具有一维带限Weierstrass分形特征实际路面电磁散射FDTD研究

Study on Electromagnetic Scattering from Actual Pavement with 1D Band Limited Weierstrass Fractal Characteristics Using FDTD

一般的实际路面系统是由沥青混凝土面层、水泥碎石联结层、水泥稳定碎石基层和路基层等构成的多层介质,可以看作是具有一维带限Weierstrass分形特征的水泥混凝土路面系统。运用时域有限差分方法(FDTD)研究了这种实际的水泥混凝土路面系统电磁散射,具体计算了3层路面系统电磁散射的双站散射系数,得出了散射系数随散射角和入射波频率变化的曲线。分析了散射系数随路面分维数、入射波频率、入射角、路面材料介电常数、面层厚度、基层厚度等参数变化的规律,讨论了面层存在圆柱形空洞时,空洞内填充物变化对散射系数的影响,得到了具有一维带限Weierstrass分形特征的实际路面系统电磁散射的特性。数值计算结果表明:路面分维数、入射波频率、入射角、路面材料介电常数、面层厚度、基层厚度、面层存在的空洞对散射系数的影响是非常复杂的。

The general road system is composed of the actual surface layer of asphalt concrete,cement,gravel link layer,cement stabilized crushed stone base and road grass-roots form of multi-media,which can be regarded as a cement concrete pavement system with characteristics of one-dimensional band-limited Weierstrass fractal.The electromagnetic scattering from this practical system of cement concrete pavement is studied by Finite-Difference Time-Domain method（FDTD）,the bistatic scattering coefficient from three-layer pavement system is calculated concretely,the curves of scattering coefficient with varying angle and the frequency of incident wave are obtained.The varying regularity of scattering coefficient with the dimension of fractal of pavement,the frequency of incident wave,angle of incidence,the dielectric constant of pavement materials,the thickness of surface and base layer is analyzed,the influence of the packing of the cavity with a cylindrical shape inside surface layer on the scattering coefficient is discussed,the characteristics of electromagnetic scattering from the actual pavement system with band limited Weierstrass fractal is obtained.The numerical results show that the influence of fractal dimension of pavement,the incident wave frequency,angle of incidence,the dielectric constant of pavement materials,the thickness of surface layer,the thickness of the grass-root,the existence of empty surface on the scattering coefficient is very complex.