Nonlinear model for Galfenol cantilevered unimorphs considering full magnetoelastic coupling

This article presents a fully coupled, nonlinear model for the dynamic response of Galfenol-driven unimorph actuators in a cantilever configuration. The hysteretic magnetomechanical behavior of Galfenol is modeled using a discrete energy-averaged model, and the structural behavior of the unimorph is modeled using the finite element method. The weak form equations that describe bending of the unimorph are obtained using the principle of virtual work. Since the local strain and stress are nonlinearly coupled with both the vertical and horizontal displacements, a nonlinear solver is developed to approximate the coupled finite element equations. The nonlinear solver is verified against the analytical solution and experimental data for the case of a passive beam. The analytical solution is obtained using beam theory for free and harmonic responses. The analytical model and experimental data verify that the nonlinear solver correctly quantifies the first natural frequency of the composite beam. The numerical simulations match the analytical solutions for both free and harmonic responses. Finally, the dynamic response of the nonlinear magnetoelastic model is investigated and experimentally validated from 0.1 to 500 Hz, the range in which the model is accurate without the need for adjustable parameters.