Theoretical study of the influence of the electromechanical constants and nonlinear mechanical losses of various piezoelectric materials on their performances in power transducers

A simple analytical model is developed in longitudinal resonance mode taking into account the piezoelectric and mechanical constants of the materials as well as a mechanical loss tangent depending on the relative mean strain S : tanδ_m = tanδ_mo + αS², where tanδ_mo is the low power mechanical loss tangent and α a coefficient characteristic of the non-linearity. For a given acoustical load, the power supplied to the load, the mechanical losses and the maximum internal stress are expressed as a function of the applied electric field at the series resonance frequency for various materials: hard PZT, hard BaTiO₃ and PMN-PT ceramics and a PMN-PT single crystal. In steady state, the limitation factor would be the loss power for PMN-PT ceramic and single crystal and the maximum stress for hard PZT and BaTiO₃. In longitudinal mode , the very high compliance s₃₃^E of the single crystal goes against it, however, its low acoustical impedance significantly reduces the internal stresses. The hard lead-free BaTiO₃ could be similar in radiated power to the hard PZT but it should be fed with higher electric fields. The respective influences of tanδ_mo and α on the performances are discussed. Finally, some single crystals and textured ceramics seem promising for 31 transducers.