Document Type: Research Paper

Authors

Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

Abstract

In this paper, a new algorithm for studying elastic wave propagation in the phononic crystals is presented. At first, the displacement-based forms of elastic wave equations are derived and then the forms are discretized using finite difference method. So the new algorithm is called the displacement-based finite difference time domain (DBFDTD). Three numerical examples are computed with this method and the results are compared with experimental measurements and the conventional FDTD method. Also, the computational cost of the new approach is compared with the conventional FDTD method. The comparison showed that the calculation time of the DBFDTD method is 37.5 percent less than that of the FDTD method.

Keywords

Main Subjects

[1[ M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites”, Phys. Rev. Lett., Vol. 71, No. 13, pp. 2022-2025, (1993).

[2[ R. Martinez-Sala, J. Sancho, J. V. Sanchez, V. Gomez, J. Llinares, and F. Meseguer, “Sound attenuation by sculpture”, Nature., Vol. 378, No. 6554, pp. 241-241, (1995).

[3[ F. R. Montero de Espinosa, E. Jime´nez, and M. Torres, “Ultrasonic Band Gap in a Periodic Two-Dimensional Composite”, Phys. Rev. Lett., Vol. 80, No. 6, pp. 1208-1211, (1998).

[4] A. Khelif, A. Choujaa, R. laihem, M. Wilm, S. Ballandras, and V. Laude, “Experimental study of band gaps and defect modes in a two-dimensional ultrasonic crystal”, IEEE Ultrasonics Symposium, pp. 377-380, (2003).

[5] Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, A. Khelif, and P. A. Deymier, “Tunable filtering and demultiplexing in phononic crystals with hollow cylinders”, Phys. Rev. E., Vol. 69, 046608, (2004).

[6[ W. Liu, J. W. Chen, and X. Y. Su, “Local resonance phononic band gaps in modified two-dimensional lattice materials”, Acta Mech. Sin., Vol. 28, pp. 659-669, (2012).

[7[ M. Kafesaki, M. M. Sigalas, and N. García, “Frequency Modulation in the Transmittivity of Wave Guides in Elastic-Wave Band-Gap Materials”, Phys. Rev. Lett., Vol. 85, No. 19, pp. 4044-4047, (2000).

[8] A. Khelif, B. Djafari-Rouhani, J. O. Vasseur, and P. A. Deymier, “Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials”, Phys. Rev. B., Vol. 68, No. 2, 024302, (2003).

[9[ Y. Yao, Z. Hou, and Y. Liu, “The two-dimensional phononic band gaps tuned by the position of the additional rod”, Phys Let. A., Vol. 362, No. 5-6, pp. 494-499, (2007).

[10[ B. Wu, R. Wei, H. Zhao, and C. He, “Phononic Band Gaps in Two-Dimensional Hybrid Triangular Lattice”, Acta Mech. Solida Sin., Vol. 23, No. 3, pp. 255-259, (2010).

[11[ Y. Tanaka, Y. Tomoyasu, and S. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch”, Phys. Rev. B., Vol. 62, No. 11, pp. 7387-7392, (2000).

[12[ P. Hsieh, T. Wu, and J. Sun, “Three-Dimensional Phononic Band Gap Calculations Using the FDTD Method and a PC Cluster System”, Ieee T. Ultrason. Ferr., Vol. 53, No. 1, pp. 148-158, (2006).

[13] D. García-Pablos, M. Sigalas, F. R. Montero de Espinosa, M. Torres, M. Kafesaki, and N. García, “Theory and Experiments on Elastic Band Gaps”, Phys. Rev. Lett., Vol. 84, No. 19, pp. 4349 -4352, (2000).

[14] A. Khelif, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Dobrzynski, “Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency”, J. Appl. Phys., Vol. 94, No. 3, pp. 1308-1311, (2003).

[15] J. H. Sun, and T. T. Wu, “Analyses of mode coupling in joined parallel phononic crystal waveguides”, Phys. Rev. B., Vol. 71, 174303, (2005).

[16] Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. Vasseur, and A. C. Hladky-Hennion, “Phononic crystals and manipulation of sound”, Phys. Status Solidi C., Vol. 6, No. 9, pp. 2080-2085, (2009).

[17] H. F. Gao, T. Matsumoto, T. Takahashi, and H. Isakari, “Analysis of Band Structure for 2D Acoustic Phononic Structure by BEM and the Block SS Method”, CMES-Comp. Model. Eng., Vol. 90, No. 4, pp. 283-301, (2013).

[18] M. Kafesaki, and E. N. Economou, “Multiple-scattering theory for three dimensional periodic acoustic composites”, Phy. Rev. B., Vol. 60, No.17, 11993, (1999).

[19] Z. Z. Yan, and Y. S. Wang, “Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals”, J. Comput. Phys., Vol. 74, 224303, (2006).

[20] B. Djafari-Rouhani, J. O. Vasseur, A. C. Hladky-Hennion, P. Deymier, F. Duval, B. Dubus, and Y. Pennec, “Absolute band gaps and waveguiding in free standing and supported phononic crystal slabs”, Photonic Nanostruct., Vol. 6, No. 1, pp. 32-37, (2008).

[21] M. Liu, J. Xiang, Y. Zhong, “The band gap and transmission characteristics investigation of local resonant quaternary phononic crystals with periodic coating”, Appl. Acoust., Vol. 100, pp. 10-17, (2015).

[22] M. Liu, P. Li, Y. Zhong, and J. Xiang, “Research on the band gap characteristics of two-dimensional phononic crystals micro-cavity with local resonant structure”, Shock. Vib., Vol. 2015, 239832, (2015).

[23] Y. Cao, Z. Hou, and Y. Liu, “Finite difference time domain method for band-structure calculations of two-dimensional phononic crystals”, Solid State Commun., Vol. 132, No. 8, pp. 539-543, (2004).

[24] A. Taflove, Advances in Computational Electrodynamics, Artech House, London, (1999).

[25] T. T. Wu, J. H. Sun, “4G-3 Guided Surface Acoustic Waves in Phononic Crystal Waveguides”, IEEE Ultrasonics Symposium, pp. 673-676, (2006).

CAPTCHA Image