An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

Abstract

In the present work, vibration characteristics of functionally graded (FG) sandwich rectangular plates reinforced by multiwalled carbon nanotubes (MWCNTs) resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation is 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 mass density and Poisson’s ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. The proposed sandwich rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the sandwich plates are investigated.