Well-posedness issues concerning a magnetostrictive actuator model

Abstract
Modeling issues concerning magnetostrictive actuators for structural systems are considered. Such actuators utilize the realignment of magnetic moments in response to applied magnetic fields to generate strains in the material. Strains and forces generated in this manner are significantly larger than those produced by many other smart materials but also exhibit significant nonlinearities and hysteresis. An energy-based model is employed here to characterize the inherent hysteresis and nonlinearities in a manner amenable to structural applications. Well-posedness issues are considered in the context of Euler-Bernoulli and Timoshenko beam models. This provides a framework which can be directly extended to more complex structures and is adequate for ensuing control applications.