Vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional (3D) equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic two-dimensional and macroscopic one-dimensional (1D) equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are considered to investigate the end effect. It is then described how one could form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared with those of 3D finite element method and those available in the literature for composite beams with solid cross section and thin-walled cross section.
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e-mail: junsik.kim@kumoh.ac.kr
e-mail: kwwang@umich.edu
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August 2010
Research Papers
Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method
Jun-Sik Kim,
Jun-Sik Kim
Assistant Professor
School of Mechanical Engineering,
e-mail: junsik.kim@kumoh.ac.kr
Kumoh National Institute of Technology
, 243 Techno Building, Gumi, Gyeongbuk 730-701, Korea
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K. W. Wang
K. W. Wang
Stephen P. Timoshenko Collegiate Professor
Department of Mechanical Engineering,
e-mail: kwwang@umich.edu
University of Michigan
, Ann Arbor, MI 48109
Search for other works by this author on:
Jun-Sik Kim
Assistant Professor
School of Mechanical Engineering,
Kumoh National Institute of Technology
, 243 Techno Building, Gumi, Gyeongbuk 730-701, Koreae-mail: junsik.kim@kumoh.ac.kr
K. W. Wang
Stephen P. Timoshenko Collegiate Professor
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109e-mail: kwwang@umich.edu
J. Vib. Acoust. Aug 2010, 132(4): 041003 (8 pages)
Published Online: May 20, 2010
Article history
Received:
June 2, 2009
Revised:
December 22, 2009
Online:
May 20, 2010
Published:
May 20, 2010
Citation
Kim, J., and Wang, K. W. (May 20, 2010). "Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method." ASME. J. Vib. Acoust. August 2010; 132(4): 041003. https://doi.org/10.1115/1.4000972
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