Dynamic Similarity Theory Based on Geometric Distortion and Material Compensation for On-Orbit Assembled Space Rod Structures

On-orbit assembly technology is the core method for constructing extremely large space structures, with assembly modules serving as the fundamental units for structural integration. Since ground dynamic verification of full-scale modules is often restricted by laboratory space, scaled models are required for equivalent evaluation. During the scaling of systems containing high-aspect-ratio flexible rods, traditional complete geometric similarity laws lead to severe dynamic distortion in these slender elements as dimensions are reduced. To address this issue, a dynamic equivalence method based on geometric distortion and material compensation specifically for space flexible rods is proposed. This theory permits non-proportional distortion of rod cross-sections by deriving distortion similarity laws and reconstructs dynamic consistency through material substitution. Numerical validation demonstrates that the method effectively eliminates prediction errors induced by size reduction. For free single rods, the prediction errors for the first three bending frequencies are maintained within 1%; for unconstrained two-bar mechanisms connected by spatial spherical joints, the error is maintained within 0.5%. Furthermore, upon introducing sliding rail boundary constraints, the scaled model accurately reproduces the spatial mode shapes of the prototype, with primary frequency errors converging to within 0.3%. This research provides a reliable theoretical basis for the ground experimental evaluation of on-orbit assembly equipment for extremely large space structures.