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Subharmonic Orbits of Rectangular Thin Plate With Parametrically and Externally Excitations

[+] Author Affiliations
Wei Zhang, Min Sun, Qian Wang, Jianen Chen

Beijing University of Technology, Beijing, China

Paper No. IMECE2012-85868, pp. 861-870; 10 pages
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME


In this paper, the bifurcations of subharmonic orbits for a four-dimensional rectangular thin plate with parametrically and externally excitations is considered for the first time. The formulas of the rectangular thin plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The unperturbed system is composed of two independent planar Hamiltonian systems such that the unperturbed system has a family of periodic orbits. The problem addressed here is the determination of sufficient conditions for some of the periodic orbits to generate subharmonic orbits after periodic perturbations. Thus, based on periodic transformations and Poincaré map the subharmonic Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the parametrically and externally excited rectangular thin plate. The results obtained here indicate that subharmonic motions can occur in the rectangular thin plate. The method succeeds in establishing the existence of subharmonics in perturbed Hamiltonian systems as well as in discussing their bifurcations. Numerical simulation is also employed to find the subharmonic motions of the parametrically and externally excited rectangular thin plate.

Copyright © 2012 by ASME



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