Analysis of High Power Behavior in Piezoelectric Ceramics from a   Mechanical Energy Density Perspective
  In this work, a new methodology for comparing high power performance of different piezoelectric materials is presented. When comparing high power performance of piezoelectric materials of varying compositions and vibration modes, there exists an inherent problem in comparing the mechanical quality factor directly. Typically the behavior of the mechanical quality factor is reported as a function of tip vibration velocity of the sample. This paper shows why this approach can be inherently problematic and proposes an energy approach to characterize the mechanical quality factor as the solution. By utilizing mechanical energy density ($u_{e}$), the mass density of the material system ($\rho$), and the vibration mode shape (e.g. $k_{31}$ and $k_{p}$) of the sample are accounted for. Therefore, a better method to compare high power performance of varying piezoelectric compositions is introduced. Furthermore, the new method is applied to various compositions by using data available in the literature. As a result, the high power behavior of the materials appear to be significantly different when the new "energy density approach" is used to compare the mechanical quality factor rather than vibration velocity. Also, the technique's ability to be utilized to consolidate data from different resonators to determine anisotropic loss factors is demonstrated on hard and soft PZT samples of $k_{31}$ and $k_{p}$ geometries. 
Husain N. Shekhani, Erkan A. Gurdal, Seyit O. Ural, and Kenji Uchino
cond-mat.mtrl-sci