Equivalent membrane model for the dynamic analysis of a prestressed paraboloidal cable nets
Fushou Liu, Xiumin Gao, Dongping Jin
Abstract: Cable nets are an important type of mechanical structures for space engineering and have been employed in large deployable antenna and capturing mechanism for space debris. With millions of degrees of freedom in the cable-net structures, it is inevitable to seek a simplified mechanics model for dynamic analysis and vibration control. The paper studies a three-way paraboloidal cable-net structure via the energy equivalence principle in an attempt to obtain a dynamics model that equivalent to an isotropic paraboloidal membrane. The strain and kinetic energies of free vibration of the paraboloidal cable-net structure and its equivalent membrane are respectively calculated first, and then the energy equivalence principle is adopted to give the equivalent parameters of membrane. Afterwards, the analytic expression of the frequency equations and mode shapes of the membrane are obtained based on the equations of motion of the transverse free vibration of the prestressed paraboloidal membrane of revolution. Finally, the natural vibrations of a cable-net structure and its equivalent membrane are illustrated with a large hoop deployable antenna structure. The results show that the natural frequencies and mode shapes are all in good agreement between the two equivalent models.
原文链接: https://www.researchgate.net/publication/284921913_Equivalent_membrane_model_for_the_dynamic_analysis_of_a_prestressed_paraboloidal_cable_nets
