空间多柔体系统缩比等效动力学建模方法研究

With the increase in size and flexibility of space structures, it is necessary to design a scale-down prototype to carry out ground experiments, where the feasibility of the designed structure and its dynamic characteristics can be verified. To predict the dynamic behavior of the full-scale structure more accurately through the scale-down model, this paper presents a method to design dynamically scaled equivalent models for flexible multibody systems based on similarity theory and sensitivity analysis of flexible multibody systems. Firstly, the similarity relationships are simplified based on dimensional analysis and the PI theorem, making the measurement of fundamental dimensions the only concern in the design of similar systems. Then, a standard procedure is provided to design dynamically equivalent scale-down models for flexible multibody systems more efficiently than the traditional method. Secondly, the Lie groups and Lie algebras and the geometrically exact formulation are utilized to establish the dynamic model of flexible beams. Thirdly, to overcome the challenges of manufacturing scale-down models, sensitivity analysis on the derived dynamic model is carried out in order to adjust the design of the scale-down models. The feasibility of building scale-down models is improved by releasing the strong restriction on the design of scale-down models due to the similarity relationships. Meanwhile, the preservation of the similarity relationship of the critical parameters makes the designed scale-down models able to resemble the dynamic characteristics of the original model with high accuracy. Finally, numerical simulations are carried out to verify the feasibility and accuracy of the designed dynamically scaled equivalent models for flexible multibody systems.