Influence of graded agglomerated CNTs on vibration of CNT-reinforced annular sectorial plates resting on Pasternak foundation

The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded CNT-reinforced (CGCNTR) annular sectorial plates resting on Pasternak elastic foundation. The elastic foundation is considered as a Pasternak model with adding a shear layer to the Winkler model. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. An embedded CNT in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanics model of agglomeration is employed. In this research work, 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 CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Then, the influence of graded agglomerated CNTs, elastic foundation stiffness parameters and various geometrical parameters on the vibration characteristics of the annular sectorial plates resting on Pasternak elastic foundation reinforced by randomly oriented agglomerated CNTs is investigated.

► Free vibration of a continuously graded carbon nanotube-reinforced annular sector plates. ► Graded volume fractions of randomly oriented agglomerated SWCNTs. ► Two-parameter micromechanics model of agglomeration.