Optimization and Dynamic Modeling of Galfenol Unimorphs

Abstract

Design and modeling of a bi-laminate, Galfenol-driven composite beam is presented in which the elasticity of the adhesive layer is considered. The optimal thickness ratio necessary to maximize the tip deflection is found by minimization of the internal energy of the beam. Model simulations show that use of a substrate material with high modulus leads to larger tip deflections. Stainless steel was therefore utilized as substrate in the experiments. In order to reduce eddy currents, a laminated silicon steel frame was employed to magnetize the beam. A dynamic model is proposed by coupling the structural dynamics of the beam and adhesive layer with the magnetostriction generated by the Galfenol layer. The latter is described with a linear piezomagnetic law with uniform magnetic field distribution along the length of the beam. Galerkin discretization combined with Newmark numerical integration are employed to approximate the dynamic response of the beam. The model is shown to describe both the transient and steady-state response of the composite beam tip displacement under harmonic excitation between 10 and 320 Hz. The RMS error between model and data range between 1.44% at 10 Hz and 6.34% at 320 Hz, when the same set of model parameters (optimized at quasistatic frequency) is utilized.