中文摘要：

针对大多数脉冲涡流检测解析模型假设试件壁厚均匀减薄,其解析解中仅包含z方向（试件厚度）信息,不能求解探头覆盖区等依赖r方向（平行试件表面）信息的问题,本文提出平底孔试件脉冲涡流检测解析模型.该模型在z和r方向均存在介质分界面,边界条件复杂,求解困难.为此,本文首先假设平底孔所在层导体与空气区域的横向波数和纵向波数均相同,且横向波数为仅与r方向结构有关的实数,纵向波数为与该层横向波数和导体区域材料有关的复数,在此假设基础上应用电磁波反射和折射理论,构造各层波动方程;然后通过引入r方向结构系数W_n,将Cheng的矩阵法扩展,用扩展的矩阵法求解波动方程,得到模型的解析表达式.将该模型应用到16MnR平底孔试件检测实例中,并对其进行实验验证.模型计算结果与实验结果基本符合,证明了模型的正确性.平底孔试件脉冲涡流检测解析模型有助于加深对脉冲涡流检测结果的理解,同时能够为r方向逆问题求解提供理论依据.

英文摘要：

Ferromagnetic structures such as pipes or vessels are widely used in petroleum, chemical and power generation industries. Periodical nondestructive testing（NDT） is vital for continued safe operation. As a NDT technology, pulsed eddy current testing（PECT） technology which is excited by a square-wave pulse rather than a sinusoidal waveform has been widely used for its advantages of non-contact and acquisition of information at various depths in one excitation process. In PECT, the analytical modeling is important because it gives a better understanding of the signal and benefits the inverse process of PECT in extracting information of structures. The foundation of theoretical model of PECT is the Dodd-Deeds model presented by Dodd and Deeds in 1968, Theodoulidis and Kriezis represented the integral solution of Dodd-Deeds model in the form of series by using the truncated region eigenfunction expansion（TREE） method. Using the Dodd-Deeds model and the TREE method, other analytical modelings have been solved. However, most modelings assume that the wall thinning of the specimen is uniform, and the analytical solution only contains the variables in the z direction（the direction perpendicular to the surface of the specimen）, such as the thickness of the specimen. With the rapid development of PECT, problems such as the footprint of the probe, the quantitative analysis of local wall thinning also need to be solved. These problems are related to the variable in the r direction（the direction parallel to the surface of the specimen）, so the analytical modelings mentioned above are not available any more. To solve these problems, the analytical modeling of the plate with a flat-bottom hole is proposed. Considering the fact that the boundary condition in the analytical modeling of the plate with a flat-bottom hole is complicated, the assumption that the transverse wave number and the longitudinal wave number in the layer where the flat-bottom hole located are the same is made in this paper, and the transve