Analysis of nonlinear transient responses of piezoelectric resonators

The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q_m for piezoelectric resonators with nonlinear behaviors was also proposed.