Flutter margin evaluation for discrete-time systems

A Butter prediction method using a new parameter is proposed, and its effectiveness is examined by numerical and experimental analysis. In this method, the aeroelastic system is identified as the autoregressive moving average (ARMA) model from the random response of a wing excited by flow turbulence, so that no special excitation device is needed. The new parameter is based on a stability test for discrete-time systems and is calculated algebraically from the autoregressive coefficients of the estimated ARMA model. Numerical calculation using a two-dimensional wing model shows that the parameter decreases almost linearly toward zero with increasing dynamic pressure. This is a superior property as a Butter predictor in comparison with damping coefficients and the stability parameter used conventionally. The method is applied to supersonic wind-tunnel Butter test data to examine the validity in actual data analysis. The results obtained under different test conditions demonstrate the advantage of the present method for an accurate and reliable Butter prediction. Moreover, an analytical consideration reveals that the calculated values of the proposed parameter are nearly equal to that of the Butter margin introduced by Zimmerman and Weissenburger (Zimmerman, N. H., and Weissenburger, J. T., "Prediction of Flutter Onset Speed Based on Flight Testing at Subcritical Speeds," Journal of Aircraft, Vol. 1, No. 4, 1964, pp. 190-202).