第一作者刘充男，硕士生，1989年6月生

通信作者保宏男，博士，教授，博士生导师，1971年生

边界几何参数对空间平面张拉膜结构固有频率影响研究

刘充，李玉宇，保宏, 杜敬利

(西安电子科技大学电子装备结构设计教育部重点实验室，西安710071)

摘要：针对空间张拉薄膜阵面结构，用归一化动态响应函数法确定薄膜边界几何参数对固有频率影响关系。用Bessel函数作为薄膜横向振动偏微分方程的解，建立任意边界形状凸单连通薄膜及复杂边界薄膜固有频率求解模型；针对平面张拉薄膜分别求解圆形、L-形、分段圆弧边界固有频率；分析研究一定应力条件下边界几何参数对薄膜固有频率影响的内在关系。结果表明，边界形状导致薄膜面积减小、固有频率增加，反之亦然。

关键词：空间张拉薄膜结构；归一化动态响应函数；固有频率；有限元模型

基金项目：国家自然科学基金(51305321；51105290；51035006； 51175398)；上海航天科技创新基金项目(SAST201413)

收稿日期：2014-07-16修改稿收到日期：2014-10-17

中图分类号:TN957.3

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.20.033

Abstract:For a kind of space pre-tensioned membrane structures, a dimensionless dynamic influential function method has been proposed, which can efficiently figure out the frequencies of arbitrarily shaped, homogeneous membranes with fixed boundaries. A model using the Bessel function as the solution to the partial differential equation for transverse vibration of thin membrane was established which can be used to calculate the natural frequencies of membrane with different radius of curvature and chord length. For planar pre-tensioned membrane, the natural frequencies of membrances with circular, L-shape and subdivided arc boundary conditions were calculated. On the condition of unchanged stresses, the relationships between the natural frequencies and boundary geometrical parameters of membrane were analysed. It is indicated that the boundary which makes the area of membrane larger matches higher frequencies and vice versa.

Natural frequencies of pre-tensioned membrane structure with different boundary geometrical parameters

LIUChong,LIYu-yu,BAOHong,DUJing-li(School of Electromechanical Engineering, Xidian University, Xi’an 710071, China)

Key words:space pre-tensioned membrane structure; dimensionless dynamic influential function; natural frequency; finite element model

大型空间平面张拉膜结构因质量轻、包装折叠效率高、易于展开等特点，广泛用于太空可展开结构，如太阳帆、空间望远镜防护罩、可展开反射阵列天线等。周边索网张拉薄膜结构，见图1、图2。该结构由支撑杆、张拉悬索、平面薄膜组成，其中，张拉悬索包括外悬索、牵连索、内悬索。

针对该类型张拉薄膜结构，Sakamoto[1]理论上证明薄膜外形为圆弧状时膜内应力为最佳张紧状态，能有效避免褶皱产生；并研究该结构在膜、索给定应变条件下内外悬索截面积、索膜总质量随圆弧数目变化的函数关系。……