3D-spatial vibration global modes of a flexible arm-supported ring antenna and its dynamic analysis

Due to the complexity and high degrees of freedom of the structure, dynamical modelling of ring truss antenna (RTA) is a challenging job. The three-dimensional (3D) vibration of each component of RTA is spatial and coupled to each other, and thus assumed modes cannot depict its vibration accurately and dynamical models obtained by FEM generally have high dimensions, by which it is very hard to either conduct dynamical analysis or design its vibration controller. To overcome these obstacles, a dynamical modeling method named the 3D-Global Mode Method is proposed to obtain the low-dimensional analytical dynamical model of a flexible arm-supported ring antenna (ASRA) that vibrates spatially. The natural characteristics of a RTA is investigated by simplifying it as a flexible arm-supported closed multi-beam structure. Natural frequencies and the corresponding analytical 3D global modes are obtained by solving the eigen-equation formed by the spatial matching conditions and the boundary conditions. Orthogonality relations of the 3D analytical global modes are established and then used to transform the partial differential equations of spatial motion into a set of reduced-order ordinary differential equations. Taking the simulation results obtained from the FEM as a reference, the validity of the proposed method is verified by comparing the natural frequencies and 3D global mode shapes with those obtained from FEM. The mode localization phenomenon of ASRA is found and the influence of the parameters of RTA on mode characteristics is investigated. Through the proposed model, dynamical responses of the ASRA excited by orbital maneuvering acceleration are simulated numerically. This study paves an effective way to obtain the analytical global modes of spatially vibrating ASRAs and other similar spatial flexible combined structures, and to establish the low-degree-of-freedom dynamical model.