Nonlinear reduced-order modelling for limit-cycle oscillation analysis

A nonlinear model reduction based on eigenmode decomposition and projection for the prediction of sub- and supercritical limit-cycle oscillation is presented herein. The paper focuses on the derivation of the reduced-order model formulation to include expansion terms up to fifth order such that higher-order nonlinear behaviour of a physical system can be captured. The method is applied to a two degree-of-freedom pitch-plunge aerofoil structural model in unsteady incompressible flow. Structural stiffness nonlinearity is introduced as a fifth-order polynomial, while the aerodynamics follow linear theory. It is demonstrated that the reduced-order model is capable of accurately capturing sub- and supercritical limit-cycle oscillations arising both from initial disturbances and gust excitation. Furthermore, an analysis of the computational cost associated with constructing such reduced-order model and its applicability to more complex aeroelastic problems is given.