Asymptotic behavior of a low-dimensional model for magnetostriction for periodic input

Models for magnetostrictive actuators need to include rate-independent hysteresis phenomena, magneto-elastic coupling, and eddy current losses that vary nonlinearly with the frequency of the input. In this paper, we study a low dimensional model for magnetostrictive rod actuators that describes the physical phenomena which are most prominent in the frequency range 0-800Hz. We show that the solution of the system is asymptotically periodic for bounded, continuous and periodic voltage inputs and with general conditions on a Preisach operator modeling rate-independent hysteresis. The results of this paper are crucial for developing a parameter identification methodology for the model that is addressed in [9].