Quantification of hysteresis and nonlinear effects on the frequency response of ferroelectric and ferromagnetic materials

Ferroelectric (e.g., PZT and PMN) and ferromagnetic (e.g., Terfenol-D) materials exhibit high energy densities, broadband drive capabilities, and the capacity for both actuating and sensing. This makes them attractive as compact transducers for a wide range of applications. However, the materials also exhibit hysteresis and constitutive nonlinearities, at all drive levels, that must be quantified and accommodated to achieve stringent tracking requirements. Whereas considerable effort has been made on model development and understanding these materials in the parameter space and time domain, comprehensive quantification of these effects in the frequency domain is currently lacking. In this paper, we employ the homogenized energy model, in combination with thin beam theory, to quantify the frequency domain behavior of ferroelectric and ferromagnetic materials. This model combines energy analysis at the lattice level with stochastic homogenization techniques to provide a framework that effectively quantifies the effect of hysteresis, constitutive nonlinearities, bias fields and AC drive levels on the material dynamics in both the time and frequency domains. Aspects of the model are illustrated and validated through numerical and experimental examples