Micro-Control Actions of Segmented Actuator Patches Laminated on Deep Paraboloidal Shells

Abstract

Deep paraboloidal shells of revolution are common components for horns, nozzles, rocket fairings, etc. This study is to investigate the micro-control actions and distributed control effectiveness of precision deep paraboloidal shells laminated with segmented actuator patches. Mathematical models and governing equations of the paraboloidal shells laminated with distributed actuator layers segmented into patches are presented first, followed by formulations of distributed control forces and micro-control actions including meridional/circumferential membrane and bending control components based on an assumed mode shape function and the Taylor series expansion. Distributed control forces, patch sizes, actuator locations, micro-control actions, and normalized control authorities of a deep paraboloidal shell are analyzed in a case study. Analysis indicates that 1) the control forces and membrane/bending components are mode and location dependent, 2) the meridional/circumferential membrane control actions dominate the overall control effect, 3) there are optimal actuator locations resulting in the maximal control effects at the minimal control cost for each natural mode.