Stability and bifurcation of a cantilever functionally graded material plate subjected to the transversal excitation

Abstract

The stability and bifurcation behaviors for a cantilever functionally graded materials rectangular plate subjected to the transversal excitation in thermal environment are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1:1 internal resonances and 1/2 subharmonic resonance. Four types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, a double zero and a pair of pure imaginary eigenvalues, a simple zero and a pair of pure imaginary eigenvalues as well as two pairs of pure imaginary eigenvalues in non-resonant case, respectively. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained, which may lead to static bifurcation and Hopf bifurcation. The numerical solutions obtained by using fourth-order Runge-Kutta method agree with the analytic predictions.