Optimal actuator locations and precision micro-control actions on free paraboloidal membrane shells

Flexible paraboloidal shells, as key components, are increasingly utilized in antennas, reflectors, optical systems, aerospace structures, etc. To explore precise shape and vibration control of the paraboloidal membrane shells, this study focuses on analysis of microscopic control actions of segmented actuator patches laminated on the surface of a free paraboloidal membrane shell. Governing equations of the membrane shell system and modal control forces of distributed actuator patches are presented first, and followed by the analysis of dominating micro-control actions based on various natural modes, actuator locations and geometrical parameters. Finally, according to the parametric analysis, simulation data reveal main factors significantly influencing active control behavior on smart free-floating paraboloidal membrane shell systems, thus providing design guidelines to achieve optimal control of paraboloidal shell systems.