Rapid heating of FGM plates resting on elastic foundation

In this research, the thermally induced vibration of the plates on the elastic foundation has been investigated. The plate is made of functionally graded materials (FGMs) that is graded along the thickness. All mechanical and thermal properties dependent on temperature are taken into account. To apply the temperature dependence of thermomechanical properties, the well-known Touloukian equation is used. The two-parameter elastic foundation, Winkler–Pasternak, is considered to be linear, isotropic, and homogeneous. The general formulation and equations governing the phenomenon of thermally induced vibration have been written under the assumptions of linear uncouple thermoelasticity. The one-dimensional transient heat conduction equation has been discretized with the help of the finite element method in the direction of thickness, and it has been solved over time by applying the Crank–Nicolson method. Also, the thermally induced force and moment resultants in each time step have been calculated based on the temperature profile. To obtain the equations of motion, Hamilton’s principle based on the first-order shear deformation theory has been used, and the obtained equations and boundary conditions have been discretized by applying the generalized differential quadrature (GDQ) method and solved by using Newmark time marching scheme.