Prediction of aeroelastic limit-cycle oscillations based on harmonic forced motion oscillations

Abstract

Aeroelastic limit-cycle oscillations due to aerodynamic non-linearities are usually investigated using coupled fluid-structure interaction simulations in the time domain. These simulations can become computationally expensive, especially if the global bifurcation behaviour is of interest. To reduce the computational effort of parameter studies, an extension of the well-known p-k method is developed. In this frequency domain method, the aerodynamic forces and moments are now not only dependent on the frequency, but also on the oscillation amplitudes and the phase angle between the degrees of freedom. The first harmonic components of the aerodynamic forces are interpolated in the parameter space applying response surface modelling. The limit-cycle oscillation amplitude and mode shape are then found iteratively. The amplitude-dependent p-k method is verified and validated using an analytical testcase; the two-degree-of-freedom van der Pol oscillator. Excellent agreement with the time domain solution and the analytical solution is obtained. The amplitude-dependent p-k method is then applied to a two-degree-of-freedom airfoil system where the aerodynamic forces are computed from Euler simulations. Fluid-structure interaction simulations are performed for validation of the method. Both methods show good agreement in the bifurcation behaviour of the limit-cycle oscillation amplitude and mode shape.