Calculations of the bounds on limit cycle oscillations in nonlinear aeroelastic systems based on equivalent linearization

The nonlinear aeroelastic system of an airfoil with an external store was investigated, with emphasis on the bounds of limit cycle oscillations (LCOs). Based on the equivalent linearization, an approach was proposed to calculate the bounds on LCOs over the full flight envelope. The bounds are determined directly without solving LCOs one by one as the flow speed varies. The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise. Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results. The speed threshold can be predicted to a relative error less than 0.1%, and the maximal LCO amplitude to about 3%. The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach.