Abstract
We investigate the global bifurcations and multipulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations. We analyze directly the nonautonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multipulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulations including the phase portraits and Lyapunov exponents are used to analyze the complex nonlinear dynamic behaviors of the laminated composite piezoelectric rectangular thin plate.
Highlights
Piezoelectric materials can be used as the actuators and sensors in engineering structures 1
Zhang et al 9 improved the extended Melnikov method given by Camassa et al 8 and employed it to study the multipulse Shilnikov-type chaotic dynamics for a nonautonomous buckled rectangular thin plate
The multipulse chaotic dynamics of a supported laminated composite piezoelectric rectangular thin plate under the combination of the parametric and transverse excitations was investigated by the proposed method
Summary
Piezoelectric materials can be used as the actuators and sensors in engineering structures 1. Zhang et al 4 established the nonlinear governing equations of motion for a supported laminated composite piezoelectric rectangular plate under combined parametric and transverse excitations and studied the periodic and Mathematical Problems in Engineering chaotic dynamics in the case of one-to-two internal resonance. Zhang et al 9 improved the extended Melnikov method given by Camassa et al 8 and employed it to study the multipulse Shilnikov-type chaotic dynamics for a nonautonomous buckled rectangular thin plate. The multipulse chaotic dynamics of a supported laminated composite piezoelectric rectangular thin plate under the combination of the parametric and transverse excitations was investigated by the proposed method. The multipulse chaotic dynamics of the supported laminated composite piezoelectric rectangular plate under combined parametric and transverse excitations is investigated by using the extended Melnikov method improved in paper 9. The nonlinear terms, which were missing through simplification by normal form theory in paper 10 , are retained in this paper and added small positive parameter
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