Mathematical Modeling and Numerical Simulation of a Magnetostrictive Euler‐Bernoulli Beam

Abstract

Magnetostrictive (MS) materials change their mechanical behavior in response to the application of an external magnetic field and are widely used as sensors and actuators in different areas. This paper is aimed at the description of the magneto‐mechanical coupling using a model of an isotropic Euler‐Bernoulli‐beam. The simple structure of the model enables the full understanding of the effect of coupling. The main focus lies on the mathematical formulation of a coupled magneto‐elastic problem by means of a PDE with appropriate boundary conditions. The numerical modeling is performed by using the Finite Element Method. Considering linear material laws, stationary and time‐dependent cases have been analyzed. To confirm the theoretical results, corresponding simulations carried out with Matlab are presented. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)