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首页> 外文期刊>Science, Measurement & Technology, IET >Field distribution around a long crack in a conductive half space excited by an arbitrary-frequency alternating-current-carrying coil of arbitrary shape
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Field distribution around a long crack in a conductive half space excited by an arbitrary-frequency alternating-current-carrying coil of arbitrary shape

机译：任意形状的任意频率载流线圈激励的导电半空间中长裂纹周围的场分布

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摘要

The authors propose a semi-analytical solution for evaluation of field distributions around a long crack in a conductive half space because of a three-dimensional (3D) current-carrying inducing coil at arbitrary frequency. The governing Helmholtz equation is solved in three dimensions by separation of variables. The solution is obtained by developing a two-dimensional (2D) Fourier series model and using exponential functions in the third dimension. To expand all possible field components in the conductor, the authors assume it as a lossy material with very large loss-tangent. In this regard, transverse electric and transverse magnetic modes are introduced to account for the contributions made by induced eddy current in the conductor as well as the displacement current passing through the crack opening. The authors use the mode matching technique and solve the resultant linear system of AX = B for the unknown coefficients. The accuracy of the proposed modelling technique is demonstrated by comparing their results with those available in the literature for the special case of a long rectangular 2D coil and with those obtained by experiment for a 3D inducing coil.
机译：作者提出了一种半解析解决方案，用于评估导电半空间中长裂纹周围的磁场分布，这是因为在任意频率下都带有三维（3D）载流感应线圈。掌控的亥姆霍兹方程通过变量分离在三个维度上求解。通过开发二维（2D）傅里叶级数模型并在第三维中使用指数函数来获得解决方案。为了扩展导体中所有可能的场分量，作者认为它是损耗正切非常大的有损耗材料。在这方面，引入了横向电磁模式和横向电磁模式，以解决导体中感应涡流以及穿过裂纹开口的位移电流所产生的影响。作者使用模式匹配技术，针对未知系数求解所得的线性系统AX =B。通过将其结果与文献中针对长矩形2D线圈的特殊情况以及通过3D感应线圈的实验获得的结果进行比较，可以证明所提出建模技术的准确性。

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