柔性压电智能反射面的静态形状控制

Abstract

The finite element formulation of a flexible piezoelectric smart reflector was presented based on Kirchhoff classical laminated theory, and its structural mechanic modeling and optimization algorithms were investigated. Firstly, the smart reflector with the honeycomb core was modeled with the equivalent laminate plate theory, and its finite element formulation was derived according to virtual work theory. The honeycomb core equivalent elastic modulus was calculated by using equivalent theory. Then, a simple four-node quadrilateral element was used in the model, and one electric potential degree of freedom was introduced to each active element. Accordingly, the relation between the mean square root error of reflector and the control voltages of actuators was derived, the optimization model for static shape control was created and the voltage limitation for piezoelectric actuator patches was imposed to maintain its control voltage within a practical range. The optimal control voltages were determined by using Lagrange multipliers to minimize the Root Mean Square (RMS) error. Finally, a numerical example of plane smart reflector was given to demonstrate the feasibility of smart mirror concept and the effectiveness of optimization algorithm. Simulation results indicate that the square root error of the smart reflector is reduced by above 90%, and the control voltage of each actuator is in a practical range.