TE-GDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring

Abstract

This article investigates the free vibration response of a conical system supported by an intermediate solid ring. The ingredients of the shell are considered a polymer reinforced with graphene platelets (GPLs). The distribution of GPLs is assumed to be uniform, and their orientation is considered random in each layer of the composite. The variation of GPL weight fraction within layers is based on the functionally graded patterns. Effective material properties are calculated utilizing the Halpin–Tsai homogenization procedure. The fundamental formulation of the shell is founded by the first-order shear deformation theory and Donnell’s kinematic assumptions. The motion equations and associated boundary and compatibility conditions are derived by Hamilton’s principle. Solving the governing equations due to the existence of a solid frequency control ring is not possible using conventional numerical methods. For this reason, a new type of GDQ method is applied, which is a combination of this technique with a finite element procedure (GDQE). By combining this method with the method of trigonometric expansion (TE) analysis, the equations of motion of the structure are solved. After illustrating the validation studies, parametric examples are given to investigate the effect of material properties, boundary conditions, and ring position on the shell frequencies.