On Extremum Properties of the Generalized Rayleigh Quotient Associated with Flutter Instability,

The extremum properties of the generalized Rayleigh quotient related to flutter instability are investigated. It is shown that, in addition to the well-known stationary property, under centain circumstances the quotient exhibits maximum-minimum properties which are in contrast to those of the classical Rayleigh quotient. One consequence is that a Rayleigh-Ritz type of stability analysis using these results leads to a lower bound as opposed to an upper bound in the classical case. The results are applied to multiple-parameter systems and a physical interpretation is given for the generalized Rayleigh quotient, leading to the proof of a convexity theorem. Author