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Most of the early studies on plates vibration were focused on two-dimensional (2D) theories; these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3D elasticity solution for free vibration analysis of 2D continuously graded carbon nanotube-reinforced (CGCNTR) annular plates resting on a two-parameter elastic foundation. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness and radial directions. Various material profiles along the thickness and radial directions are illustrated using the 2D power-law distribution. An equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). A semi-analytical approach composed of 2D differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The convergence of the method is demonstrated and comparisons are made between the present results and results reported by well-known references and have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach to reveal the impacts of the volume fractions of oriented CNTs and different CNTs distributions on the vibrational characteristics of annular plates which are assumed to be graded in one (or more) direction(s).

This article deals with free vibration analysis of thick nanocomposite laminated curved panels with finite length resting on two‐parameter elastic foundations, based on the three‐dimensional elasticity theory. The main objective of this research paper is to present a 3D elasticity solution for free vibration analysis of thick laminated curved panels with continuously graded carbon nanotube‐reinforced sheets. The structure is supported by an elastic foundation with Winkler's (normal) and Pasternak's (shear) coefficients. The volume fractions of oriented, straight single‐walled carbon nanotubes are assumed to be a three‐parameter power‐law distribution which is graded in the radial direction of the panels. An equivalent continuum model based on the Eshelby‐Mori‐Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes. Because of using two‐dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. The convergence of the method is demonstrated and comparisons are made between the present results and results reported by well‐known references and have confirmed accuracy and efficiency of the present approach. This study serves as a benchmark for assessing the validity of numerical methods or two‐dimensional theories used to analysis of laminated curved panels. POLYM. COMPOS., 38:E563–E576, 2017. © 2016 Society of Plastics Engineers