Axisymmetric and beam-type vibrations of thin cylindrical shells.

Abstract : Considerable attention has been devoted in recent years to the use of shell equations for the prediction of the dynamic behavior of thin cylindrical shells as an element in a missile or spacecraft. The complexity involved in the use of the shell equations must be tolerated for problems that require modes having several circumferential waves (e.g., prediction of panel flutter or response to acoustic loading). Moreover the minimum natural frequency usually corresponds to a mode having two or more circumferential waves. For prediction of overall vehicle behavior, however, one is primarily interested in axisymmetric (n = o) and beam-type (n = 1) modes; in these instances the problem can be considerably simplified by considering the cylinder as a bar for n = 0 modes or a compact beam for n = 1 modes. The present paper examines the accuracy of these engineering approximations as compared with exact solutions from Flugge's shell equations and discusses the error in terms of frequency, mode shape, modal forces, and generalized mass. Consideration is given to the effect of shell bending stiffness and the influence of boundary conditions on these parameters. (Author)