Periodic average structures in phononic quasicrystals

Abstract

Periodic average structures for the pentagonal, heptagonal, octagonal and dodecagonal tilings were constructed and used for the interpretation of transmission spectra of corresponding two-dimensional phononic quasicrystals (QPNCs). In the hard scattering regime of steel rods in water, the transmission behaviour of QPNCs resembles that of disordered periodic phononic crystals. The average structures allow prediction of position and width of the first bandgap. Additionally, the type of deviation of the quasiperiodic from its periodic average structure is shown to support the understanding of the shape of the transmission spectra and may assist the choice of an optimal structure for specific phononic crystal applications.

Acknowledgements

We gratefully acknowledge discussions with B. Djafari-Rhouhani, Y. Pennec and J.O. Vasseur and provision of the FDTD-code we were adapting.