A Semi-analytical Solution for 3-D Dynamic Analysis of Thick Continuously Graded Carbon Nanotube-reinforced Annular Plates Resting on a Two-parameter Elastic Foundation

The The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of elastically supported continuously graded carbon nanotube-reinforced (CGCNTR) annular plates. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. 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 2-D differential quadrature method and series solution is adopted to solve the equations of motion. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs and different CNTs distributions on the vibrational characteristics of CGCNTR annular plates.

Keywords:

Three-dimensional free vibration , Continuously graded carbon nanotube-reinforced , Annular plates , Two-parameter elastic foundations