On a low dimensional model for magnetostriction

In recent years low dimensional models for thin magnetostrictive actuators that incorporated magneto-elastic coupling, inertial and damping effects, ferromagnetic hysteresis and classical eddy current losses have been developed. Some of the classical Preisach operators, which models the hysteretic constitutive relation between the Magnetic Field and Magnetization in the axial direction, have been proved very successful in capturing dynamic hysteresis effects in the range of 0-50 Hz frequencies. However it is well known that for soft ferromagnetic materials there exist excess eddy current losses in addition to the classical one. In this work we propose a model for a magnetostrictive rod actuator at higher frequencies which includes excess losses via a nonlinear resistive element in the actuator circuit. We then show existence and uniqueness of solutions for the proposed model for inputs in the space L2[0,T] Linf[0,T].