Limit-Cycle Oscillation Induced by Nonlinear Aerodynamic Forces

Abstract

The aerodynamic e ow state on launch vehicle payload fairings and aircraft wings can change abruptly during transonic e ight if the angle of attack reaches a critical value. The nonlinear pressure variation associated with a e ow-state change induces transient structural responses that may converge to a limit-cycle oscillation (LCO). In this steady state, the work conducted during thee ow-statechangesbalances theenergy dissipation from structural damping.AnalysisofthistransonicLCOphenomenonisoftenconductedusingasemi-empirical,unsteadypressure variation in which the levels for the e ow states are determined from steady wind-tunnel test data. The presented theory addresses the condition in which the e ow-state changes occur near a quasi-steady, nonzero angle of attack. The analysis for the resulting asymmetric forcing function complements the authors’ existing derivations for a symmetric forcing function at zero angle of attack. Both the asymmetric and the symmetric analyses develop closed-form equations for the structural response frequency and amplitude. These expressions show that the solution space contains a subcritical Hopf bifurcation when the critical angle of attack equals the quasi-steady angle of attack. They also show that a saddle-node bifurcation, or fold, corresponds to the critical angle of attack beyond which LCO will not occur for a given quasi-steady angle of attack.