Circumferentially traveling wave flutter of a circular cylindrical shell.

Abstract

A nonlinear analysis is presented for calculating the limiting amplitudes of cylindrical shell flutter using a four-mode approximation for the shell deflection. The aerodynamic pressure is approximated by linear piston theory, and the nonlinearity enters the problem through the nonlinear shallow shell equations for the cylinder. The governing equations are reduced to four modal equations by applying Galerkin's method, and limit-cycle solutions are obtained by the method of harmonic balance. Stability of the limit cycles is investigated numerically by integrating the modal equations on a digital computer. The limit-cycle calculations predict the occurrence of circumferentially traveling wave flutter similar to that previously observed experimentally. It was found that this traveling wave flutter can occur at aerodynamic pressures below the linear flutter boundary. This fact may help to explain why recent results indicate a difference between experiments and linear theory for the flutter of cylindrical shells.