Prediction of Bragg-scattering-induced band gaps in phononic quasicrystals

We have studied ultrasonic wave propagation in two-dimensional quasiperiodic steel/water heterostructures with 8-, 10-, 12-, and 14-fold Patterson symmetry. The formation of band gaps in this kind of quasiperiodic phononic crystal (QPNC) is mainly governed by multiple Bragg scattering. The particular role of the periodic average structure of the QPNC in prediction and understanding of their transmission spectra is shown. The smaller the deviations from average periodicity, the greater is the similarity of transmission spectra of the quasiperiodic and periodic heterostructures. Consequently, QPNC's with 8-fold symmetry (QPNC-8's) show much better defined transmittance bands and gaps than QPNC-10's and QPNC-14's, whose spectra resemble more those of disordered periodic systems. Smoother transmission spectra with clear gaps can be obtained by replacement of the cylinders of QPNC-10's by star-shaped prisms.