期刊
COMPOSITES PART B-ENGINEERING
卷 42, 期 3, 页码 402-413出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.compositesb.2010.12.010
关键词
Plates; Vibration; Analytical modeling; Numerical analysis; Functionally graded materials
资金
- National Natural Science Foundation of China (NNSFC) [10972026, 10732020, 11072008]
- Science Foundation of Beijing Municipal Education Commission [KM200910772004]
- Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the jurisdiction of Beijing Municipality (PHRIHLB)
Nonlinear dynamic analysis of a cantilever functionally graded materials (FGM) rectangular plate subjected to the transversal excitation in thermal environment is presented for the first time in this paper. Material properties are assumed to be temperature dependent. The nonlinear governing equations of motion for the FGM plate are derived based on Reddy's third-order plate theory and Hamilton's principle. The first two vibration mode functions satisfying the boundary conditions of the cantilever FGM rectangular plates are chosen to be the admissible displacement functions. Galerkin's method is utilized to convert the governing partial differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms under combined external excitations. The present study focuses on resonance case with 1:1 internal resonance and subharmonic resonance of order 1/2. The asymptotic perturbation method is employed to obtain four nonlinear averaged equations which are then solved by using Runge-Kutta method to find the nonlinear dynamic responses of the plate. It is found that chaotic, periodic and quasi-periodic motions of the plate exist under certain conditions and the forcing excitations can change the form of motions for the FGM rectangular plate. (c) 2010 Elsevier Ltd. All rights reserved.
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