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Research Papers

Homotopy Perturbation Method for Nonlinear Vibration Analysis of Functionally Graded Plate

[+] Author and Article Information
Ali A. Yazdi

Department of Mechanical Engineering,
Quchan Institute of Engineering and Technology,
Quchan, P. O. Box 94717-84686, Iran
e-mail: aliaminyazdi@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 3, 2012; final manuscript received November 28, 2012; published online March 18, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(2), 021012 (Mar 18, 2013) (6 pages) Paper No: VIB-12-1191; doi: 10.1115/1.4023252 History: Received July 03, 2012; Revised November 28, 2012

In this paper, the Homotopy perturbation method (HPM) is used to analysis the geometrically nonlinear vibrations of thin rectangular laminated functionally graded material (FGM) plates. The Von Karman's strain-displacement relations have been employed to model structural nonlinearity of the system. The material properties of the plate are assumed to be graded continuously in direction of thickness. The effects of initial deflection, aspect ratio and material properties are investigated. Based on the results of this study, the first order approximation of the HPM leads to highly accurate solutions for geometrically nonlinearity vibration of FGM plates. Moreover, HPM in comparison with other traditional analytical methods (e.g., perturbation methods) has excellent accuracy for the whole range of oscillation amplitude and initial conditions.

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Figures

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Fig. 1

Geometry of thin rectangular FGM plate

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Fig. 2

Variation of frequency ratios versus nondimensional amplitude ratio for square FGM plate for different n

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Fig. 3

Variation of frequency ratios versus nondimensional amplitude ratio for square FGM plate with different aspect ratios

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Fig. 4

Effect of aspect ratio on frequency ratio for different vibration amplitude

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Fig. 5

Variation of frequency ratio versus the different values of n for Wmax/h = 0.5

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