Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

Abstract

Based on the third-order shear deformation theory (TSDT), the investigation of the free vibration response of a continuously graded carbon nanotube-reinforced (CGCNTR) cylindrical shell is presented. The volume fractions of randomly oriented straight single-walled carbon nanotubes are assumed to be graded in the thickness direction. An embedded carbon nanotube 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. The Mori–Tanaka scheme as an accurate micromechanics model is used for estimating the homogenized material properties of nanocomposites reinforced with equivalent fibers. The equations of motion and the associated boundary conditions are derived using the Hamilton’s principle based on TSDT. The discretization of the system by means of the Generalized Differential Quadrature Method leads to a standard linear eigenvalue problem. Detailed parametric studies have been carried out to study the impacts of the various types of equivalent fiber distribution, different boundary conditions and geometrical parameters on the vibration characteristics of CGCNTR cylindrical shells. The interesting finding of the present study is that the graded CNT volume fractions with symmetric distribution through the shell thickness have high capabilities to reduce or increase the natural frequency in comparison with uniformly and asymmetric CNT distribution.