The evaluation of the κ factor for lossy and composite (Langevin-type) piezoelectric elements

The most important property of a piezoelectric material for practical applications is its ability to convert electrical energy into mechanical energy and vice versa. As it is well known, the electromechanical coupling factor κ fully characterize this energy conversion. In a previous work we demonstrated that, like in static conditions, it is possible to define the κ factor also in dynamic situations as a ratio of energies. We also showed that the value of the κ factor computed in this way (κ_ω) coincides with the one obtained by using the empirical relation of the effective coupling factor κ_eff. In this work we show that the proposed definition of the κ factor as ratio of energies can be extended to lossy elements, but, in this case, the k_eff does not give accurate estimation of the coupling factor. For composite Langevin-type structures, both κ, and κ_eff-fails