Precision Microscopic Actuations of Parabolic Cylindrical Shell Reflectors

An open parabolic cylindrical shell panel plays a key role in radial signal collection, reflection, and/or transmission applied to radar antennas, space reflectors, solar collectors, etc. Active vibration control can suppress unexpected fluctuation and maintain its precision surface and operations. This study aims to investigate the distributed active actuation behavior of adaptive open parabolic cylindrical shell panels using piezoelectric actuator patches. Dynamic equations of parabolic cylindrical shells laminated with piezoelectric actuator patches are presented first. Then, the actuator induced modal control force is defined based on a newly derived mode shape function. As the actuator area varies due to the curvature change, the normalized actuation effectiveness (i.e., modal control force per unit actuator area) is further evaluated. When the actuator area shrinks to infinitesimal, the expression of microscopic local modal control force is obtained to predict the spatial microscopic actuation behavior on parabolic cylindrical shells. The total control force and its three components exhibit distinct characteristics with respect to shell geometries, modes, and actuator properties. Analyzes suggest that the control force contributed by the membrane force component dominates the total actuation effect. The bending-contributed component increases with the corresponding mode number, while the membrane-contributed component decreases. Actuation effectiveness of two shell geometries, from shallow to deep, and actuator sizes are evaluated. Analysis of optimal actuator locations reveals that actuators placed at the maximal shell curvature are more effective and maximize the control effects.