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Nonlinear dynamic response of a simply supported rectangular functionally graded material plate under the time-dependent thermalmechanical loads

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Abstract

An analysis on nonlinear dynamic characteristics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in the time dependent thermal environment. Here we look the FGM Plates as isotropic materials which is assumed to be temperature dependent and graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The geometrical nonlinearity using Von Karman’s assumption is introduced. The formulation also includes in-plane and rotary inertia effects. In the framework of Reddy’s third-order shear deformation plate theory, the governing equations of motion for the FGM plate are derived by the Hamilton’s principle. Then the equations of motion with two-degree-of-freedom under combined the time-dependent thermomechanical loads can be obtained by using Galerkin’s method. Using numerical method, the control equations are analyzed to obtain the response curves. Under certain conditions the periodic and chaotic motions of the FGM plate are found. It is found that because of the existence of the temperature which relate to the time the motions of the FGM plate show the great difference. A period motion can be changed into the chaotic motions which are affected by the time dependent temperature.

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Authors and Affiliations

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

    Y. X. Hao

  2. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100042, China

    W. Zhang

  3. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, VIC, 3083, Australia

    J. Yang

  4. Tianjin key labratory of Information Sensing and Intelligent Control, Ttianjin University of Technology and Education, Tianjin, 300222, China

    S. Y. Li

Authors
  1. Y. X. Hao
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  2. W. Zhang
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Correspondence to W. Zhang.

Additional information

This paper was recommended for publication in revised form by Editor Yeon June Kang

W. Zhang received his Ph.D. in 1997 from Department of Mechanics, Tianjin University and Post Doctoral Fellow in 1999 from University of Western Ontario, Canada. He is a director of Dynamics and Control Division and a fellow for the Chinese Society of Theoretical and applied Mechanics. His research interests include the global bifurcations and chaotic dynamics of high-dimensional nonlinear systems, the global dynamics of nonlinear continuous systems and nonlinear dynamics of mechanical systems induced by flow.

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Hao, Y.X., Zhang, W., Yang, J. et al. Nonlinear dynamic response of a simply supported rectangular functionally graded material plate under the time-dependent thermalmechanical loads. J Mech Sci Technol 25, 1637–1646 (2011). https://doi.org/10.1007/s12206-011-0501-1

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  • DOI: https://doi.org/10.1007/s12206-011-0501-1

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