Stability and local bifurcation analysis of functionally graded material plate under transversal and in-plane excitations

Abstract

In this paper, stability and local bifurcation behaviors for a simply supported functionally graded material (FGM) rectangular plate subjected to the transversal and in-plane excitations in the uniform thermal environment are investigated using both analytical and numerical methods. Three kinds of degenerated equilibrium points of the bifurcation response equations are considered, which are characterized by a double zero eigenvalues, a simple zero and a pair of pure imaginary eigenvalues as well as two pairs of pure imaginary eigenvalues in nonresonant case, respectively. With the aid of Maple and normal form theory, the explicit expressions of transition curves are obtained, which may lead to static bifurcation, Hopf bifurcation and 2-D torus bifurcation. Finally, the numerical solutions obtained by using fourth-order Runge–Kutta method agree with the analytic predictions.