Bending-torsion coupling bursting oscillation of a sandwich conical panel under parametric excitation

Abstract

Regarding the dynamic behavior of the functionally graded materials (FGM) conical panels under the static and harmonic in-plane loading, most studies focus on parametric resonances and dynamic instability which determine the stability regions. Studies on the bursting oscillation of the conical panels under the lower frequency excitation are quite rare. In this paper, we present a novel nonautonomous system of the cantilever functionally graded materials sandwich conical panels with a slowly varying parametric excitation and study the bending-torsion coupling bursting oscillations. The face sheets and core layer are the metal ceramic composite layer and homogeneous metal layer, respectively. In two surfaces layers, the component materials are gradually changed in the transverse direction and the temperature dependent properties show the form of the power law distribution. The excitations in the meridional direction include the static preload and lower frequency harmonic excitation. The mode functions of the first-order bending mode and the first-order torsion mode are obtained in terms of Chebyshev polynomials with the help of energy principle. The bending-torsion coupling nonautonomous nonlinear oscillation system is derived by Lagrange equations. Under the slowly varying in-plane load, the equilibrium solutions of the system are obtained by treating them as a generalized autonomous system and they will be no longer stable through the pitchfork bifurcation with the symmetry breaking. The bursting oscillations of the novel dynamic system are analyzed by numerical methods. It is interesting to find that the mechanisms of bursting oscillation are associated with the pitchfork bifurcation with the symmetry breaking.