Date of Award

Winter 1994

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Jen-Kuang Huang

Committee Member

Sebastian Bawab

Committee Member

Gene Hou

Committee Member

Chuh Mei


Panel flutter is a large-deflection limit-cycle motion excited by the airflow, which is only on one side of a panel. The objective of this research is to analytically study the panel flutter limit-cycle suppression using nonlinear vibration control techniques with piezoelectric actuation. It is well known that piezoelectric materials are characterized by their ability to produce an electrical charge when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a panel by applying an electrical field. Piezoelectric actuators are driven by feedback controllers, and control the panel dynamics. For a simply supported panel with piezoelectric layers, the nonlinear dynamic equations of motion are derived by applying Galerkin's method to von Karman's large deflection equation. The aerodynamic force is predicted by using the first-order piston theory or quasi-steady supersonic theory. For controller design, controllers are developed for the bending-moment actuation with given inplane force. For linear feedback control, linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) dynamic compensator and proportional derivative (PD) controllers are used, and compared. For nonlinear control, Lyapunov's direct method is applied to the nonlinear dynamic model. The controller consists of two parts. One is the linear part which is designed by solving a Riccati equation, and another is the nonlinear part which is obtained by making the time derivative of a Lyapunov function to be negative. Numerical simulations based on the nonlinear dynamic model are performed. The numerical study shows that the maximum suppressible dynamic pressure can be increased about five times of the critical dynamic pressure, and the bending moment is much more effective in flutter suppression than the piezoelectric inplane force. Within the maximum suppressible dynamic pressure, limit-cycle motion can be completely suppressed, which means that the flutter free region is enlarged. For the actuator design, three kinds of configurations are considered, two-set, one-patched and shaped actuators, which are implemented by changing the shapes of electrodes. Two-set actuators perform better than one-patched actuator, and one-patched actuator may have better performance than the completely covered actuator. For a shaped actuator, the methods to design the shape and location of the actuator are developed. The best location of an actuator is near the leading edge of the panel. Beside the design of shape and location of actuators, the method to design the optimal thickness of actuators is also presented. For a collocated actuator and sensor or a self-sensing actuator, the shape of actuator is very important when the PD controller is used. For the sensor design, the method to design the shape and location of the piezoelectric sensors is developed. The optimal control performance can be achieved by shaped sensors with a simple fixed-gain PD controller. Numerical results demonstrate that piezoelectric materials are effective in panel flutter limit-cycle suppression. The flutter free region can be further enlarged, if the actuator is activated before the critical dynamic pressure being reached.


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