Dynamic modeling and analytical global mode shapes of a folded beam-ring structure for a truss antenna reflector with two arms

Abstract

The large-aperture hoop truss antenna is considered as an ideal deployable antenna, whose dynamic performance largely limits the practical application. Extracting a reasonable and solvable model is the essential prerequisite and foundation for analyzing the dynamic characteristics of an antenna. In this paper, a folded beam-ring structure composed of two beams and one ring is proposed to model a hoop truss antenna. The governing equations of motion and boundary conditions for the folded beam-ring structure are derived by using the Hamilton principle. After applying the method of separation of variables, the frequencies and global mode shapes are theoretically calculated by solving the linear parts of governing equations and boundary conditions. The reliability of dynamic model proposed for the folded beam-ring structure is proven by comparison of frequencies and mode shapes. The influences of geometrical and physical parameters on natural frequencies of folded beam-ring structures are analyzed. The parametric rule of frequencies is important for analyzing the resonant relations of the structure. The analytical global mode shapes are beneficial for constructing precise nonlinear dynamic model for the antenna system. And the modeling method presented here can be used as a reference to dynamic analyses of other complex structures.