Chaos and chaotic transients in an aeroelastic system

Chaotic motions of a two dimensional airfoil with coupled structural nonlinearities, both in pitch as well as plunge degrees of freedom, are investigated via a numerical integration method. The original system of coupled integro-differential equations governing the motion of the present aeroelastic model is transformed into a simple system of six ODEs. Complex dynamical behaviors are revealed and identified through the means of bifurcation diagrams, the phase portraits, the amplitude spectra and the Poincare maps. Besides, a more quantitative method, namely that of observing the evolution of the largest Lyapunov exponent (LLE) is also applied to diagnose the motions. Two peculiar phenomena, namely, long (perhaps super-persistent) chaotic transients, and fluctuating Lyapunov exponents, are observed; in the two such cases the LLE method fails to work. In addition, the effects of various system parameters, namely, the position of the elastic axis, the frequency ratio, the airfoil/air mass ratio, the viscous damping ratios, and the location of the center of mass, on the response of the aeroelastic system, are investigated. & 2014 Elsevier Ltd. All rights reserved.