A Modified Indicial Functions Approximation for Nonlinear Aeroelastic Analysis

Abstract

The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of high aspect ratio wings using a novel indicial aerodynamics in subsonic flow is investigated. Using the nonlinear beam theory, the structural model is derived including the in-plane and out-of-plane bending and torsion motions, all nonlinearities up to cubic order arising from large deformation, mass distribution, and cross-sectional mass imbalance. Based on new approximations of the indicial functions, a comprehensive unsteady aerodynamic model is used. Such an indicial aerodynamics while being coupled to nonlinear structural equations can result in a unified nonlinear aeroelastic formulation in both the incompressible and subsonic compressible flow. The effect of flight conditions, wing tip initial disturbances, stiffness ratio between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results show that the compressibility can affect the LCO boundary up to 12 percent which implies that an appropriate Mach-dependent aerodynamics is required to achieve a more reasonable and realistic description of dynamic behavior of the system. It is shown that the presence of LCO before the linear flutter speed depends on initial disturbances as well as wing characteristics.