Vibration Frequency Analysis of Beam–Ring Structure for Circular Deployable Truss Antenna

The circular truss antenna of the large aperture is considered to be a flexible structure which may cause vibration in space and may affect its performance. The frequency analysis of the circular truss antenna is an important problem for understanding its vibration mechanism. In this paper, we investigate the frequency characteristics of a beam–ring structure which is proposed for the first time to model the circular truss antenna in the case of the antenna expended and locked. Based on describing the displacements of the beam–ring system in detail, the kinetic energy and potential energy are calculated. The partial differential governing equations of motion and boundary conditions for the beam–ring structure are derived by Hamilton principle. From the linear parts of the governing equations of motion and the corresponding boundary conditions, the linear frequencies of the beam–ring structure are theoretically obtained. The effects of the physical parameters on the frequency characteristics of the beam–ring structure are studied, which are further verified by the numerical results. The finding phenomena of this paper are helpful for designing and controlling the beam–ring structure such as the circular truss antenna.