Agglomeration effects on free vibration characteristics of three-phase CNT/polymer/fiber laminated truncated conical shells

Abstract

This paper investigates the effect of carbon nanotubes (CNTs) agglomeration on the free vibration characteristics of three-phase CNT/polymer/fiber laminated truncated conical shells surrounded by an elastic foundation. The shell material is considered to be composed of a CNT-reinforced polymer enriched by the oriented reinforcing fibers. The material density and the effective elastic properties are calculated based on the rule of the mixture, and the Eshelby–Mori–Tanaka scheme along with Hahn's homogenization technique, respectively. The third-order shear deformation theory (TSDT) is used for the analysis of the shear flexible shell and the foundation is modeled based upon the Winkler-Pasternak theory. A set of governing equations are derived using Hamilton's principle, and solved numerically by the generalized differential quadrature method (GDQM). After confirming the convergence and accuracy of the results, a parametric study is carried out to examine the influences of various parameters on the natural frequencies of the three-phase CNT/polymer/fiber laminated truncated conical shells such as boundary conditions, circumferential mode number, the geometrical parameters including the ratios of thickness/length to radius, and the semi-vertex angle, the material parameters contain the mass fractions of CNTs and fibers, chiral numbers as well as the agglomeration characteristics of CNTs, and finally the foundation parameters including the Winkler stiffness and shearing layer stiffness.