Prediction of Aeroelastic Limit-Cycle Oscillations Based on Harmonic Forced-Motion Oscillations

Abstract

Aeroelastic limit-cycle oscillations due to aerodynamic nonlinearities are usually investigated using coupled fluid–structure interaction simulations in the time domain. These simulations are computationally expensive, especially if a large number of limit-cycle oscillation solutions must be computed to study the Hopf bifurcation behavior in the immediate surroundings of the flutter point. To facilitate such bifurcation parameter studies, an adaptation of the well-known p-k flutter analysis method is proposed in this paper. In this method, the first harmonic of the motion-induced unsteady aerodynamic forces is no longer assumed to be solely determined by constant-coefficient frequency response functions. Instead, the nonlinear dependence on the oscillation amplitudes and the phase angle between the input degrees of freedom are additionally taken into account. Therefore, the first harmonic Fourier components of the aerodynamic forces are sampled and interpolated in advance. The limit-cycle oscillation solution is then found iteratively. The proposed amplitude-dependent p-k method is applied to a classic two-degree-of-freedom spring-mounted airfoil system, where the nonlinear aerodynamic forces are computed from Euler simulations. Fluid–structure interaction simulations are performed for validation of the method. Both methods show good agreement. Furthermore, the amplitude-dependent p-k method is shown to be a useful tool to rapidly study structural parameter variations.