Derivation of magnetostrictive losses from admittance spectra

There are three types of losses for magnetostrictors, elastic loss, magnetic loss and piezomagnetic coupling loss, similar to the loss mechanism of a piezoelectric (elastic, dielectric and piezoelectric losses) that our group has established recent years. By introducing these losses factors we can characterize magnetostrictive losses using complex parameters. Here we derived the relationship of mechanical quality factors and losses factor based on admittance spectra expression we have established previously. By measuring accurately the mechanical quality factors Q _A for the resonance and Q _B for the anti-resonance in the admittance/impedance curve, we can derive these three physical losses to characterize magnetostrictive hysteresis loss.