The evaluation of the /spl kappa/ 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 /spl kappa/ fully characterize this energy conversion. In a previous work we demonstrated that, like in static conditions, it is possible to define the /spl kappa/ factor also in dynamic situations as a ratio of energies. We also showed that the value of the /spl kappa/ factor computed in this way (/spl kappa//sub /spl omega//) coincides with the one obtained by using the empirical relation of the effective coupling factor /spl kappa//sub eff/. In this work we show that the proposed definition of the /spl kappa/ factor as ratio of energies can be extended to lossy elements, but, in this case, the k/sub eff/ does not give accurate estimation of the coupling factor. For composite Langevin-type structures, both /spl kappa/, and /spl kappa//sub eff/-fails.