On the Nonlinear Behavior of Piezoelectric Actuators

Abstract

In this paper we present a theoretical and experimental study of the nonlinear behavior of piezoelectric actuators. The nonlinearities are introduced as quadratic terms in the piezoelectric constitutive relations. These relations are employed, together with supporting experimental results, to establish an engineering description of the nonlinearities present in piezoelectric materials. We present a lumped-parameter representation of a system consisting of a piezoactuator driving a mass. The representation is valid in the vicinity of the primary resonance. The resulting nonlinear differential equation of motion is analyzed by the method of harmonic balance to study the effects of nonlinearities on the dynamics of forced vibrations. Experimental measurements of the steady-state mechanical response to harmonic electrical excitation over a range of excitation frequencies and amplitudes quantify the nature and level of nonlinear behavior. The nonlinear behavior, which is mainly evident around the resonant frequency, is shown to be of the softening type and becomes more pronounced at higher drive voltage levels. Numerical simulations based on the developed nonlinear model have shown significant improvement over previous linear models in predicting the experimental behavior of piezoelectric materials at the vicinity of primary resonance.