Flexible flapping wings can exhibit quasi-periodic motion!

Abstract

The dynamics of a flexible flapping wing is investigated by modelling it as a coupled nonlinear fluid-structure interaction (FSI) system in the low Reynolds number flow regime in accordance to the flight of flapping wing micro air vehicles (MAVs). A bifurcation analysis, by varying the free-stream wind velocity (U∞) as the control parameter, revealed the presence of a new dynamics in the form of a quasi-periodic attractor in the flapping wing motion. The structural and aerodynamic nonlinearities present in the system cause a supercritical Hopf bifurcation, where stable limit cycle oscillation emerges from fixed point response beyond a critical value of the free-stream velocity. Further increasing the control parameter, another bifurcation named Neimark-Sacker bifurcation takes place and as a result, the flapping wing exhibits quasi-periodic motion. The presence of Neimark-Sacker bifurcation in the flapping flow-field dynamics is an interesting find and the present work focuses on it's associated dynamical behaviour. Various dynamical system tools like frequency spectra, phase space, Poincaré section, first return map have been implemented successfully to confirm the presence of quasi-periodicity.