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

Abstract

Ferroelectric (e.g., PZT and PMN) and ferromagnetic (e.g., Terfenol-D) materials exhibithigh energy densities, broadband drive capabilities, and the capacity for both actuatingand sensing. This makes them attractive as compact transducers for a wide range ofapplications. However, the materials also exhibit hysteresis and constitutive nonlinearities,at all drive levels, that must be quantified and accommodated to achieve stringent trackingrequirements. Whereas considerable effort has been made on model development andunderstanding these materials in the parameter space and time domain, comprehensivequantification 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 ferromagneticmaterials. This model combines energy analysis at the lattice level with stochastichomogenization techniques to provide a framework that effectively quantifies theeffect of hysteresis, constitutive nonlinearities, bias fields and AC drive levels onthe material dynamics in both the time and frequency domains. Aspects of themodel are illustrated and validated through numerical and experimental examples.