The use of real or complex coupling coefficients for lossy piezoelectric materials

Two competing approaches for calculating coupling coefficients for lossy piezoelectric materials, one producing a real result and the other a complex result, are compared and analyzed. It is found that the complex coupling coefficient suffers from mathematical difficulties, which the real coupling coefficient does not exhibit. Moreover, it is pointed out that a prediction made by the complex coupling coefficient theory conflicts with experiment while the corresponding real coupling coefficient theory prediction does not. When a coupling coefficient of interest has been computed from the real coupling coefficient theory using piezoelectric equations having intensive independent variables, the resulting expression has the same algebraic form as the corresponding static coupling coefficient formula. Moreover, only the real parts of the piezoelectric, elastic, and dielectric material properties appear.