The electromechanical coupling factor in static and dynamic conditions

Piezoelectric materials are widely used in practical applications to generate and to detect stress waves. From this point of view, the coupling factor k is the most useful parameter, in fact it is able to fully characterize this energy conversion. Many different k factors are defined in the literature: the k(ij), or the so-called material coupling factor (k(mat)), defined in static conditions; the effective coupling factor k(eff) defined in dynamic conditions; and the coupling factor defined by Berlincourt et al., valid in static and dynamic conditions. In this work, according to the I. E. E. E. Standards on Piezoelectricity, we define the k factor as the ratio between the energy converted from electric to mechanic form (or vice versa) and the total energy involved in a transformation cycle and we demonstrate that this definition can be applied both in static and dynamic cases. We also show that the effective coupling factor k(eff) has indeed this precise physical meaning and that the Ic factor defined by Berlincourt, computed at the antiresonance frequency of the piezoelement, has the same value as the k(eff) A simple unified treatment of the Ic factor is given in the work.