Geometrical nonlinear aeroelastic stability analysis and active control with piezoelectric actuators of a high-aspect-ratio flexible wing

The aeroelastic stability analysis and the active control technique using the piezoelectric actuators to improve the stability properties of a high-aspect-ratio flexible wing with structurally geometric nonlinearity are investigated. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the largely deformed structure are obtained, based on which, the unsteady aerodynamics are calculated by the DLM, furthermore, the state-space equations of flexible wing with piezoelectric actuators can be established by Hamilton’s principle. Then, by solving the standard complex eigenvalue problem, the aeroelastic stability of the system is analyzed for both linear and nonlinear cases. Finally, the active control law are designed for the two conditions respectively. The work shows that the geometric nonlinearity induced by the large structural deformation could change the instability pattern from flutter in linear case to divergence in nonlinear case and motion coupling relationship of the flexible modes leading to the decrease of the unstable velocity. In addition, the active control system using piezoelectric actuators functions well to improve the unstable velocity by 14.83% and 16.09% for linear and nonlinear conditions respectively, which verifies the effectiveness of the piezoelectric control strategy proposed in this study.