Membrane Vibrations of Conical Shells

Abstract

The vibrations of conical shells are due to the inertial and external forces acting the transverse, circumferential and meridional directions of the cone. For small vibrations, the system is linear, thus, the effects of these three forces may be treated separately. It may be due to the mathematical dificulty, the transverse vibration, so far, is solved by numerical methods only, such as Rayleigh-Ritz method, Galerkin procedure, power series, matrix method, and the finite element method. A comprehensive literature review on the conical shell vibrations is provided in [8].