Dispersion relations for SH-wave propagation in nanoscale periodic piezoelectric composite layered structures

The influence of the small-scale effects on propagation behavior of horizontally polarized shear waves (SH-waves) in a nano scale periodic piezoelectric-polymeric layered structure which are composed of piezoelectric thin films bonded perfectly with polymeric thin films alternately is investigated. The research using the transfer matrix method based on the nonlocal piezoelectricity continuum theory. The analytical expressions of the phase velocity equations of SH-waves propagation in the periodic layered piezoelectric structure with size effect are obtained for the case of wave propagation in the direction normal to the interface. The nonlocal effect has an obviously effect on the high frequency waves, but the effect on the lower frequency is not obvious, and the first band gap width can be decreased slightly when taking account of the nonlocal effect, and near the cut-off frequency, the bands are dense and flat, which imply that a strong wave localization phenomenon occurs. Furthermore, a cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure, and the size effect influence on the cut-off frequency and the wave propagation behavior are discussed.