Three numerical techniques to evaluate the low frequency magnetic shielding of two-dimensional metallic structure

The reduction of magnetic fields is a topic of concern to the electric utility industry. One technique to reduce the magnetic fields is to use metal plates and enclosures for shielding. Unfortunately, the calculation of low-frequency magnetic shielding of metal shields has usually required substantial expertise in the fields of integral equations, numerical analysis, and/or electromagnetics or has produced approximations that have known deficiencies.; This dissertation introduces three new methods to analyze the low-frequency magnetic shielding effectiveness of two-dimensional shields of arbitrary shape. All three methods discretize the structure into an array of metal cylinders. The first method uses Faraday's Law of Induction to calculate the self- and mutual-impedances of the cylinders, from which the eddy currents induced in the cylinders and the induced magnetic fields are calculated. In the second method, Ampere's Current Law was used to develop an alternative approach to calculating the eddy currents induced in a metal shield. This method used magnetic scattering theory to advance the development. After the eddy currents were found, the second method used either the Biot-Savart Law or magnetic scattering theory to calculate the magnetic shielding afforded by the array of cylinders. The final method used magnetic scattering theory, including multiple scattering effects, to calculate the magnetic shielding of a two-dimensional shield. All three methods were successfully validated both analytically and experimentally.; The validations showed that the methods produce results that are within 5% of experimental values and within 1% of the analytical values. As a result, three powerful new design tools for approximate analyses have been developed. These methods permit accurate calculations of magnetic shielding (and induced eddy currents) yet can be performed by persons of limited mathematical training. In addition, this dissertation shows an improved method of shield discretization (over the current use of finer discretizations) and that non-ferrous shields can provide substantial amounts of magnetic shielding at low frequency. This is in contradiction with many researchers' beliefs that non-ferrous metal plates do not provide magnetic shielding at power frequencies.