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Multi-Pulse Chaotic Dynamics of Laminated Composite Piezoelectric Rectangular Plate

[+] Author Affiliations
Wei Zhang, Ming-Hui Yao, Dong-Xing Cao

Beijing University of Technology, Beijing, China

Paper No. SMASIS2009-1218, pp. 365-374; 10 pages
doi:10.1115/SMASIS2009-1218
From:
  • ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
  • Volume 1: Active Materials, Mechanics and Behavior; Modeling, Simulation and Control
  • Oxnard, California, USA, September 21–23, 2009
  • Conference Sponsors: Aerospace Division
  • ISBN: 978-0-7918-4896-8 | eISBN: 978-0-7918-3857-0
  • Copyright © 2009 by ASME

abstract

The multi-pulse orbits and chaotic dynamics of the simply supported laminated composite piezoelectric rectangular plates under combined parametric excitation and transverse loads are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motions for the laminated composite piezoelectric rectangular plates are derived from von Karman-type equation and third-order shear deformation laminate theory of Reddy. The four-dimensional averaged equation under the case of primary parametric resonance and 1:2 internal resonances is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plates. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plates. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plates are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plates.

Copyright © 2009 by ASME

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