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Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances

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  • Y. X. Hao
  • W. Zhang
  • X. L. Ji

Abstract

The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.

Suggested Citation

  • Y. X. Hao & W. Zhang & X. L. Ji, 2010. "Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:738648
    DOI: 10.1155/2010/738648
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