Free vibration analysis of rotating functionally graded GPL-reinforced truncated thick conical shells under different boundary conditions

Abstract

In this article, the forward and backward wave frequencies of rotating truncated conical thick shells are investigated. The shell is composed of epoxy as the matrix and functionally graded (FG) graphene nanoplatelets (GPLs) as the reinforcement, which are dispersed with four different patterns through the thickness direction. The effective material properties are estimated using the Halpin-Tsai model and the rule of mixture. The influence of shear deformation in the shell is taken into account based on the third-order shear deformation theory (TSDT). By considering a constant angular velocity, and also considering the effects of the initial hoop tension, Coriolis and centrifugal accelerations, a set of governing equations is derived using Hamilton’s principle and is solved for different boundary conditions using generalized differential quadrature method (GDQM). A parametric study is carried out to investigate the influences of various parameters on the forward and backward traveling wave frequencies with respect to the following cases: the boundary conditions, circumferential wave number, rotating speed, geometrical parameters of the shell as well as the mass fraction, distribution pattern, and width and thickness of the GPLs. The numerical results indicates that dispersing more GPL reinforcements near the inner and outer surfaces of the rotating shells leads to a remarkable increase in both forward and backward wave frequencies.