A REDUCED ORDER MODEL-BASED NONLINEAR DAMPING MODEL: FORMULATION AND APPLICATION TO POST FLUTTER AEROELASTIC BEHAVIOR

摘要

Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) have suggested the presence/effects of a nonlinear structural damping in addition to potential other sources of nonlinearity. A mechanism for the appearance of nonlinearity in the damping which has received little attention are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is on developing a model of these effects which can complement other nonlinearities for the prediction of LCO amplitudes. To this end, existing nonlinear reduced order modeling (ROM) methods will first be extended to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An evaluation approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response are next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed 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 sensitivity of the LCO amplitude and frequency with respect to the parameters of the Kelvin-Voigt model are analyzed.