Nonlinear thermo-inertial stability of thin circular FGM plates

Abstract

In this research, linear and non-linear stability behaviour of a thin circular FGM plate subjected to the uniform temperature rise and the constant angular velocity loadings is analyzed. Properties of the FGM media are distributed across the thickness based on a power law form. Each property of the metal or ceramic constituents is considered to be the function of temperature based on the Touloukian model. General equilibrium equations for such conditions are obtained based on the classical plate theory. At first, the non-linear governing equations are established in a complete asymmetrical form. After that, two different analytical methods are presented to study the bifurcation behaviour. Existence of bifurcation phenomenon is examined. Pre-buckling analysis is performed for a plate with the immovable clamped edge. Stability equations are obtained based on the adjacent equilibrium criterion. The resulted equations are solved via the two distinct methodologies, i.e. the exact solution in terms of Coulomb wave functions and the power series method. A non-linear solution is also presented to detect the equilibrium path of the heated rotating FGM plate. It is found that the angular speed may stabilize the homogeneous circular plate which buckles during uniform heating. Furthermore, snapping may occur for FGM plates under the simultaneous action of heating and uniform rotation.