空间聚光太阳电池阵柔性透镜薄膜结构的力学分析

运用线性Kirchhoff平板理论建立柔性菲涅耳透镜薄膜结构的静力学模型，给出柔性透镜的静力学求解方法，得到柔性透镜变形的解析解。分析透镜纵向应变、背衬厚度、透镜纵向长度对柔性透镜特性的影响，获得上述参数对透镜变形和几何光学性能的影响规律。基于圆柱薄壳振动理论，建立柔性透镜动力学模型，然后根据Reissner理论确定的有限长开口圆柱壳振动方程的一般解，给出柔性透镜动力学模型的求解方法，计算柔性透镜的振型和固有频率，分析透镜纵向应变、背衬厚度和轴向波数对柔性透镜固有频率的影响。结果表明：在设计柔性透镜结构时，适当增加透镜的纵向应变并减小透镜的背衬厚度有利于减小透镜的变形。柔性透镜的固有频率与纵向应变和透镜背衬厚度密切相关，需选择合适的纵向应变与背衬厚度。柔性透镜的变形随着透镜纵向长度的增加而增大，但纵向长度太小会增加相同太阳电池阵面积上聚光组件的安装数量，因此纵向长度的选择需综合权衡。

Mechanical Analysis of Flexible Thin Lens Structure of Spacial Concentrator Solar Array

The static model of flexible arched Fresnel lens is established by the linear Kirchhoff plate theory. Given the solving method of static equations, the analytical solution of lens deformation is obtained. The effect of longitudinal strain ratio, back-thickness and longitudinal length of flexible lens  on lens distortion is analyzed, and the effect of these parameters on geometric distortion and optical properties of the lens is obtained. The dynamics model of flexible lens is established according to the cylindrical-shell vibration theory. The solving method of dynamics model is obtained according to the general solution of finite-length and open cylindrical-shell vibration equations given by Reissner theory.  Flexible lens' modal formation and natural frequency are calculated, and the curves of effect of longitudinal strain ratio, back-thickness and axial wave number on natural frequency are also analyzed. The results show that both increasing the longitudinal strain ratio and reducing the lens back-thickness appropriately can decrease the lens deformation. The natural frequency of the flexible lens is closely related to the longitudinal strain ratio and the back-thickness, so the suitable longitudinal strain ratio and back-thickness should be selected. It is proven that deformation of the flexible lens augments with the increase of the longitudinal length of the lens, but short longitudinal length will increase the number of concentrator components installed on the solar array of same area, so the choice of longitudinal length requires tradeoff.