Reduced-Order Nonlinear Damping Model: Formulation and Application to Postflutter Aeroelastic Behavior

Recent studies of postflutter limit-cycle oscillations (LCOs) have suggested the presence/effects of a nonlinear structural damping in addition to other potential sources of nonlinearity. Such a nonlinearity occurs, for example, for structures with linear viscoelastic properties when their responses are in the nonlinear geometric regime. The present effort focuses on such situations; first on developing a structural reduced-order model (ROM) which could be used in aeroelastic analyses. Adopting a linear Kelvin-Voigt constitutive model in the undeformed configuration, the ROM governing equations are obtained and found to be of a generalized Van der Pol-Duffing form. A nonintrusive identification approach is next developed to determine the parameters of these governing equations from a structural finite element model constructed in a commercial software. Finally, the effects of this nonlinear damping on postflutter response are analyzed on the Goland wing assuming a linear aerodynamic model. It is found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit-cycle oscillations, even when the stiffness-related nonlinear geometric effects and aerodynamic nonlinearities are neglected. The dependence of the LCO amplitude and frequency on the parameters of the Kelvin-Voigt model is analyzed to provide insight into this nonlinearity.