An experimental and analytical investigation of the nonlinear behaviour and modal analysis of a structurally nonlinear, two-dimensional airfoil in subsonic flow

Modal testing is often employed in the determination of natural frequencies and damping levels in aircraft structures. In aircraft flutter testing, potentially dangerous flight regimes are avoided by obtaining modal frequency and damping values at airspeeds well below the flutter speed and extrapolating the data to estimate the airspeed at which the onset of flutter instabilities is expected to occur. In the modal analysis, the structure is typically assumed to be linear and the parameters to be time-invariant. Nonlinearities in aeroelastic systems can arise from both structural and aerodynamic sources and may initiate aeroelastic instabilities both above and below the flutter speed predicted by linear theory. Typical nonlinear responses include limit cycle oscillations and in some cases, chaotic response. For aeroelastic systems containing even small nonlinearities, the nonlinear frequency response curve may be distorted, and this distortion can contribute to errors in the values of frequency and damping obtained during modal testing. The current study includes an analytical and an experimental investigation into the modal testing of a nonlinear aeroelastic system.; In the case of aeroelastic systems containing limited structural nonlinearities, the nonlinearity, although it changes the system frequency and damping values and distorts the transfer function, does not substantially affect the critical flutter speed. For this reason, the nonlinearity behaves a little like "noise" in that it prevents accurate values of frequency and damping from being obtained during the modal test. One solution to this problem is to separate the linear and nonlinear portions of the frequency response using spectral decomposition methods. In the analytical portion of this study, a specific spectral decomposition technique is tested on numerical data, and the results show that the technique may be used to separate the linear and nonlinear portions of the transfer function obtained from the nonlinear aeroelastic system response to a random forcing input.; In the experimental portion of the study, subsonic wind tunnel experiments are performed on a two degree-of-freedom wing section with a freeplay-type nonlinearity in the pitching degree-of-freedom. The experiments demonstrate the effect of the freeplay on the aeroelastic response, including the presence of limit cycle flutter for specific parameter combinations. The effects of variations in both freeplay length and frequency ratio of the underlying linear system are examined for both the damped and the limit cycle response. Time histories of the damped response are used to estimate frequency and damping values, and to predict critical flutter speeds. The amplitude and frequency of the LCO response is presented for three different freeplay lengths and five frequency ratios.; The experimental setup is modeled analytically, and the equations solved numerically to obtain time-history data for the free response of the airfoil to initial displacements in each of its two degrees-of-freedom. The results are used to validate the mathematical model of the aeroelastic system subject to subsonic flow. Numerical results are obtained for the transient behaviour of the system including the damped and limit cycle responses observed during the experimental portion of the study. The model is used to demonstrate the influence of frictional forces on the response of the experimental system.; In conclusion, three additional techniques of nonlinear dynamical analysis are investigated for their potential within the context of the nonlinear aeroelastic modal analysis problem. Two of the methods are tested on the experimental time-history data, while the third is shown to be applicable to the simulated data for the forced response of the system.