Fang H., Yang B., Ding H., Hah J., Huang J.

Deployable telecommunication reflectarray antennas are being developed at Jet Propulsion Laboratory for future space missions. A reflectarray antenna in consideration consists of thin-film membranes that are pre-tensioned by a deployable frame. Advantages of using thin-film membranes in such an antenna design include ultra-light weight, small packaging volume, and large deployed aperture for operation. A thin membrane, because of its little bending resistance, is easy to get wrinkled. This renders the stress distribution and dynamic behaviors of the membrane sensitive to loading and boundary conditions, which in turn imposes challenging problems in modeling and analysis. This paper presents a free vibration analysis of an eight-meter diameter membrane reflectarray antenna, which is composed of a thin membrane and a deployable frame. The proposed analysis has two main steps. In the first step, a two-variable-parameter (2-VP) membrane model is developed to determine the in-plane stress distribution of the membrane due to pre-tensioning, which eventually yields the out-of-plane stiffness or differential stiffness of the membrane. The 2-VP model is capable of predicting taut, wrinkled and slack states of the membrane in a consistent manner, and avoids numerical instability that is commonly encountered in stress iteration with finite element method. In the second step, the differential stiffness obtained is incorporated in a dynamic equation governing the transverse vibration of the membrane-frame assembly. This dynamic equation is then solved by a semi-analytical method, called the Distributed Transfer Function Method (DTFM), which produces the natural frequencies and mode shapes of the antenna. The combination of the 2-VP model and the DTFM provides an accurate prediction of the in-plane stress distribution and modes of vibration for the antenna. The results so obtained will be verified with finite element analysis, and be correlated with experiments.