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.