Study of the conditions that cause chaotic motion in a two-dimensional airfoil with structural nonlinearities in subsonic flow

Abstract

Because of various nonlinearities, aeroelastic systems exhibit a variety of phenomena, such as limit cycle oscillation (LCO) and chaos. This paper investigates the cause of chaos in a two-dimensional airfoil in subsonic flow. The aeroelastic equation of the airfoil in matrix form was derived. The differential equation was then integrated numerically using a Runge–Kutta method to produce the time history of the aeroelastic response. A theoretical analysis from an energy perspective and a numerical verification have shown that both freeplay and hysteresis nonlinearities can be approximately represented by rational polynomials (RP). For the system with a cubic nonlinearity in pitching motion, chaos was obtained as suggested by the phase trajectory and the Poincaré section of the airfoil time histories. Then, the effects of the elastic center position, the airfoil/air mass ratio, and the structural preload on the chaotic motion were investigated using bifurcation diagrams. From the analysis of the nonlinear restoring moment in pitching, “energy flat” was determined to be a necessary condition for chaotic motion.