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Mathematical Problems in Engineering
Volume 2010, Article ID 738648, 12 pages
Research Article

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

1College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, China
2College of Mechanical Engineering, Beijing University of Technology, Beijing 100142, China
3National Key Laboratory of Mechatronics Engineering and Control, Beijing Institute of Technology, Beijing 100081, China

Received 17 November 2009; Revised 29 April 2010; Accepted 1 May 2010

Academic Editor: Carlo Cattani

Copyright © 2010 Y. X. Hao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.