吸波材料与微波暗室问题的数学建模

Mathematical Modeling of Absorbing Materials and Microwave Dark Room

为了分析微波暗室的性能,采用几何光学的方法,用虚像延拓来刻画辐射波在暗室诸墙面上的反射过程,从而建立微波暗室模型.问题一考虑单个尖劈几何空缺间反射过程的数学模型,利用平面镜成像原理,采用延拓的方法,将尖劈几何空缺空间延拓到一个圆柱上,将入射波在尖劈空缺间的反射过程等价地看成入射波在一个圆柱内的空间直线传播过程,称为"虚像传播直线".问题二中要分析微波暗室的性能,主要采用的指标是静区从诸墙面得到的反射信号的功率之和与从信号源直接得到的微波功率之比y.采用静区延拓的方法,将微波暗室暗箱化,首先建立一个余弦辐射体的点辐射源到一有界平面的辐射模型,然后通过该模型计算点辐射源到各个静区虚像的辐射功率总和作为静区从诸墙面得到的总功率,建立微波暗室的反射模型.实验证明,当采用平板吸波材料时(垂直反射率为0.5),无法满足导引仿真要求,当采用性能较好的尖劈形吸波体时(垂直反射率为0.05),能够满足仿真要求.

In order to analyze the performance of the microwave dark room, this paper adopts the geometrical optics method, the virtual image extension, to describe the radiation wave reflection process in the dark room. Consider question one, single wedge geometrical vacancy reflection process mathematical model, use plane mirror imaging principle and extension method, the ingle wedge geometrical vacancy can be extended as cylinder. The reflection process between wedge geometrical vacanciies of the incident wave can be equivalently regarded as a spatial line communication process in a cylinder of the incident wave. In this paper, we call it ＂virtual image communication line＂. Consider question two, the microwave dark room performance analysis, the key performance indicator is the ratio that reflect signal power sum of dead zone get from metopes and microwave power of dead zone get from signal source. This paper adopts dead zone extension method and construes the microwave dark room as a black box. Firstly, this paper establishes a cosine radiator spot radiation source to a bounded plane radiation model. Secondly, with this model, calculate the sum of all spot radiation sources to each dead zone virtual ：image radiation power, and establish the microwave dark room reflection model. The experiment indicate that flat absorbing materials（vertical reflectivity is 0.5） can not satisfy the seeker simulation requirement, meanwhile, the wedge absorbing material（vertical reflectivity is 0.05） can satisfy the seeker simulation requirement.