期刊
NONLINEAR DYNAMICS
卷 59, 期 4, 页码 619-660出版社
SPRINGER
DOI: 10.1007/s11071-009-9568-y
关键词
Orthotropic functionally graded material rectangular plate; Chaotic motion; Higher-order shear deformation theory; Poincare map
资金
- National Science Foundation for Distinguished Young Scholars of China (NSFDYSC) [10425209]
- National Natural Science Foundation of China (NNSFC) [10732020]
- Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)
In this paper, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material (FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented. Heat conduction and temperature-dependent material properties are both taken into account. The material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the Reddy's third-order share deformation plate theory, the governing equations of motion for the orthotropic FGM rectangular plate are derived by using the Hamilton's principle. The Galerkin procedure is applied to the partial differential governing equations of motion to obtain a three-degree-of-freedom nonlinear system. The resonant case considered here is 1:2:4 internal resonance, principal parametric resonance-subharmonic resonance of order 1/2. Based on the averaged equation obtained by the method of multiple scales, the phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the orthotropic FGM rectangular plate. It is found that the motions of the orthotropic FGM plate are chaotic under certain conditions.
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