HIGH-ORDER EQUIVALENT PLATE DYNAMIC MODELING AND ANALYSIS OF SPACECRAFT PLATE-LIKE SPACE TRUSSES

A high-order equivalent plate dynamic modeling method based on a third-order displacement field is proposed to address the overprediction of natural frequencies and distortion of higher-order mode shapes in conventional equivalent plate models, which arise from the stiffness difference between chord and web members in spacecraft plate-like space trusses. First, an unconstrained third-order displacement field suitable for periodic spacecraft plate-like space trusses is constructed, and the mapping between discrete nodal displacements and the continuum displacement field is established. Then, based on the principle of energy equivalence, the strain energy and kinetic energy expressions of the truss unit cell are derived. Equivalent stiffness and inertia matrices that simultaneously characterize tension/compression, bending, transverse shear, thickness stretching, and their coupling effects are formulated, and the governing equation of free vibration is established by combining static condensation with Hamilton's principle. The proposed model is validated using 10 × 10 and 6 × 6 tetrahedral unit cell array trusses as numerical examples, and a parameter sensitivity analysis is performed. The results show that the mean absolute relative errors of the first several natural frequencies predicted by the present model for the two cases are 1.21% and 1.98%, respectively, which are significantly lower than those of the first-order shear deformation equivalent model (5.23% and 6.41%). Moreover, the present model can capture higher-order mode shapes more accurately. Under a cantilever boundary condition with point force excitation, the model can predict the structural frequency response function and time-domain response characteristics with good accuracy, and the resonance peak locations and response amplitudes agree well with those obtained from refined finite element models. The sensitivity analysis indicates that the chord length is the dominant geometric parameter influencing the dynamic characteristics of the plate-like space truss. The proposed method improves dynamic prediction accuracy while maintaining low model dimensionality, and can serve as a reference for dynamic analysis, parameter optimization, and on-orbit vibration control modeling of spacecraft plate-like space trusses.