Actuator Placement and Control Efficiency of Paraboloidal Shell Structures

Paraboloidal shells of revolution are commonly used in communication systems, precision opto-mechanical systems and aerospace structures. This study is to investigate the precision distributed control effectiveness of paraboloidal shells laminated with segmented actuator patches. Mathematical models of the paraboloidal shells laminated with distributed actuator layers subjected to mechanical, temperature, and control forces are presented first, followed by formulations of distributed control forces with their contributing meridional/circumferential membrane and bending control components using an assumed mode shape function. Studies of actuator placements, control forces, contributing components, and normalized control authorities of paraboloidal shells are carried out. These forces and membrane/bending components basically exhibit distinct modal characteristics influenced by shell geometries and other design parameters. Analyses suggest that the membrane contributed components dominate the overall control effect. Locations with larger normalized forces indicate the areas with high control efficiencies, i.e., larger induced control force per unit actuator area. With limited actuators, placing actuators at those locations would lead to the maximal control effects.