Electrode grouping optimization of electrostatic forming membrane reflector antennas

This paper presents an electrode grouping optimization approach for electrostatic forming membrane reflector antennas. The analytical model of a membrane reflector is constructed based on the virtual work principle. Referring to the electrostatic forming theory, the reflector shape could be adjusted by regulating the arrangement and corresponding voltages of the electrodes. The advantage of the use of distributed electrodes to mitigate the effects of external disturbances is investigated. Generally speaking, the shape accuracy is higher when the electrodes are more individually controlled. However, in some cases, the use of distributed electrodes does not realistically satisfy the weight, power, and cost constraints. Additionally, distributed electrodes suffer from the problems of insufficient electrostatic force, due to the finite supplied voltage, and the electro-discharge and wrinkles, due to complex multiple-voltage distribution. Therefore, an optimization approach is proposed to reduce the reflector system complexity while ensuring the shape accuracy of the reflector. The optimization mathematical model is constructed and solved. The simulation process is presented. Typical numerical simulations demonstrate the validity and rationality of this optimization approach.