An approximation to the planar harmonic impedance for interface waves in piezoelectric body

TIt is well known that spatial-temporal Green function
characterizes sufficiently the elastic media. For the case of elastic interface
waves which propagate at the interface between two, perfectly mechanically
contacting piezoelectric half-spaces, this function, or its scalar counterpart
that is the planar harmonic impedance, provides full characterization of
electric properties observed at the interface, which can be applied in analysis
of interdigital transducers embedded there, for instance. This impedance however
is not easy for evaluation as a function of complex wave-number in the most
interesting domain near the cut-off wave-number of bulk waves. Here, a
perturbation analysis is presented exploiting the Stroh matrix formulation for
piezoelectrics which yields the analytical approximation to the investigated
electric impedance at the crystal planar cross-section.