Fully coupled, dynamic model of a magnetostrictive amorphous ribbon and its validation

Magnetostrictive amorphous ribbons are widely used in electronic article surveillance as well as for magnetoelastic sensors. Both applications utilize the fact that the ribbons' resonant frequency can be read out remotely by applying external magnetic AC fields. This paper proposes a magnetomechanical model to simulate the dynamics of such ribbons. The goal was to only use general material properties as input parameters, which are usually denoted in the data sheet of amorphous metals. Thus, only the magnetization curve at zero stress has to be gained via measurement. The magnetization under stress is calculated thereof. The equation of motion for a longitudinally oscillating ribbon is derived and coupled to Maxwell's equations for magnetostatics. The fully coupled initial value problem is solved simultaneously by a finite difference approach. The model is validated by comparing calculated and measured resonant frequencies of various amorphous ribbons, which turned out to be in good agreement. When slightly adapting single material properties from the data sheet, the match is almost perfect. The model is then used to calculate the local magnetic and mechanical properties inside static and vibrating ribbons. These local distributions can be directly linked to the field dependence of the resonant frequency and its higher harmonics