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Research Papers

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

[+] Author and Article Information
Jun-Sik Kim1

School of Mechanical Engineering, Kumoh National Institute of Technology, 243 Techno Building, Gumi, Gyeongbuk 730-701, Koreajunsik.kim@kumoh.ac.kr

K. W. Wang

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109kwwang@umich.edu

1

Corresponding author.

J. Vib. Acoust 132(4), 041003 (May 20, 2010) (8 pages) doi:10.1115/1.4000972 History: Received June 02, 2009; Revised December 22, 2009; Published May 20, 2010; Online May 20, 2010

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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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 9

Normalized second mode shapes of a CUS box beam, S=60: (a) u3 and (b) u2; ●: 3D FEM, – –: FAMBA-0th, –: FAMBA-2nd, and –⋅–: VABS, NABSA, and Jung (18)

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Figure 1

Geometry and coordinates of rectangular solid composite beams

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Figure 2

The first coupled mode shapes of a 30 deg composite strip

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Figure 3

Normalized eigenvalues of a composite strip with varying fiber angles

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Figure 4

Cross section of thin-walled composite box beams

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Figure 5

Normalized first eigenvalues of an orthotropic box beam with varying length-to-height ratios

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Figure 6

Normalized first eigenvalues of a CUS box beam with varying length-to-height ratios

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Figure 7

Normalized second eigenvalues of a CUS box beam with varying length-to-height ratios

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Figure 8

Normalized first mode shapes of a CUS box beam, S=60: (a) u3 and (b) u2; ●: 3D FEM, – –: FAMBA-0th, –: FAMBA-2nd, and –⋅–: VABS, NABSA, and Jung (18)

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Figure 10

Normalized eighth mode shapes of a CUS box beam, S=60: (a) u3 and (b) u2; ●: 3D FEM, – –: FAMBA-0th, –: FAMBA-2nd, and –⋅–: VABS, NABSA, and Jung (18)

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