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.
N.N. SARAWATE and M.J. Dapino, “Magnetization dependence on dynamic strain in ferromagnetic shape memory Ni-Mn-Ga,” Applied Physics Letters, Vol. 93, Issue 6, 11 August 2008.