Reduced Cost Rational-Function Approximation for Unsteady Aerodynamics

An improved method is developed for the approximation of generalized, unsteady aerodynamic forces by a rational transfer function in the Laplace domain. The new method results in a large reduction in the computational cost of an optimized aeroelastic stability analysis when compared with the previous procedures for a given accuracy. Also, while the previous methods produce an ill-conditioned eigenvalue problem when the optimized values of two or more poles of the transfer function are close to one another, the present scheme accounts for such frequent cases consistently. These improvements are due to the use of higher-order poles (as against the simple poles of the conventional methods), without increasing the total number of aerodynamic states of the system, and they make the method applicable to routine transient response calculations. The method employs a nongradient optimizing process for the selection of the nonlinear parameters of the transfer function. Approximations are presented for the three dimensional, subsonic aerodynamics of a high-aspect-ratio wing, and flutter analysis is carried out to demonstrate the advantages of the present method.