Parametric Instability of Rotating Functionally Graded Graphene Reinforced Truncated Conical Shells Subjected to Both Mechanical and Thermal Loading Conditions

Abstract

This article focuses on parametric instability of rotating functionally graded (FG) truncated conical shells reinforced by graphene platelets (GPLs) and subjected to both mechanical and thermal loading conditions. The GPL nanofillers are uniformly dispersed in each concentric conical layer but its weight fraction varies continuously along thickness direction, which induces the position-dependent effective material properties. Based on Love’s thin shell theory and Galerkin approach, the equations of motion for the conical shells are derived with the effects of the periodic axial loads, thermal expansion deformation, rotation-induced initial hoop tension, gyroscopic and centrifugal forces taken into account. Then, the parametric instability under combination parametric resonance for the conical shells is performed by the method of multiple scales, and the analytical solutions of both instability boundaries are obtained. A comprehensive parametric study is conducted which focuses on instability regions and vibration characteristics of the conical shell. Of particular interest in this process is the combined effect of the rotation, dynamic loads and thermal effects on dynamic stability of FG-GPL reinforced truncated conical shells.