Aeroelastic Stability Estimation of Control Surfaces with Freeplay Nonlinearity

This work discusses the quantitative stability evaluation of aeroelastic problems with freeplay in the control surfaces. Stability estimation of linear time invariant and linear time periodic systems rely on eigenanalysis of state transition matrices and implies simplifications on the problems governed by nonlinear non-autonomous equations. Lyapunov Characteristic Exponents directly provide quantitative information on the stability of nonlinear non-autonomous dynamical systems. Stability estimation using Lyapunov Characteristic Exponents does not require a special reference solution and is consistent with the eigensolution of linear time invariant and Floquet-Lyapunov analysis of linear time periodic systems. Thus, they represent a natural generalization of conventional stability analysis. The Discrete QR method is used to practically estimate the Lyapunov Characteristic Exponents. The method is applied to a three-dimensional aeroelastic problem with freeplay introduced to the control surface.