Geometrically Non-Linear Rapid Heating of Temperature-Dependent Circular FGM Plates

Abstract

Abstract Based on the uncoupled thermoelasticity assumptions, axisymmetric thermally induced vibrations of a circular plate made of functionally graded materials (FGMs) are analyzed. Each thermomechanical property of the circular plate is assumed to be functions of temperature and thickness coordinate. Solution of the transient one-dimensional heat conduction equation with the arbitrary type of time-dependent boundary conditions is carried out employing the central finite difference method combined with the Crank–Nicolson time marching scheme. Afterwards, with the establishment of the associated Hamilton's principle and the accountancy of the von Kármán type of geometrical non-linearity, the motion equations are obtained with the aid of the conventional multi-term Ritz method. The solution of highly coupled non-linear motion equations is obtained utilizing a hybrid iterative Newton–Raphson–Newmark scheme. After validating the developed computer code, some parametric studies are accomplished to show the influences of various involved parameters. It is shown that temperature dependency, geometrical non-linearity, plate thickness, power law index, and the type of thermal in-plane and out-of-plane mechanical boundary conditions, all affect the temporal evolution of plate characteristics. Keywords: Circular plateFGMHybrid Newton–Raphson–Newmark methodRitz methodTemperature dependencyThermally induced vibrationsvon Kármán non-linearity Notes Color versions of one or more of the figures in the article can be found online at www.tandfonline. com/uths.