Form-Finding Analysis and Active Shape Adjustment of Cable Net Reflectors with PZT Actuators

High-precision cable net reflectors are widely required for future communications and observations. Concerning the improvement of their surface accuracy, the active cable structure constructed by incorporating a piezoelectric (PZT) actuator into flexible cables has been proposed to achieve active shape control or active correction of the reflector surface. Two design stages of the cable net reflector with active cables, the form-finding analysis and active shape adjustment, are investigated. The form-finding analysis is derived from nodal force equilibrium equations by the minimum norm method-solving linear equations. An active shape adjustment method with the aid of active cables is then proposed to find the actuation voltages of PZT actuators for the prescribed shape. The adjustment method is divided into three parts: a finite-element model of the active cable net reflector, an active adjustment optimal model, and its solving method using the multidimensional advance-retreat algorithm. Finally, numerical examples of a parabolic cable net reflector are analyzed. Simulation results demonstrate that the proposed methods can warrant cable tension forces, which fall into a specified range, and the deformed cable net reflector surface can match the one designed by PZT actuators.