Effects of geometric structural nonlinearity on flutter and limit cycle oscillations of high-aspect-ratio wings

Abstract

In this paper structural equations of motion based on nonlinear beam theory and the ONERA aerodynamic stall model are used to study the effects of geometric structural nonlinearity on flutter and limit cycle oscillations (LCO) of high-aspect-ratio wings. For example, the effects of large static pre-flutter deformations in the vertical or torsional direction are considered. In particular, static deformations in the vertical and torsional directions caused by a static angle of attack, gravity and/or manufactured curvature generally decrease system stiffness and flutter stability. The structural nonlinearity also leads to a sensitivity to initial conditions as well as any parameter that influences the static equilibrium condition. A dynamic perturbation equation about a nonlinear static equilibrium is derived which is used to determine the small perturbation flutter boundary. The effects of the geometric structural nonlinearity of the beam theory on both the perturbation flutter boundary and the nonlinear response are significant. Onset of a limit cycle oscillation is dependent upon the delicate between stall aerodynamics and structural nonlinear forces. LCO above and below the perturbation flutter boundary generally occurs over a limited range of flow velocity. LCO can occur below the perturbation flutter velocity due to large initial disturbances.