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Advances in Acoustics and Vibration
Volume 2014, Article ID 401042, 7 pages
Research Article

S1-ZGV Modes of a Linear and Nonlinear Profile for Functionally Graded Material Using Power Series Technique

1Laboratory of Physics Materials, Faculty of Sciences, University of Sfax, B.P. 1171, 3000 Sfax, Tunisia
2Superior Institute of Applied Science and Technology, University of Gabes, 6072 Zrig, Gabes, Tunisia

Received 14 May 2014; Revised 24 July 2014; Accepted 5 August 2014; Published 21 September 2014

Academic Editor: Rama B. Bhat

Copyright © 2014 M. Zagrouba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present work deals with functionally graded materials (FGM) isotropic plates in the neighborhood of the first-order symmetric zero group velocity (S1-ZGV) point. The mechanical properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate and obey a power law of the volume fraction of the constituents. Governing equations for the problem are derived, and the power series technique (PST) is employed to solve the recursive equations. The impact of the FGM basic materials properties on S1-ZGV frequency of FGM plate is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus. The gradient coefficient does not affect the linear dependence of ZGV frequency as function of cut-off frequency ; only the slope is slightly varied.