The Flutter of a Uniform Cantilever Wing

Abstract

Abstract The flutter speed of a uniform cantilever wing (one with a built-in root and with constant mass and stiffness characteristics along its entire span) is determined by integration of the differential equations for the wing motion. The solution is free of the dynamical approximations usually made during flutter analyses of the Rayleigh-Ritz type. A brief discussion of the procedures conventionally employed for the solution of the flutter problem is given, followed by a detailed derivation of the exact method for finding the flutter speed. It is found that a Rayleigh-Ritz type analysis, based on the fundamental uncoupled bending and torsion modes, is entirely adequate for the flutter analysis of a uniform wing. In addition to yielding a flutter speed which is in excellent agreement with the true value, the approximate method adequately predicts the wing shape at flutter. Additional parts of the paper deal with the relation between the uncoupled and the ground modes for the uniform wing, and with the nature of the wing response resulting from forced excitation while in flight.