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Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

Published online by Cambridge University Press:  03 June 2015

S. Jafari Mehrabadi ,
B. Sobhaniaragh  and
V. Pourdonya
S. Jafari Mehrabadi*
Affiliation:
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
B. Sobhaniaragh
Affiliation:
Young Researchers Club, Arak Branch, Islamic Azad University, Arak, Iran
V. Pourdonya
Affiliation:
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
*
*Corresponding author. Email: s-jafari@iau-arak.ac.ir
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Abstract

Based on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Keywords

35G0537N1574S30Carbon nanotube-reinforcedfunctionally gradedHamilton’s principleEshelby-Mori-Tanakasymmetric profilesextended rule of mixture
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 90 - 112
Copyright
Copyright © Global-Science Press 2013

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