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Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory

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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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Authors and Affiliations

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Wei Zhang

  2. Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Jie Yang

  3. College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing, 100192, China

    Yuxin Hao

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  1. Wei Zhang
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  2. Jie Yang
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  3. Yuxin Hao
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Correspondence to Wei Zhang.

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Zhang, W., Yang, J. & Hao, Y. Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory. Nonlinear Dyn 59, 619–660 (2010). https://doi.org/10.1007/s11071-009-9568-y

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  • DOI: https://doi.org/10.1007/s11071-009-9568-y

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