Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory (Advances in Applied Mathematics and Mechanics, 2018)
Based on the Mindlin's first-order shear deformation plate theory this paperfocuses on the free vibration behavior of functionally graded nanocompositeplates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs).The material properties of simply supported functionally graded carbonnanotube-reinforced (FGCNTR) plates are assumed to be graded in the thicknessdirection. The effective material properties at a point are estimated by eitherthe Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types ofsymmetric carbon nanotubes (CNTs) volume fraction profiles are presented in thispaper. The equations of motion and related boundary conditions are derived usingthe Hamilton's principle. A semi-analytical solution composed of generalizeddifferential quadrature (GDQ) method, as an efficient and accurate numerical method,and series solution is adopted to solve the equations of motions. The primarycontribution of the present work is to provide a comparative study of the naturalfrequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method.The detailed parametric studies are carried out to study the influences varioustypes of the CNTs volume fraction profiles, geometrical parameters and CNTs volumefraction on the free vibration characteristics of FGCNTR plates. The results revealthat the prediction methods of effective material properties have an insignificantinfluence of the variation of the frequency parameters with the plate aspect ratioand the CNTs volume fraction.