Stability analysis of a composite laminated piezoelectric plate subjected to combined excitations

Abstract

The aim of this paper is to discuss the stability of a symmetric cross-ply composite laminated piezoelectric plate subject to combined excitations. Multiple timescale perturbation method is implemented to solve the nonlinear governing equations including the second-order approximation. The case of 1:1:3 internal resonance and primary resonance case is investigated. The stability of the system is discussed using frequency, force response curves. A bifurcation analysis was performed using the amplitude of parametric excitation force as the bifurcation parameter. It is found that there are two Hopf bifurcation points: the first one is at \(f_{11}=5.592\), and the other one is at \(f_{11}=13.96\). It is observed that the system is dominated by the periodic attractor in the ranges of \((5.592< f_{11 }< 7.21)\) and \((13.31< f_{11 }< 13.96)\). The system is enriched with period doublings which are the main way leading to chaotic behavior. Some recommendations regarding the parameters limit of the dynamic system are reported.