The use of a non-linear model for a more realistic calculation of the “ΔE effect” in magnetoelastic ribbons

In the current paper an exact analytic expression in a closed form is given for the impedance Z of a finite size coil having as a core a magnetoelastic thin ribbon along its axis. From the impedance formula, the resonance and anti-resonance frequencies fR and fA are calculated and their ratio is related to the “ΔE effect” of the magnetoelastic materials. This is of great importance for these materials because the “ΔE effect” reveals information about their internal structure and also the resonance and anti-resonance frequencies are relatively easy to measure. Our analysis is more realistic than previous attempts to do similar calculations which overestimate the anti-resonance frequency because a) a more accurate non-linear model is used in the current work to describe the magnetic behavior of the magnetoelastic thin ribbon, and b) finite size coils are assumed as is the case in real experiments. The results show that even though fR depends on the “ΔE effect” and ribbon properties (material and geometry), fA depends additionally on the geometry of the excitation coil.