Elaborate Modeling Approach for Ultra-Long Space Deployable Masts

This paper presents an elaborate transfer matrix method (TMM)-based modeling approach for ultra-long space cable-strut deployable articulated masts, focusing on high-accuracy prediction of their vibration characteristics. The proposed method accounts for stiffness variations of compression struts under prestress, the axial stiffness of tension cables, the inertia of corner joints, and lumped mass of locking mechanism—factors often neglected in conventional TMM formulations. Transfer matrices are established for each element, and the periodicity of the structure is used to assemble the global system transfer matrix. The characteristic equation is formulated by incorporating the boundary conditions, and the natural frequencies and mode shapes are subsequently determined. To verify the advantage of the modeling method, the natural frequencies and mode shapes of the deployable mast are obtained with numerical simulations by the TMM, finite element analysis (FEA), and ground vibration tests (GVTs) respectively. The first four natural frequencies predicted by the TMM agree well with the ground vibration test results, with all relative deviations within 2%, and the first-mode Modal Assurance Criterion (MAC) value exceeds 0.99 through the MAC analysis, which shows that the TMM-based results show good consistency with the experimental measurements. In addition, the time cost to complete the modal analysis by TMM is five minutes, while forty-three minutes by FEA. These results experimentally support the rationality of the proposed componentlevel modeling strategy and demonstrate its good predictive accuracy and computational efficiency within the measured low-frequency range. Beyond predictive accuracy and efficiency, the proposed TMM framework extends conventional TMM formulations from truss-like deployable structures to cable-strut deployable articulated masts. Cable-induced prestress is introduced into the axial force state of the struts and incorporated into their bending vibration transfer matrices, thereby establishing a prestress-dependent cable-strut coupled state-vector transfer framework. Corner-joint compliance and inertia, as well as locking-mechanism lumped mass, are further retained within the unit-by-unit transfer-matrix assembly procedure, providing a modeling basis for sensitivity studies, onorbit frequency tuning, and structural vibration control of ultra-long deployable masts.