Graphical technique for analyzing marginally stable dynamic systems

Abstract

It is shown how important qualitative and quantitative information on the dynamic stability characteristics of a linear system can be extracted rather easily from the Argand diagram of the characteristic equation for sinusoidal motion. This diagram reveals directly whether the system possesses marginally stable eigenvalues and also if violent instability may occur for a system with fluid flow (e.g., flutter). In addition, accurate estimates of marginally stable eigenvalues, including amplification or decay rates, may be obtained from the diagram. The method is applied to a model problem of membrane flutter which previously has been employed in a problem of boundary-layer stability. This model exhibits three essentially different classes of instability which are believed to be basic to all problems involving flowing fluids. Some simple cases of flutter are also considered which demonstrate the practical usefulness of the method and its accuracy.