Nonlinear free vibration of size-dependent functionally graded microbeams

Ke, Liao-Liang, Wang, Yue-Sheng, Yang, Jie and Kitipornchai, Sritawat (2012) Nonlinear free vibration of size-dependent functionally graded microbeams. International Journal of Engineering Science, 50 1: 256-267. doi:10.1016/j.ijengsci.2010.12.008


Author Ke, Liao-Liang
Wang, Yue-Sheng
Yang, Jie
Kitipornchai, Sritawat
Title Nonlinear free vibration of size-dependent functionally graded microbeams
Journal name International Journal of Engineering Science   Check publisher's open access policy
ISSN 0020-7225
Publication date 2012-01-01
Year available 2012
Sub-type Article (original research)
DOI 10.1016/j.ijengsci.2010.12.008
Volume 50
Issue 1
Start page 256
End page 267
Total pages 12
Place of publication Philadelphia, PA United States
Publisher Elsevier Inc.
Collection year 2012
Language eng
Abstract 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 Kármán 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.
Keyword Couple stress theory
Functionally graded materials
Microbeam
Nonlinear vibration
Size effect
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
 
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Created: Wed, 29 Oct 2014, 21:42:08 EST by Jeannette Watson on behalf of School of Civil Engineering