Elastic wave localization in two-dimensional phononic crystals with one-dimensional quasi-periodicity and random disorder
- 1 Downloads
The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered (in one direction) phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity (Fibonacci sequence) in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.
Key wordsphononic crystal quasi phononic crystal disorder localization factors plane-wave-based transfer-matrix method periodic average structure
Unable to display preview. Download preview PDF.
- Vasseur, J.O., Djafari-Rouhani, B., Dobrzynski, L. and Deymier, P.A., Acoustic band gaps in fibre composite materials of boron nitride structure. Journal of Physics: Condense Matter, 1997, 9: 7327–7341.Google Scholar
- Vasseur, J.O., Deymier, P.A., Khelif, A., Lambin, Ph., Djafari-Rouhani, B., Akjouj, A., Dobrzynski, L., Fettouhi, N. and Zemmouri, J., Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range: A theoretical and experimental study. Physical Review E, 2002, 65: 056608.CrossRefGoogle Scholar
- Yan, Z.Z. and Wang, Y.S., Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals. Physical Review B, 2006, 74: 1.Google Scholar
- Yan, Z.Z., Wang, Y.S. and Zhang, C.Z., Wavelet method for calculating the defect states of two-dimensional phononic crystals. Acta Mechanica Solida Sinica. 2008, 21: 105–109.Google Scholar
- Sigalas, M.M., Defect states of acoustic waves in a two-dimensional lattice of solid cylinders. Journal of Applied Mechanics, 1998, 84: 3026–3030.Google Scholar
- Zhang, Y.P., Yao, J.Q., Zhang, H.Y., Zheng, Y. and Wang, P., Bandgap extension of disordered 1D ternary photonic crystals. Acta Photonica Sinica, 2005, 34: 1094–1098 (in Chinese).Google Scholar
- Aynaou, H., Boudouti, E.H.EI., Djafari-Rouhani, B., Akjouj, A. and Velasco, V.R., Propagation and localization of acoustic waves in Fibonacci phononic circuits. Journal of Physics: Condensed Matter, 2005, 17: 4245–4262.Google Scholar
- Velasco, V.R., Perez-Alvarez, R. and Garcia-Moliner, F., Some properties of the elastic waves in quasiregular heterostructures. Journal of Physics: Condensed Matter, 2002, 14: 5933–5957.Google Scholar