为了增加大口径望远镜次镜支撑结构的抗扭转刚度, 降低次镜支撑结构对主镜的遮拦, 提出了采用预紧力八翼梁结构来取代原有的四翼梁结构。根据Euler-Bernoulli梁理论将次镜支撑结构简化为一个由质量点和简支梁组成的简化模型, 并进一步将该模型简化为两个更为简单的动力学模型的组合。通过选取恰当的振型函数, 使用Rayleigh和Dunkerley方法推导了简化模型的第一阶模态频率数值解, 得到的计算结果与有限元仿真结果吻合得很好。针对预紧力的作用, 理论推导了预紧力对这种结构第一阶模态值的影响, 并使用有限元法对这种结构进行了模拟, 两者得到的结果趋势相同, 大小一致, 从而证明该简化方法可以用于类似结构的动力学特性计算。仿真结果显示, 当预紧力施加到20 kN时, 结构的第一阶模态值由11.6 Hz上升到23 Hz, 大大提高了结构的抗扭转刚度, 并有效减轻了次镜支撑结构的重量和遮拦比。该结论对于大口径望远镜次镜支撑的设计具有参考价值。

To increase the anti-torsion stiffness of secondary mirror support structure of a telescope and to reduces the obscuration from the support structure, an imposed preload of 8-vane spider was designed to replace the original 4-vane spider. According to the Euler-Bernoulli beam theory, the mirror support structure was simplified as a simple model consisting of a beam and a mass point, and then the simplified model was divided into two more simple kinetic models. By selecting the appropriate mode function, the numerical solution of the first order modal for the simplified model was deduced with Rayleigh and Dunkerley approaches. Obtained calculated results are in good agreement with that from Fnite Element Analysis (FEA). Moreover, in order to solve the impact of the preload on this structure, a coefficient was deduced in theory. Then, the model was simulated by FEM and the result obtained in FEM is the same as that calculatedone one in theory. The analysis results prove that the method is available for the calculation of the similar structural dynamics characteristics. The simulations show that the first order modal of the structure can change from 11.6 Hz to 23 Hz when the preload increases up to 20 kN, which proves that the preload can effectively impact on the anti-torsion stiffness and reduce the secondary mirror support weight and obscuration ratio. The results can give a reference for designing secondary mirror support structures.