On a low-dimensional model for magnetostriction

In recent years, a low-dimensional model for thin magnetostrictive actuators that incorporated magneto-elastic coupling, inertial and damping effects, ferromagnetic hysteresis and classical eddy current losses was developed using energy-balance principles by Venkataraman and Krishnaprasad. This model, with the classical Preisach operator representing the hysteretic constitutive relation between the magnetic field and magnetization in the axial direction, proved to be very successful in capturing dynamic hysteresis effects with electrical inputs in the 0-50 Hz range and constant mechanical loading. However, it is well known that for soft ferromagnetic materials there exist excess losses in addition to the classical eddy current losses. In this work, we propose to extend the above mentioned model for a magnetostrictive rod actuator by including excess losses via a nonlinear resistive element in the actuator circuit. We then show existence and uniqueness of solutions for the proposed model for electrical voltage input in the space L2(0,T)∩L∞(0,T) and mechanical force input in the space L2(0,T).