Using eshelby–mori–tanaka scheme for 3D free vibration analysis of sandwich curved panels with functionally graded nanocomposite face sheets and finite length

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