Geometric nonlinearity in dynamic modeling of gyroelastic structure

Large-scale flexible space structures (e.g., space solar power stations and ultra-large aperture antennas) represent critical future space infrastructure, where control moment gyroscopes (CMGs) serve as specialized actuators for attitude control, vibration suppression, and shape regulation. The coupled CMG-flexible structure systems, termed gyroelastic structures, currently lack comprehensive modeling of significant deformations. This study addresses this gap by developing a geometrically nonlinear dynamic model through synergistic integration of the floating frame of reference formulation (FFRF) and Kane's method, incorporating higher-order strain-deformation relationships in flexible plates. The model's validity is rigorously demonstrated through comparative analysis with commercial finite element software under large deformation conditions. Systematic simulations reveal CMG-induced effects on three key structural characteristics: (1) deflection patterns, (2) vibration attenuation properties, and (3) fundamental frequency shifts. Sobol global sensitivity analysis quantifies that angular velocity dominates geometric nonlinearity, explaining 99.8% (deformation) and 99.9% (frequency) of total variance. A novel dual-criterion framework employing second-order polynomial functions with angular velocity as the target variable is established based on these findings. Comparative evaluation demonstrates the deformation-based criterion's superior sensitivity, recommending its priority in nonlinearity assessment for gyroelastic structures.