Prediction of Limit Cycle Oscillation in an Aeroelastic System using Nonlinear Normal Modes

Abstract

There is a need for a nonlinear flutter analysis method capable of predicting limit cycle oscillation in aeroelastic systems. A review is conducted of analysis methods and experiments that have attempted to better understand and model limit cycle oscillation (LCO). The recently developed method of nonlinear normal modes (NNM) is investigated for LCO calculation. Nonlinear normal modes were used to analyze a spring-mass-damper system with nonlinear damping and stiffness to demonstrate the ability and limitations of the method to identify limit cycle oscillation. The nonlinear normal modes method was then applied to an aeroelastic model of a pitch-plunge airfoil with nonlinear pitch stiffness and quasi-steady aerodynamics. The asymptotic coefficient solution method successfully captured LCO at a low relative velocity. LCO was also successfully modeled for the same airfoil with an unsteady aerodynamics model with the use of a first order formulation of NNM. A linear beam model of the Goland wing with a nonlinear aerodynamic model was also studied. LCO was successfully modeled using various numbers of assumed modes for the beam. The concept of modal truncation was shown to extend to NNM. The modal coefficients were shown to identify the importance of each mode to the solution and give insight into the physical nature of the motion. The quasi-steady airfoil model was used to conduct a study on the effect of the nonlinear normal mode's master coordinate. The pitch degree of freedom, plunge degree of freedom, both linear structural mode shapes with apparent mass, and the linear flutter mode were all used as master coordinates. The master coordinates were found to have a significant influence on the accuracy of the solution and the linear flutter mode was identified as the preferred option. Galerkin and collocation coefficient solution methods were used to improve the results of the asymptotic solution method. The Galerkin method reduced the error of the solution if the correct region of integration was selected, but had very high computational cost. The collocation method improved the accuracy of the solution significantly. The computational time was low and a simple convergent iteration method was found. Thus, the collocation method was found to be the preferred method of solving for the modal coefficients.