A new approach for calculating the unsteady aerodynamic loads based upon the indicial functions concept in combination with a fully third-order nonlinear structural model has been developed to analyze the aeroelastic behavior of high-aspectratio wings over the entire range of subsonic flow. The resulting aeroelastic equations including all structural geometric nonlinearities associated with large deformations and mass distributions, along with nonlinear terms due to mass imbalance at wing's cross section, are then rewritten in the state-space form, introducing an efficient and appropriate approach to use in both eigenvalue and time response analysis. To validate the developed aeroelastic equations, the linear and nonlinear aeroelastic behaviors of a specified wing are compared with those presented for an incompressible aerodynamic case. Quantitative and qualitative agreement between the present results and available ones confirms the unsteady indicial aerodynamics, nonlinear structural modeling, and, consequently, the developed nonlinear aeroelastic model. By changing the wing model and applying the unsteady compressible aerodynamic loads, the nonlinear aeroelastic behavior of Goland wing is then investigated, including the flutter boundary, limit cycle oscillations, pre-flutter, flutter, and post-flutter time responses, phase plane diagrams, and also the effect of flight conditions such as altitude and air speed on the aeroelastic behavior. The results represent the necessity of applying appropriate Mach-dependent aerodynamic loads to provide reasonable description of the aeroelastic analysis in the compressible flight speed regime.

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The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of High-Aspect-Ratio (HAR) wings using novel indicial aerodynamics in subsonic ow was investigated. Using the nonlinear beam theory, the structural model was derived with in-plane and out-of-plane bending and torsional 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 was used. Coupling such indicial aerodynamics to nonlinear structural equations can result in a uni ed nonlinear aeroelastic formulation in both incompressible and subsonic compressible ows. The e ects of ight conditions, wing tip initial disturbances, Sti ness Ratio (SR) between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results showed that compressibility could a ect the LCO boundary up to 12 percent, which implied that appropriate Mach-dependent aerodynamics was required to achieve a more reasonable and realistic description of dynamic behavior of the system. It was observed that the presence of LCO before the linear utter speed depended on the initial disturbances as well as wing characteristics.