Vibrations of a System Connecting Two Cylindrical Shells

Abstract

Many reports on vibrations of cylindrical shells have already been published. But it seems that the vibrations of a system connecting two cylindrical shells of different thicknesses have not been studied yet. In this paper, the authors investigate the vibrations of combined cylindrical shells free at one end and clamped at the other or clamped at both ends. The Lagrangian of the combined system is expressed by unknown boundary values alone, and the frequency equations and modal patterns of vibration are obtained by minimizing the Lagrangian as to the unknown boundary values. From the results of the numarical calculations, it is recognized that there is little difference between the non-dimensional frequencies of the combined system and those of a cylindrical shell of uniform thickness with the same boundary conditions.