Journal
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
Volume 53, Issue 3, Pages 612-622Publisher
SCIENCE PRESS
DOI: 10.1007/s11431-010-0074-8
Keywords
angle-ply composite laminated plate; third-order shear deformation theory; parametric excitation; chaotic motion
Funding
- National Natural Science Foundation of China [10732020, 10872010]
- National Science Fund for Distinguished Young Scholars [10425209]
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An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations. According to the Reddy's third-order plate theory, the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle. Then, the Galerkin procedure is applied to the partial differential governing equation to obtain a two-degrees-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. Such equations are utilized to deal with the resonant case of 1:1 internal resonance and primary parametric resonance-1/2 subharmonic resonance. Furthermore, the stability analysis is given for the steady-state solutions of the averaged equation. Based on the averaged equation obtained by the asymptotic perturbation method, the phase portrait and power spectrum are used to analyze the multi-pulse chaotic motions of the angle-ply composite laminated rectangular thin plate. Under certain conditions the various chaotic motions of the angle-ply composite laminated rectangular thin plate are found.
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