期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 50, 期 1, 页码 256-267出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2010.12.008
关键词
Functionally graded materials; Nonlinear vibration; Couple stress theory; Size effect; Microbeam
资金
- National Natural Science Foundation of China [11002019]
- Ph.D. Programs Foundation of Ministry of Education of China [20100009120018]
- Fundamental Research Funds for the Central Universities [2009JBM073]
Nonlinear free vibration of microbeams made of functionally graded materials (FGMs) is investigated in this paper based on the modified couple stress theory and von Karman geometric nonlinearity. The non-classical beam model is developed within the framework of Timoshenko beam theory which contains a material length scale parameter related to the material microstructures. The material properties of FGMs are assumed to be graded in the thickness direction according to the power law function and are determined by Mori-Tanaka homogenization technique. The higher-order nonlinear governing equations and boundary conditions are derived by using the Hamilton principle. A numerical method that makes use of the differential quadrature method together with an iterative algorithm is employed to determine the nonlinear vibration frequencies of the FGM microbeams with different boundary conditions. The influences of the length scale parameter, material property gradient index, slenderness ratio, and end supports on the nonlinear free vibration characteristics of the FGM microbeams are discussed in detail. It is found that both the linear and nonlinear frequencies increase significantly when the thickness of the FGM microbeam is comparable to the material length scale parameter. (C) 2010 Elsevier Ltd. All rights reserved.
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