Analysis of vibration waveforms of electromechanical response to determine piezoelectric and electrostrictive coefficients

We developed a possible method to determine both coefficients of piezoelectricity (d) and electrostriction (M) at the same time by a waveform analysis of current and vibration velocity in the resonance state. The waveforms of the current and vibration velocity were theoretically described using the equations of motion and piezoelectric constitutive equations, considering the dissipation effect. The dissipation factor of the d coefficient and M coefficient is dielectric loss tangent tan δ. The waveforms measured in all of the ceramics, such as Pb(Zr,Ti)O₃ (PZT), Pb(Mg,Nb)O₃ (PMN), and 0.8Pb(Mg_1/3Nb2/3)O₃–0.2PbTiO₃ (PMN–PT), were well fitted with the calculated waveform. This fitting produced both the d and M coefficients, which agreed with those determined via the conventional methods. Moreover, the respective contributions of both piezoelectricity and electrostriction to the d value determined in the resonance-antiresonance method were clarified.