Analysis of limit cycle oscillations of a typical airfoil section with freeplay

A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the nonlinearity of the airfoil section’s freeplay. There are two critical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincaré map is constructed for the limit cycle oscillations by using piecewise-linear solutions with and without contact in the system. Through analysis of the Poincaré map, a series of equations which can determine the frequencies of period-1 limit cycle oscillations at any flight velocity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agreement is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. Moreover, there exist multi-periods limit cycle oscillations and even complicated “chaotic” oscillations may occur, which are usually found in smooth nonlinear dynamic systems.