Flutter Analysis of a Two-Dimensional Airfoil Containing Structural Nonlinearities

摘要

Nonlinear flutter of a two-dimensional airfoil undergoing plunging and pitching motions is studied using a time marching finite difference scheme. The structural nonlinearity considered is of the type due to a spring with preload and freeplay. Flutter is determined from solutions of the structural dynamic equations of motion when either divergent or limited amplitude oscillations are encountered. Case studies using various airfoil parameters and values of preload and freeplay are carried out. The effect of initial condition, which is important in nonlinear prolbems, is investigated by varying the displacement from equilibrium of the pitch angle at the beginning of the airfoil motion. For nonzero values of the preload, three types of oscillatory motion are possible, namely; damped, limited amplitude and divergent. The divergent flutter boundary is practically identical to that for the linear flutter case. The location of the limit-cycle flutter boundary varies for different airfoil and spring parameters. For zero preload, damped oscillations are not encountered even for air speeds down to 15 percent of the linear flutter speed which is the lowest used in this study. The limited amplitudes of the pitch and plunge motions are found to be independent of initial angular displacement. The characteristics of the oscillations and the development of higher harmonics in the various regions defined by the flutter boundary curves are investigated.