Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2013, Article ID 958219, 27 pages
http://dx.doi.org/10.1155/2013/958219
Research Article

Multipulse Heteroclinic Orbits and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China

Received 21 March 2013; Accepted 21 May 2013

Academic Editor: Qingdu Li

Copyright © 2013 Minghui Yao and Wei Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the multipulse global bifurcations and chaotic dynamics for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate by using an energy phase method in the resonant case. Using the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of 1 : 2 internal resonance and primary parametric resonance. The energy phase method is used for the first time to investigate the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The paper demonstrates how to employ the energy phase method to analyze the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications. Numerical simulations show that for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate, the Shilnikov type multipulse chaotic motions can occur. Overall, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists.