Supersonic Flutter of a Cylindrical Shell

Abstract

(1) SUMMARY The aerodynamic instability of traveling waves on a cylindrical shell exposed to an external supersonic air stream and containing an internal fluid is examined on the hypothesis of short wave length (compared with the radius and length of the shell). The stability criterion for an empty isotropic shell and the negative damping ratio when this criteria is not met are determined. It is shown that the negative damping ratio calculated in the absence of structural damping decreases monotonically with an increase in structural damping, but structural damping cannot prevent in­ stability and may render an otherwise stable motion weakh^ unstable. HE FOLLOWING ANALYSIS of the dynamic instability (panel flutter) of thin-walled cylindrical shells under the action of an exterior supersonic flow is pre­ sented as a sequel to an earlier formulation of the twodimensional problem.1 In that paper panel flutter was studied as a traveling wave phenomenon, following Kelvin's classical analysis of the surface waves pro­ duced by wind blowing over water. We remark at the outset that all of the essential features of this approach to panel flutter are elucidated by the two-dimensional analysis without recourse to any approximations beyond those implicit in the assumptions of small disturbances, a perfect fluid, and an infinite surface; however, further analysis and additional approximations are necessary in order to render the results applicable to practical con­ figurations.!