Chaotic Dynamics of an Airfoil with Higher-Order Plunge and Pitch Stiffnesses in Incompressible Flow

Abstract

Dynamical properties of a two-dimensional airfoil model with higher-order strong nonlinearities are investigated. Firstly, a state-space model is derived considering the plunge and pitch stiffnesses as generalized functions. Then, a stiffness function having square, cubic, and fifth-power nonlinearities is considered for both plunging and pitching stiffnesses, and the dimensionless state equations are derived. Various dynamical properties of the proposed model are investigated using equilibrium points, eigenvalues, and Lyapunov exponents. To further analyze the dynamical behavior of the system, bifurcation plots are derived. It is interesting to note that the new airfoil model with higher-order nonlinearities shows multistability with changing airspeed, and there are infinitely countable number of coexisting attractors generally called as megastability. Both multistability and megastability features of the airfoil model were not captured earlier in the literatures. To be clear, it is the first time a megastable feature is exposed in a physical system. Finally, to analyze the multifrequency effects of the airfoil model, we have presented the bicoherence plots.