Propagation of thermomechanical waves in annular disks made of functionally graded materials under thermal shock

In this paper, using the coupled Lord-Shulman generalized thermoelasticity theory and considering the nonlinear thermal effects, the thermoelastic behavior of annular disks made of functionally graded materials (FGMs) under internal thermal shock is investigated. To this end, the governing equations of problem are first derived within the framework of polar coordinates system. It should be noted that the energy equation is kept in its original nonlinear form in this derivation process. The solution procedure is then presented based on the generalized differential quadarature method. In the numerical results, the effects of important parameters such as FG index and magnitude of applied thermal shock on the propagation of thermomechanical waves in the disks are studied. The results show that with increasing the FG index, displacement and stress decrease as time evolves. Also, with presenting results for various magnitudes of thermal shock it is shown that conducting a nonlinear thermal analysis is necessary when the thermal shock magnitude is considerable. In addition, it is revealed that the fluctuations in the temperature are reduced as the relaxation time decreases. Moreover, increasing this parameter leads to the temperature variations, whereas the frequency of system decreases.