【作者】 胡靖；

【导师】 高普云；

【作者基本信息】 国防科学技术大学 ， 力学， 2007， 硕士

【摘要】 天线结构由反射面和支撑反射面的背架结构组成,其中反射面是天线发射和接收电磁信号的主要构件,其表面形状的精度直接影响着天线电磁性能的发挥。本文应用弹性力学中的薄壳理论研究抛物面天线反射面在外载作用下的变形性质,并针对工程实际中几种常见反射面的边框约束,对不同边框条件下反射面的位移场和应力场进行了计算和分析,总结了常见边框约束对反射面变形的影响特点。与以往天线结构力学分析采取数值计算方法不同的是,本文从解析法的思路出发研究天线反射面的力学性质。分析过程中,将抛物面天线反射面看作抛物面薄壳结构,而将背架结构对反射面的支撑和约束作用简化为作用于反射面顶点处的中心体支撑和壳边处的边框约束。在对薄壳的变形方程进行了由偏微分方程转化为常微分方程、消元、积分等一系列化简后,整理为以位移法求解反射面变形的基本方程,同时提出了中心体支撑以及边框约束的边界条件,从而确立了应用解析法研究反射面变形的定解问题。计算过程中,提出了一种幂级数方法和一种按照方程中的小参数展开进行求解的方法用以解决反射面变形方程的求解问题,分别对小口径和大口径抛物面天线反射面进行了具体算例的计算,得到了反射面位移场和应力场的解析表达式,在此基础上对反射面的变形性质进行了分析。考虑到边框约束对反射面变形的影响,对不同边框条件下反射面的变形进行了求解和比较分析,着重总结了刚性边框和弹性边框对位移场的约束效果,及其与反射面几何参数之间的影响规律。更多还原

【Abstract】 Antenna structure is composed of reflector and antenna frame which is used to support the reflector. Reflector is the primary component of antenna structure to send and receive electromagnetism signal. So the surface precision of reflector direct influences the electromagnetic performance of antenna. In this paper, the deformation property of reflector under loading effect is researched by elasticity theory of thin shell. The displacement and stress fields of reflectors constrained by several different types of edge in engineering are analyzed and compared, and the law of edge constraint effect on reflector’s deformation property is summarized. Different from previous mechanical analysis of antenna structure, the displacement and stress fields of reflectors are obtained by analytic method in this paper.At analyzing antenna structure’s mechanical property, the reflector is seen as a thin shell model, and its constraints are simplified as a top point support and an edge constraint. After the simplification including the steps of changing partial differential equations into constant differential equations, element elimination and integral, the shell deformation equation is turned into the displacement method basic equation. And the boundary condition of top point support and edge constraint is proposed. Thus the definite problem of reflector deformation equation is established.In calculation process, a power series method and a method based on expansion reflector deformation equation according a small parameter in the equation are used to resolve small-diameter and large-diameter paraboloid antenna reflectors deformation problem respectively. On the based of the result of displacement and stress fields, the deformation characteristic of reflector is analyzed detailedly.For embodying the influence of edge constraint to reflector’s deformation property, the deformation characteristics of reflectors constrained by free edge, rigid edge and elastic edge are all analyzed and compared in this paper, which rigid edge and elastic edge effect on reflector’s displacement fields, and the relation between the effect and the geometric parameters of reflector are summarized emphatically.更多还原