Expressions for the Rates of Change of Critical Flutter Speeds and Frequencies with Inertial, Aerodynamic and Elastic Coefficients

摘要

Formulae are derived which give the rates of change of the critical speeds and frequencies for flutter of an aeroelastic system of a general number of degrees of freedom, with each of the dynamical coefficients occurring in the equations of motion. The formulae enable the effect of a small change in one or more of the coefficients to be obtained when once the critical speed corresponding to a standard set has been found. A number of summation relations between the rates of change are obtained which serve as a check on the accuracy of the calculated values. Special forms of the formulae for binary flutter are given, and simple formulae for the rates of change of the critical speeds and frequencies when all the coefficients of a given type are changed in the same ratio are obtained for this particular case. The use of the formulae is illustrated in three worked examples. In an appendix the formulae are generalised to include the case when structural and artificial damping terms are present in the equations of motion.