Part I. The Stability of a Membrane in a Subsonic Flow. Part II. The Stability of a Grid of Panels in a Supersonic Flow

Citation

Stearman, Ronald Oran (1961) Part I. The Stability of a Membrane in a Subsonic Flow. Part II. The Stability of a Grid of Panels in a Supersonic Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TE64-4652. https://resolver.caltech.edu/CaltechETD:etd-12212005-160627

Abstract

Part I.

An experimental investigation has been made on the stability of small aspect ratio rectangular membranes in a subsonic flow. The leading and trailing edges of the membrane were attached to rigid streamlined supports while the two streamwise edges were free. Both surfaces of the membrane were exposed to the airstream, and the membrane tension was applied through the trailing edge.

The results of the test show that two types of flutter (instability) occur. The first to appear as the wind speed was increased from zero, with a fixed tension level in the membrane, was a small amplitude flutter which has a shallow wave like motion traveling in the streamwise direction. At higher wind speeds this motion was damped out. A narrow equilibrium zone or boundary existed which separated the first type of flutter from a second type of motion having a traveling wave of larger amplitude and greater speed. This second type of flutter had no tendency to damp out, but became more violent as the wind speed was increased.

The span of the slender membrane is the physical parameter that uniquely determines and controls the first flutter boundary; its mass plays no part here, but does affect the equilibrium zones.

Appendix A contains an obvious formulation of the slender membrane flutter problem.

Part II.

A theoretical investigation has been made on the stability of a grid of panels in a supersonic flow. The problem is formulated by considering this structure as a limiting case of a more general configuration composed of a ring of panels (i.e. an axially stiffened cylindrical shell) whose outer surface is exposed to a supersonic flow parallel to its axis. It is shown that the stability analysis of this more general 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 inter-element (panel) coupling and is subject to the sole restriction that the dynamic phenomenon be satisfactorily described by linear theory.

It is shown that at least five different multi-panel configurations can be obtained from this general problem by taking the appropriate limiting process. The stability (flutter) analysis of one of these limiting cases is discussed for high Mach number flows where only an elastic coupling exists between neighboring panels.

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