Time-harmonic finite element analysis of guided waves generated by magnetostrictive patch transducers

Transducers made of thin magnetostrictive patches and magnetic circuits have been recently developed as an effective means for non-destructive guided wave inspection of elastic structures. However, important characteristics of transducers, such as their wave radiation patterns, have been tested only by experiments or a first-order theoretical analysis. There have been some finite element analyses related to magnetostrictive actuators, but no numerical analysis has been performed to predict the wave radiation patterns of various magnetostrictive patch transducers. In this paper, we formulate a finite element procedure and implement it to predict the wave radiation pattern of a magnetostrictive patch transducer installed on a plate. In particular, a linearized model determining coupling matrix appearing in the magnetostrictive constitutive equation of a magnetostrictive patch in a transducer is developed. The developed model is then used to deal with the arbitrarily polarized static magnetic field induced in the transducers. For numerical efficiency, time-harmonic analysis is carried out and a technique to extract data corresponding to target guided wave modes is used. The validity of the developed finite element analysis is checked by comparing the simulated wave radiation patterns from the present analysis with experimental results. The reasons why certain radiation patterns are obtained for selected magnetic circuits are explained by physical reasoning and simulation results.