Electromagnetic acoustic transducers (EMATs) operating in transmitting mode are examined. Two different finite element formulations, derived for two different definitions of source current density, are compared in order to show the importance of skin and proximity effects. An EMAT consisting of six source conductors is modeled as an example. Results obtained with an earlier method are compared with new FEM results at two different frequencies. The effect of lift-off and distance between conductors is investigated. Index Terms-EMAT, finite element method, NDE, time domain analysis.

Three finite-element formulations based on different definitions of current density are compared. Formulations I and II are based on incomplete equations for total and source current densities, respectively. Formulation III is based on a complete equation for source current density. To validate the third formulation, a one-dimensional test problem is solved analytically for the magnetic field intensity. The formulations are applied to a nondestructive testing example and a three-phase bus-bar example. Results show that errors due to the use of incomplete equations for current densities increase with frequency and conductor dimensions.

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This paper presents the governing electrodynamic equations of electromagnetic acoustic transducers (EMATs) and extends them to the derivation of the magnetic- and acoustic-field equations in terms of the magnetic vector potential (MVP) and the acoustic wave particle displacement vector (PDV), respectively. It also provides formulations for calculating forces and current densities in the case of two-dimensional (2D) models of EMAT configurations in Cartesian coordinates. Existing methods solve the governing electrodynamic equations for field quantities to analyze EMATs. However, they ignore skin and proximity effects and rely on simple 2D configurations for EMAT coils. Taking into account skin and proximity effects in complex 2D EMAT coil configurations requires the application of the finite element method (FEM). The FEM can be applied to solve the equations stated in terms of the MVP and PDV in the modeling of EMATs. These formulations and expressions facilitate the development and presentation of the FEM for the modeling and analysis of EMATs.

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