Comparing theory and experiment for the supersonic flutter of circular cylindrical shells.

Abstract

The flutter boundaries obtained from recent experiments on the supersonic flutter of circular cylindrical shells are compared with various theoretical predictions. Following Voss, a modal analysis of Donnell's equations is used in conjunction with piston theory and the potential solution of Leonard and Hedgepeth. It was found that the pressurized cylindrical shells fluttered at a lower level of freestream energy than predicted by either theory. Of the two results, that using piston theory appears to correspond more closely to the experiment. The influence of the viscous boundary layer is discussed in the light of recent investigations, and it is concluded that for the thicknesses of boundary layer present in the experiments this influence is not overly important. A nonlinear analysis is presented for calculating amplitudes of flutter based on a two-mode, piston-theory approximation. The shallow-shell equations of Marguerre are solved by Galerkin's method, and a limit-cycle solution is obtained by the method of Krylov and Bogoliubov.