Flutter of a ring of panels

Abstract

A theoretical investigation has been made on the flutter characteristics of a ring and longeron-stiffened cylindrical shell whose outer surface is exposed to a supersonic flow parallel to its axis. It is shown that the flutter analysis of this configuration can be reduced to the analysis of an equivalent single panel using the circulant matrix idea. The reduction procedure, applicable to most cyclic configurations, allows for all types of interelement (panel) coupling and is subject to the sole restriction that the dynamic phenomenon be satisfactorily described by linear theory. An approximate flutter solution is obtained for this configuration in the limit when the number of panels become large, and the unsteady aerodynamic pressures may be computed from simple linear piston theory. This solution indicates that, at the critical flutter speed, all panels of the shell flutter in exactly the same mode shape, the same magnitude of occurrence of this mode shape, and with a phase shift equal to TT occurring between successive panels.