Sliding-Window Matrix Pencil Method for Whirl Flutter Bifurcation Analysis

This paper investigates a sliding-window matrix pencil method for predicting flutter points and limit-cycle oscillation amplitudes of nonlinear aeroelastic systems that experience whirl flutter. The approach applies the matrix pencil method to a short time window that slides along the free decay of a quantity of interest, quantifying the variation in the system's recovery rate to equilibrium with amplitude. The recovery rates at each amplitude and various forward speeds are extrapolated to predict the critical forward speed of zero recovery rate at those amplitudes. This process yields a set of limit-cycle oscillation solutions that can be visualized as a bifurcation diagram. The approach is demonstrated using output data from transient simulations of a propeller-nacelle test case with hardening structural nonlinearities. The impact of each parameter in the sliding-window matrix pencil method is first characterized via sensitivity analyses. Next, the bifurcation diagram is predicted using the recovery rates for the optimal parameter values. The results are compared with direct time marching and with the extrapolation of recovery rates estimated from envelope functions. The proposed method accurately captures the bifurcation diagram using two pre-flutter transient simulations with no need for envelope functions. This approach shows promise for output-based bifurcation analysis of nonlinear aeroelastic systems exhibiting limit-cycle oscillations associated with whirl flutter.