Nonlinear and hysteretic magnetomechanical model for magnetostrictive transducers
The growing interest on magnetostrictive materials for generation of strains and forces in smart structure systems motivates the development of increasingly accurate models of the performance of these materials as used in transducers. The proposed magnetomechanical model provides a characterization of the material magnetization as well as the strain and force output by a transducer in response to quasistatic applied magnetic fields. The model is built in three steps. In the first, the mean field model for ferromagnetic hysteresis originally developed by Jiles and Atherton is used to compute the magnetization arising from the application of magnetic fields. While this model provides an accurate characterization of the field-induced magnetization at constant stress, it is insufficient in cases where the stress state of the magnetostrictive driver varies significantly during operation. To model the stress-induced magnetization changes, or magnetomechanical effect, a 'law of approach' to the anhysteretic magnetization is considered. The magnetization hysteresis model in combination with this law of approach provides a more realistic representation of the bidirectional energy transduction taking place in magnetostrictive transducers. In the second step, an even-term series expansion posed in terms of the magnetization is employed to calculate the magnetostriction associated with magnetic moment rotations within domains. While the magnetostriction provides a good description of the total material strain at the low field levels where elastic dynamics are of secondary significance, it is highly inaccurate at higher drive levels, in which the elastic response gains significance. This elastic or material response is considered in the third and last step, by means of force balancing in the form of a PDE system with magnetostrictive inputs and boundary conditions consistent with the transducer mechanical design. The solution to this PDE system provides the longitudinal displacements and corresponding strains and forces generated by the magnetostrictive driver. Since the formulation precludes analytic solution, a Galerkin discretization is employed to express the PDE in the form of a temporal system, which is subsequently solved using finite difference approximations. The ability of the model to accurately characterize the magnetomechanical behavior of magnetostrictive transducers is demonstrated via comparison of model simulations with experimental measurements collected from two Terfenol-D transducers.