Equivalent dynamic modeling and analysis for a novel dual-ring truss space antenna

For the space antennas featuring the novel double-ring truss structures, the equivalent dynamic modeling serves as one of the key prerequisites for the design of vibration control strategies. In comparison to the conventional planar truss structures, the double-loop trusses exhibit greater complexity by connecting multiple periodic beam units through rigid joints and cable-driven mechanisms. This study proposed a more concise equivalent anisotropic Timoshenko beam model based on the energy equivalence principle and a static condensation method, under the condition of applying initial stress to enhance structural stiffness. The relationship between geometric parameters and material parameters was established by considering the displacement expressions of the center points of periodic elements. Subsequently, the stiffness matrix and mass matrix of the entire structure were obtained by connecting multiple equivalent elements along the circumference. Verification of the vibration characteristics of the proposed equivalent dynamic model was achieved by comparing the modal tests, full-scale finite element simulations, and numerical solutions. Simulation results indicate that in single basic unit modal tests, the maximum error for low-order structural frequencies is approximately 3.8%. For a dual-ring truss structure with 25 m diameter, the variations in the first eight natural frequencies under different pre-stress conditions are discussed in detail. The relative error of modal frequencies is roughly within 2.5%. Furthermore, the low-order frequencies of structures with 50 m and 100 m diameters are calculated, with the proposed equivalent dynamic model achieving computational times only 1/10 of those required by the finite element model. The model demonstrated good accuracy and broad engineering applicability.