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.
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The authors would like to express their gratitude to the editor and referees for their encouragement and constructive comments in revising the paper.
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Sayed, M., Mousa, A.A. & Mustafa, I.H. Stability analysis of a composite laminated piezoelectric plate subjected to combined excitations. Nonlinear Dyn 86, 1359–1379 (2016). https://doi.org/10.1007/s11071-016-2969-9
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DOI: https://doi.org/10.1007/s11071-016-2969-9