Stability analysis and active control of a nonlinear composite laminated plate with piezoelectric material in subsonic airflow

Abstract

The stability analysis and active control of a nonlinear composite laminated plate in subsonic airflow are studied. The equation of motion of a plate with a piezoelectric patch in subsonic air flow is established by using the Hamilton’s principle with the assumed mode method. The perturbation aerodynamic pressure is derived from linear potential flow theory. For the linear system, the eigenfrequencies of the system are calculated for different flow velocities, and the critical instability flow velocity and the flutter flow velocity are obtained. For the nonlinear system, the bifurcation of the transverse displacement with respect to the flow velocity is analyzed by solving the equations of equilibrium of the nonlinear dynamic system. The effects of the ply angles on the critical instability flow velocities of the plate are analyzed. According to the mechanism for the instability of the plate in subsonic flow, the displacement feedback control strategy is adopted to stabilize the system. The influences of the control gain on the critical instability velocity of the plate are analyzed. From the analysis and numerical simulations, it can be concluded that with the ply angle increasing from \(0^{\circ }\) to \(90^{\circ }\), the critical instability flow velocity of the plate has a maximum at a finite critical angle. When the flow velocity exceeds the critical instability flow velocity, the stable point of the nonlinear system deviates from the zero point of the system. It also can be concluded that the displacement feedback control can effectively improve the aerodynamic properties of the plate by providing the active stiffness for the unstable system. With displacement feedback control gain increasing, the critical instability flow velocity increases.