期刊
MECCANICA
卷 47, 期 4, 页码 985-1014出版社
SPRINGER
DOI: 10.1007/s11012-011-9491-4
关键词
Functionally graded materials; Rectangular plates; Asymptotic perturbation method; Chaotic motion; Higher-order plate theory; Poincare map
类别
资金
- National Natural Science Foundation of China (NNSFC) [10732020, 11072008, 10972026]
- National Science Foundation for Distinguished Young Scholars of China (NSFDYSC) [10425209]
- Jurisdiction of Beijing Municipality (PHRIHLB)
In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy's third-order plate theory, the governing equations of motion for the plate are derived using the Hamilton's principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincar, map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.
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