Asymmetric Vibrations of Thin Shells of Revolution

Abstract

In this paper, we analyze the asymmetric vibrations of thin barrel-like shells of revolution. The equations of vibration and the boundary conditions are determined from the stationary conditions of the Lagrangian of the shells of revolution. The equations of vibration are solved exactly by a series solution and then natural frequencies and mode shapes are obtained. Effects of various parameters upon natural frequencies are clarified in a discussion of numerical results. We also compare frequencies of shells of revolution with those of circular cylindrical shells. Furthermore, we obtain natural frequencies of shells of revolution which have practically important configurations and boundary conditions such as domes with skylight and so-called bell-type nozzles of rocket engines.