A Note on the Effect of a Time-Varying Forward Flight Velocity on the Bending-Torsion Stability of a Supersonic Wing

Abstract

p TO THE PRESENT time flutter analyses have generally been carried out under the basic assumption of constant flight velocity through the critical range. This has been shown to be a reasonably valid assumption when applied to the flutter analysis of vehicles whose maximum rate of acceleration through the critical speed range is less than approximately lg. But when higher accelerations are involved, the flutter speeds ob­ tained through analysis under this assumption become increas­ ingly in error from the actual values. It was of interest to the author to investigate the degree of this error for the case of a simple two-dimensional, double-wedge airfoil. The coefficients of Eq. (8) were tabulated for various times t near the expected critical point, thus yielding several fourth- order equations with constant coefficients. Routh's stability criterion was then applied to the coefficients of each of the re­ sulting characteristic equations, and the point at which a root with v a positive real part appeared was found to be at t ~ 17.86 sec, which corresponds to a speed of 5,750 ft per sec. Now, assuming negligibly small acceleration through the critical range (U = U = 0), as is the case in classical flutter analysis, Eq. (7) with the same constant values as before becomes