Analysis of nonlinear effects in a piezoelectric resonator

A theoretical model that explains the impedance Variation due to nonlinear elasticity of piezoelectric materials is described. A modified equivalent circuit is used in order to explain the behavior of a piezoelectric resonator near its series resonance, driven by a high-amplitude signal. A simple relation between the motional impedance Z(1) and the motional branch current I-1 has been obtained, defining nonlinear impedance coefficients. This model is able to explain and predict: (1) the amplitude-frequency effect, (2) the decreasing of the mechanical quality factor, and (3) the appearance of hysteretic phenomena. An experimental method is proposed to measure the above coefficients, and is used to verify the theoretical model on disk ceramic resonators. Experimental measurements have been carried out to compare the nonlinearity of different ceramic materials. (C) 1996 Acoustical Society of America.