Aeroelastic behavior of lifting surfaces with free-play, and aerodynamic stiffness and damping nonlinearities

Aeroelastic instabilities are dangerous phenomena, where aerodynamic load interacting with the inertia and elastic structural loads can induce catastrophic failures. In this paper the effects of aerodynamic nonlinearities as well as coupled plunging/pitching structural concentrated cubic type and freeplay nonlinearities in the dynamic of a two-dimensional double-wedge airfoil immersed in supersonic/hypersonic flow has been examined. The unsteady nonlinear aerodynamic force and moment on the airfoil are evaluated using the Piston Theory Aerodynamics modified to take into account the effect of the airfoil thickness. The resulting aeroelastic equations are numerically integrated to obtain time responses and to investigate the dynamic instability of the lifting surface under various initial displacement conditions. Results of the complex nonlinear aeroelastic system are presented in the form of bifurcation diagrams constructed from the response amplitude for various types of the system nonlinearity. It is shown that there exist regions, in which the system exhibit Limit Cycle Oscillations (LCOs), strongly dependent on the initial conditions of the aeroelastic system. Concentrated structural nonlinearities, that are freeplays and cubic type nonlinearities, can have significant effects on the. utter behavior and can cause large amplitude oscillations at lower airspeeds than for a linear system. It is also shown that larger amplitude LCOs occur when a pitching freeplay is considered, as compared with the case when a plunging freeplay is taken into account.