Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Multiwalled Carbon Nanotubes/Phenolic Nanocomposite Cylindrical Panels on Elastic Foundation

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of nanocomposite cylindrical panels reinforced by multiwalled carbon nanotubes (MWCNT) are considered. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tasi equation was used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWNTs wt% range considered. Symmetric and asymmetric volume fraction profiles are provided in this article for comparison. It is shown that using only few grid points, accurate results are obtained which demonstrate the efficiency and convenience of the generalized differential quadrature method for the problem under consideration. The validity of the Young's modulus and frequency response were assessed by a comparison with available literature data, providing a good agreement. POLYM. COMPOS., 34:2040-2048, 2013. (c) 2013 Society of Plastics Engineers