Robust flutter analysis of a nonlinear aeroelastic system with parametric uncertainties

Abstract

This paper deals with the problem of robust stability of a 2-D nonlinear aeroelastic system with structural and aerodynamic uncertainties using μ-method and value set approach. The model includes a nonlinear spring in the pitch degree-of-freedom and a nonlinear aerodynamic model. Two types of uncertainty named vanishing and nonvanishing perturbation are investigated. For vanishing perturbations, μ-method can be used directly to examine the robust stability of the nonlinear aeroelastic system by analyzing its linearized system. For nonvanishing perturbations, the functional relationship between equilibrium point and uncertain parameters are expressed as Taylor series expansions in order to consider the uncertainty of the equilibrium point in μ-analysis framework. Furthermore, the value set approach is also used to examine the robust stability of the uncertain system. The value sets of the characteristic polynomials are computed and zero exclusion condition is applied to check the stability of the entire family of the characteristic polynomials. Numerical results are presented for a set of values of the flow velocities, and the lower bound and upper bound of robust flutter speeds are obtained from the V–μ graph and the motion of the value sets.