Free Vibration of a Rotating Truncated Conical Shell in Effect of Meridional Variable Thickness and Elastic Boundary Conditions

This paper aims at the free vibration of a rotating truncated conical shell with meridional variable thickness and elastic boundary conditions. Based on Donnell’s shell theory, the governing equations of the truncated conical shell with variable thickness are derived first. Then the artificial spring technique is used to model the elastic boundary conditions at both edges. Finally, a new solution formula for rotation is proposed. The present theoretical modeling based on the generalized differential quadrature (GDQ) method is validated through comparison with both finite element method (FEM) and existing studies. This study examines the individual and coupled effects of meridional variable thickness, elastic boundary conditions, and various rotational forces (e.g., Coriolis force, centrifugal force, and initial hoop tension) on the system’s frequency characteristics. The results demonstrate that the standing wave frequencies of low-wavenumber circumferential modes (LCM) are predominantly influenced by both thickness variations and boundary conditions. In contrast, the frequencies of high-wavenumber circumferential modes (HCM) are primarily governed by the shell’s average thickness. Furthermore, the effects of different spring types (e.g., meridional springs, circumferential springs, transverse springs, and rotational springs) and rotational forces on the frequency characteristics differ significantly. Finally, the slope of the frequencies with respect to the speed is also found to depend on both thickness variations and boundary conditions.