TRANSFER-FUNCTION ANALYSIS OF A FLEXIBLE TOROIDAL STRUCTURE

This paper is concerned with the modeling of a flexible toroidal structure for attitude and structural control studies. A two-dimensional elastic system, consisting of a flexible toroid and a pretensioned membrane, is analyzed in terms of the transfer function from a control torque input to the collocated sensor output. The critical tension for out-of-plane buckling is also determined. The models considered in the paper are simple enough to treat analytically, yet complicated enough to demonstrate the dynamical characteristics of future space structures with a toroidal configuration. It is shown that for such structures, the coupling between two elastic systems results in a transfer function expressed as a combination of an infinite product expansion and an infinite partial fraction expansion. Such a representation should be useful in future studies in reduced-order modeling of flexible toroidal structures. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.