Theoretical study of shear horizontal wave propagation in periodically layered piezoelectric structure

In this paper, the propagation of the shear horizontal wave (SH-wave) in the single piezoelectric layer and periodically layered piezoelectric structure is studied. Both the dispersion equation and transmission coefficients are derived to reveal the wave behavior of the corresponding structures when the piezoelectricity is ignored or the electrical circuit is open and closed. The zero-order mode of the piezoelectricity-ignored single plate is not dispersive and every higher order mode is dispersive with a cut-off frequency. Same features are found for the electrically open and closed cases except that the zero-order mode of the latter case is no more non-dispersive. The pass bands of the piezoelectricity-ignored periodically layered structure appear when the normalized frequency is an even integer under the normal incidence, and new stop bands will appear from the pass bands as the incident angle increases. The same features are observed for the band gaps of the electrically open and closed cases except that the zero-order mode of the latter case is dispersive. The stop bands of the periodic structure will change in a cycle as the geometric ratio increases from zero to one.