Hopf bifurcation for a fractional van der Pol oscillator and applications to aerodynamics: implications in flutter

Abstract

Flutter is an important instability in aeroelasticity. In this work,we derive a model for this phenomenon which naturally leads to an equation similar to a van der Pol oscillator in which the friction term is given by a fractional derivative. Motivated by these considerations,we study a fractional van der Pol oscillator and show that it exhibits a Hopf bifurcation. The model is based on a one-dimensional reduction where the instabilities associated with flutter are preserved. However, due to the fractional derivative, the bifurcation analysis differs from the standard case. We present both analytical and numerical results and discuss the implications to aerodynamics. Additionally, we contrast our qualitative results with experimental data.