Dynamic Model for Magnetostrictive Systems With Applications to Damper Design

Magnetostrictive iron–gallium alloys are able to dissipate mechanical energy via eddy currents and magnetic hysteresis. The mechanically induced eddy current loss is determined by the piezomagnetic coefficient; the hysteresis loss is usually quantified by the phase lag. This study first characterizes these losses for research grade, <100>-oriented, highly textured, polycrystalline <inline-formula><tex-math notation="LaTeX"> $\mathrm{Fe_{81.6}Ga_{18.4}}$</tex-math></inline-formula> within the structural frequency range (up to 800 Hz). The magnetic biasing is provided by applying a constant current of 500 mA on a pair of electromagnets; the mechanical excitation is a sinusoidal stress wave (3 <inline-formula><tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 0.2 MPa) superimposed on a <inline-formula><tex-math notation="LaTeX">$-$</tex-math> </inline-formula>20 MPa constant stress. As stress frequency increases, the piezomagnetic coefficient decreases from 32.27 to 10.33 T/GPa and the phase lag <inline-formula><tex-math notation="LaTeX">$|\Delta \phi |$</tex-math> </inline-formula> increases from 11.38<inline-formula><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> to 43.87<inline-formula><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula>. A rate-dependent finite element framework decoupling eddy current loss and hysteresis loss is then developed. The model accurately reproduces the experimental results in both quasi-static and dynamic regimes. Guided by the knowledge of material properties and the finite element model, a coil-less and solid-state damper is designed which can attenuate vibrations before they propagate and induce structure-borne noise and damage. Modeling results show that the loss factor of this damper can be continuously tuned from 0 to a maximum value of 0.107 by adjusting the precompression on the magnetostrictive component.