Nonlinear Stability Analysis of Control Surface Flutter with Freeplay Effects

Abstract

Results are presented from nonlinear stability analyses of control surface flutter that were conducted on a threedegree-of-freedom typical-section airfoil with free play about the control surface hinge line. The describing function (harmonic-balance) method has been used to predict response amplitudes, and a locally parameterized continuation method has been used to track all flutter modes. Themethodology is directly applicable to systems with unsteady air loads expressed in either the frequency or time domains. Both stable and unstable limit cycles have been identified. Limit cycle stability has been assessed by examining the change in growth rate due to amplitude perturbations at a given velocity. Limit cycle amplitudes predicted by the describing functionmethod,with frequency-domain unsteady aerodynamics, are shown to compare very well with the magnitudes of time-history responses obtained by direct integration of the equations of motion, using rational function approximation time-domain aerodynamics. Results from these nonlinear analyses are compared with analytical and experimental results of similar analyses from the open literature.