Emerging additive manufacturing methods facilitate the creation of enclosures with tailor-made shielding and scattering performance by using multiple conductive and dielectric layers. For a first analysis an elongated housing, with a cross-section small compared to the wavelength of the impinging electromagnetic field is replaced by an infinitely long multilayered cylinder. In a previous paper, we concluded that existing solutions of the Maxwell equations for this configuration are not accurate in calculating scattering. This also negatively impacts results for multilayer shielding. This article proposes a fast, time-harmonic formulation based on a combination of Bessel and Hankel functions as solution to the Helmholtz equation. Both electric and magnetic fields are considered and solutions are obtained independently for transversal and longitudinal source fields. These can be superpositioned to describe arbitrary source fields. The system of equations defined by the boundary conditions of the multilayer problem is solved via Gaussian elimination which can easily be automated with standard MATLAB or Octave functions. Results are compared to known approaches and applied to a dual-layer use case. The latter shows that shielding and scattering performance improves significantly with multiple layers compared to a single layer with equivalent thickness both for transversal and longitudinal fields.

中文翻译：

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多圆柱壳的低频电磁屏蔽与散射


新兴的增材制造方法通过使用多个导电层和介电层，有助于创建具有定制屏蔽和散射性能的外壳。对于第一个分析，横截面小于撞击电磁场的波长的细长外壳被无限长的多层圆柱体取代。在之前的论文中，我们得出的结论是，该配置的麦克斯韦方程组的现有解在计算散射时并不准确。这也会对多层屏蔽的结果产生负面影响。本文提出了一种基于贝塞尔函数和汉克尔函数组合的快速时谐公式作为亥姆霍兹方程的解。考虑电场和磁场，并独立获得横向和纵向源场的解。这些可以叠加来描述任意源字段。由多层问题的边界条件定义的方程组通过高斯消元法求解，可以使用标准 MATLAB 或 Octave 函数轻松实现自动化。将结果与已知方法进行比较并应用于双层用例。后者表明，与具有同等厚度的单层相比，多层的屏蔽和散射性能在横向和纵向场上显着提高。