One-dimensional phenomenological model of hysteresis. II. Applications

Abstract

A model of hysteresis is applied to determine material response to multifrequency drives, and to the output control problem. Although as presented in Paper I the model is based on a monofrequency sinusoidal drive, it can readily be generalized. The generalization is based upon the fact, at least for quasistatic drives, that the shape of the hysteresis loop is independent of the shape of the drive waveform used to produce it provided that the drive is characterized by only one wave amplitude. The material response to a given arbitrarily shaped drive can be determined if the drive is first subdivided into single-amplitude regimes or epochs. Each such regime then has associated with it a unique hysteresis loop, which can be determined from the model. Each theoretical loop is generated using a monofrequency sinusoidal drive whose amplitude is equal to the single amplitude contained within the corresponding drive epoch. The material response is then determined by correlating the level of the given drive field (and the sign of its time derivative) with that of the sinusoidal drive used to generate the associated theoretical loop. The response to the arbitrary drive is taken to be equal to the response to the sinusoidal drive at the corresponding drive level and correspondingly signed time derivative. This process is capable of inversion. Thus, not only can the material response be determined for a drive of arbitrary waveshape, but also the drive waveshape required to produce a desired output trajectory can be determined. The procedure is illustrated by determining the drive necessary to produce a monofrequency sinusoidal magnetization response from a biased, prestressed sample of Terfenol D driven at high-amplitude magnetic field.