermoelasticity of disks

Generalized thermoelasticity response of an annular disk subjected to thermal shock on its inner surface is analyzed in this research. The Lord–Shulman theory, which accounts for one relaxation time in the conventional Fourier law, is used to avoid the infinite speed of thermal wave propagation. Unlike the other available works in which the first law of thermodynamics is linearized, the nonlinearity arising from the temperature change is taken into consideration. The first law of thermodynamics in this case becomes nonlinear and the analysis under such formulation is called thermally nonlinear. Two coupled equations, i.e., the radial displacement wave equation and temperature wave propagation equation are obtained. These equations and the associated boundary conditions are discreted through the generalized differential quadrature method. Solution of the time-dependent system of equations is obtained using the Newmark time marching scheme and the successive Picard method. Numerical results are provided for both thermally linear and thermally nonlinear temperature and radial displacement wave propagations. Parametric studies reveal that at higher temperature levels, thermally nonlinear first law of thermodynamics should be considered instead of thermally linear one. Furthermore, the higher the coupling parameter and/or relaxation time, the higher the divergence of thermally nonlinear-/linear-based results.