Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

The aim of this paper is to investigate the stability of a simply supported laminated composite piezoelectric rectangular plate under combined excitations. Analysis of the amplitude and phase modulation equations with the associated nonlinear interaction coefficients, as provided by the multiple scale analyses of various 1:1 internal resonance conditions and primary resonance case, where ω2 ∼= ω1 and 3 ∼= ω1 is considered. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to the second-order approximation. All possible resonance cases at this approximation order are extracted. The stable/unstable periodic solutions are determined and are presented through frequency response plots. The analytical results are verified by comparing them with those of numerical integration of the modal equations. The influence of different parameters on the dynamic behavior of the composite laminated piezoelectric rectangular plate is studied. Variation of the some parameters leads to multivalued amplitudes and hence to jump phenomena. A comparison with the available published work is reported. A. A. Mousa · I. M. Eldesoky Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shibin El-Kom, Egypt M. Sayed (B) Department of Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt e-mail: [email protected] A. A. Mousa · M. Sayed Department of Mathematics and Statistics, Faculty of Science, Taif University, P. O. Box 888, El-Taif, Kingdom of Saudi Arabia W. Zhang College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, People’s Republic of China