High Power Characterization of Piezoelectric Ceramics Using the   Burst/Transient Method with Resonance and Antiresonance Analysis
  In this paper, a comprehensive methodology for characterizing the high power resonance behavior of bulk piezoelectric ceramics using the burst method is described. In the burst method, the sample is electrically driven at its resonance frequency, and then either a short circuit or an open circuit condition is imposed, after which the vibration decays at the resonance or antiresonance frequency, respectively. This decay can be used to measure the quality factor in either of these conditions. The resulting current in the short circuit vibration condition is related to the vibration velocity through the "force factor." The generated voltage in the open circuit vibration condition corresponds to the displacement by the "voltage factor." The force factor and the voltage factor are related to material properties and physical dimensions of the sample. Using this method, the high power behavior of the permittivity, compliance, piezoelectric charge constant, electromechanical coupling factor, and material losses can be determined directly by measuring the resonance (short circuit) and antiresonance (open circuit) frequencies, their corresponding quality factors, the force factor $A$, and the voltage factor $B$. The experimental procedure to apply this method is described and demonstrated on commercially available hard and semi-hard PZT materials of $k_{31}$ 
Husain Shekhani, Timo Scholehwar, Eberhard Hennig, and Kenji Uchino
cond-mat.mtrl-sci