We quantify the dependence of strain on dynamic magnetic field in magnetostrictive transducers. Dynamic eddy current losses are modeled as a one-dimensional (1D) magnetic diffusion problem in cylindrical coordinates. The constitutive magnetostrictive response to an average diffused magnetic field is quantified with the Jiles-Atherton model. The transducer is represented as a lumped-parameter, single-degree-of-freedom resonator with force input dictated by the magnetostriction. This equivalent force is expressed as a summation of Fourier series terms. The total dynamic strain output is obtained by superposition of strain solutions due to each harmonic of the force input.
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