Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory |
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Authors: | Wei Zhang Jie Yang Yuxin Hao |
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Institution: | 1.College of Mechanical Engineering,Beijing University of Technology,Beijing,China;2.Department of Building and Construction,City University of Hong Kong,Kowloon,Hong Kong;3.College of Mechanical Engineering,Beijing Information Science and Technology University,Beijing,China |
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Abstract: | 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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Keywords: | |
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