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- Title
Resonant Chaotic Dynamics of a Symmetric Cross-Ply Composite Laminated Plate Under Transverse and In-Plane Excitations.
- Authors
Ma, W. S.; Zhang, W.
- Abstract
The resonant chaotic dynamics of a symmetric cross-ply composite laminated plate are studied using the exponential dichotomies and an averaging procedure for the first time. The partial differential governing equations of motion for the symmetric cross-ply composite laminated plate are derived by using Reddy's third-order shear deformation plate theory and von Karman type equation. The partial differential governing equations of motion are discretized into two-degree-of-freedom nonlinear systems including the quadratic and cubic nonlinear terms by using Galerkin method. There exists a fixed point of saddle-focus in the linear part for two-degree-of-freedom nonlinear system. The Melnikov method containing the terms of the nonhyperbolic mode is developed to investigate the resonant chaotic motions of the symmetric cross-ply composite laminated plate. The obtained results indicate that the nonhyperbolic mode of the symmetric cross-ply composite laminated plate does not affect the critical conditions in the occurrence of chaotic motions in the resonant case. When the resonant chaotic motion occurs, we can draw a conclusion that the resonant chaotic motions of the hyperbolic subsystem are shadowed for the full nonlinear system of the symmetric cross-ply composite laminated plate.
- Subjects
LAMINATED materials; COMPOSITE plates; ORTHOTROPIC plates; PARTIAL differential equations; VON Karman equations; GALERKIN methods
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2020, Vol 30, Issue 7, pN.PAG
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127420501060