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.