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Supersonic flutter of circular cylindrical shells


Olson, Mervyn Daniel (1966) Supersonic flutter of circular cylindrical shells. Dissertation (Ph.D.), California Institute of Technology.


Various experimental and theoretical studies on the supersonic flutter of circular cylindrical shells are discussed. Results of experiments in the Mach number range 2.5 - 3.5 are presented. Three shells with radius-to-thickness ratios of 2,000 were subjected to radial external pressure loadings and to combinations of axial compressive loading and internal pressurization while in the presence of an external axially-directed supersonic flow. Small amounts of internal pressurization were very stabilizing with respect to flutter, but moderate amounts reduced stability to the unpressurized level. However, high internal pressures completely stabilized the shells. The axial compressive loading was slightly destabilizing for moderate amounts of internal pressurization. The flutter modes (which were standing waves in the axial direction with zero, one or two circumferential nodal lines) contained many waves around the circumference (of the order of 20) that travelled in the circumferential direction. This circumferentially travelling wave phenomenon possibly results from the nonlinear nature of cylindrical shells. Model integrity was not threatened by even the most violent flutter which occurred just prior to buckling under radial external pressure loading and just after buckling under axial compressive loading. Buckled portions of a shell did not flutter. It appears that the large local curvatures encountered in the buckling of a cylindrical shell tend to stabilize the shell locally. However, it also appears that the localized buckling usually encountered in practice reduces the stability of any unbuckled regions of the shell. The experimental flutter boundaries are compared with various theoretical predictions. Following Voss a modal analysis which satisfies the so-called freely supported shell boundary conditions is used in conjunction with different aerodynamic approximations - namely piston theory and the potential theory of Leonard and Hedgepeth. It was found that the pressurized cylindrical shells fluttered at a lower level of free stream energy than predicted by the theory. Of the two results, that using piston theory appears to correspond closest to the experiment both in stability boundary and in critical values of circumferential wave number. Both predictions yield a larger stabilizing influence of the shell internal pressure than observed in the experiment. An analysis is presented for calculating the final limiting amplitudes of flutter based on a two-mode, piston theory approximation. A Galerkin procedure is used to reduce the nonlinear shallow shell equations of Marguerre to two coupled nonlinear ordinary differential equations for the modal amplitudes. An approximate limit cycle solution to these equations is obtained by the method of Krylov and Bogoliubov. The results indicate that for practical purposes cylindrical shell flutter does not occur below the stability boundary for infinitesimal disturbances. The limit cycle amplitudes predicted by this analysis seem to agree very well with the experimental ones. The results further indicate that the flutter amplitude, frequency and mode shape should change discontinuously (or jump) as the aerodynamic pressure is increased beyond the value for first flutter.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Fung, Yuan-cheng
Thesis Committee:
  • Unknown, Unknown
Defense Date:20 May 1966
Record Number:CaltechETD:etd-12022005-075701
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4720
Deposited By: Imported from ETD-db
Deposited On:02 Dec 2005
Last Modified:26 Jun 2015 18:41

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