Simulation of Elastic Wave Propagation through Steel/Epoxy Phononic Crystal Waveguide by Displacement-Based Finite Difference Method
Author
Abstract
In order to obtain transmission spectra through a phononic crystal as well as its waveguide, a new algorithm is presented in this paper. By extracting displacement-based forms of elastic wave equations and their discretization, Displacement- Based Finite Difference Time Domain (DBFDTD) algorithm is presented. Two numerical examples are solvcd with this method and the results are compared with the conventional Finite Difference Time Domain (FDTD) method. In addition, the computational cost of the new approach has been compared with the conventional FDTD method. This comparison showed that the computation time of the DBFDTD method is 40 percent less than that of the conventional FDTD method.
Keywords
1. Kushwaha, M. S., Halevi, P., Dobrzynski, L., and Djafari-Rouhani, B., “Acoustic Band Structure of Periodic Elastic Composites”, Physical Review Letters, Vol. 71, pp. 2022-2025, 1993.
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5. Pennec, Y., Djafari-Rouhani, B., Vasseur, J. O., Khelif, A., and Deymier, P. A., “Tunable Filtering and Demultiplexing in Phononic Crystals with Hollow Cylinders”, Physical Review E, Vol. 69, pp. 046608, 2004.
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14. Khelif, A., Deymier, P. A., Djafari-Rouhani, B., Vasseur, J. O., and Dobrzynski, L., “Two-Dimensional Phononic Crystal with Tunable Narrow Pass Band: Application to a Waveguide with Selective Frequency”, Journal of Applied Physics, Vol. 94, pp. 1308-1311, 2003.
15. Sun, J. H, and Wu, T. T., “Analyses of Mode Coupling in Joined Parallel Phononic Crystal Waveguides”, Physical Review B, Vol. 71, pp. 174303, 2005.
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17. Gao, H. F., Matsumoto, T., Takahashi, T., and Isakari, H., “Analysis of Band Structure for 2D Acoustic Phononic Structure by BEM and the Block SS Method”, CMES: Computer Modeling in Engineering & Sciences, Vol. 90, No. 4, pp. 283-301, 2013.
18. Kafesaki, M.; and Economou, E. N., “Multiple-Scattering Theory for Three Dimensional Periodic Acoustic Composites”, Physical Review B, Vol. 60, pp. 11993, 1999.
19. Yan, Z. Z.; and Wang, Y. S., “Wavelet-Based Method for Calculating Elastic Band Gaps of Two-Dimensional Phononic Crystals”, Journal of Computational Physics, Vol. 74, pp. 224303, 2006.
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21. Chew, W. C., and Liu, Q. H., “Perfectly Matched Layers for Elastodynamics: A New Absorbing Boundary Condition”, Journal of Computational Acoustics, Vol. 4, pp. 341-359, 1996.
22. Sun, J. H., and Wu, T. T., “Guided Surface Acoustic Waves in Phononic Crystal Waveguides”, IEEE Ultrasonics Symposium, pp. 673-676, 2006.
23. Tanaka, Y., Yano, T., and Tamura, S., “Surface Guided Waves in Two-Dimensional Phononic Crystals”, Wave Motion, Vol. 44, pp. 501-512, 2007.
2. Martinez-Sala, R., Sancho, J., Sanchez, J. V., Gomez, V., Llinares, J., and Meseguer, F., “Sound Attenuation by Sculpture”, Nature, Vol. 378, pp. 241-241, 1995.
3. Montero de Espinosa, F. R., Jime´nez, E., and Torres, M., “Ultrasonic Band Gap in a Periodic Two-Dimensional Composite”, Physical Review Letters, Vol. 80, pp. 1208-1211, 1998.
4. Khelif, A., Choujaa, A., laihem, R., Wilm, M., Ballandras, S., and Laude, V., “Experimental Study of Band Gaps and Defect Modes in a Two-Dimensional Ultrasonic Crystal”, IEEE Ultrasonics Symposium, pp. 377-380, 2003.
5. Pennec, Y., Djafari-Rouhani, B., Vasseur, J. O., Khelif, A., and Deymier, P. A., “Tunable Filtering and Demultiplexing in Phononic Crystals with Hollow Cylinders”, Physical Review E, Vol. 69, pp. 046608, 2004.
6. Liu, W., Chen, J. W., and Su, X. Y., “Local Resonance Phononic Band Gaps in Modified Two-Dimensional Lattice Materials”, Acta Mechanica Sinica, Vol. 28, pp. 659-669, 2012.
7. Kafesaki, M., Sigalas, M. M., and García, N., “Frequency Modulation in the Transmittivity of Wave Guides in Elastic-Wave Band-Gap Materials”, Physical Review Letters, Vol. 85, pp. 4044-4047, 2000.
8. Khelif, A., Djafari-Rouhani, B., Vasseur, J. O., and Deymier, P. A., “Transmission and Dispersion Relations of Perfect and Defect-Containing Waveguide Structures in Phononic Band Gap Materials”, Physical Review B, Vol. 68, pp. 024302, 2003.
9. Yao, Y., Hou, Z., and Liu, Y., “The Two-Dimensional Phononic Band Gaps Tuned by the Position of the Additional Rod”, Physics Letters A, Vol. 362, pp. 494-499, 2007.
10. Wu, B., Wei, R., Zhao, H., and He, C., “Phononic Band Gaps in Two-Dimensional Hybrid Triangular Lattice”, Acta Mechanica Solida Sinica, Vol. 23, pp. 255-259, 2010.
11. Tanaka, Y., Tomoyasu, Y., and Tamura, S., “Band Structure of Acoustic Waves in Phononic Lattices: Two-Dimensional Composites with Large Acoustic Mismatch”, Physical Review B, Vol. 62, pp. 7387-7392, 2000.
12. Hsieh, P., Wu, T., and Sun, J., “Three-Dimensional Phononic Band Gap Calculations Using the FDTD Method and a PC Cluster System”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 53, pp. 148-158, 2006.
13. García-Pablos, D., Sigalas, M., Montero de Espinosa, F. R., Torres, M., Kafesaki, M., and García, N., “Theory and Experiments on Elastic Band Gaps”, Physical Review Letters, Vol. 84, pp. 4349-4352, 2000.
14. Khelif, A., Deymier, P. A., Djafari-Rouhani, B., Vasseur, J. O., and Dobrzynski, L., “Two-Dimensional Phononic Crystal with Tunable Narrow Pass Band: Application to a Waveguide with Selective Frequency”, Journal of Applied Physics, Vol. 94, pp. 1308-1311, 2003.
15. Sun, J. H, and Wu, T. T., “Analyses of Mode Coupling in Joined Parallel Phononic Crystal Waveguides”, Physical Review B, Vol. 71, pp. 174303, 2005.
16. Pennec, Y., Djafari-Rouhani, B., Larabi, H., Vasseur, J., and Hladky-Hennion, A. C, “Phononic Crystals and Manipulation of Sound”, Physica Status Solidi C, Vol. 6, pp. 2080-2085, 2009.
17. Gao, H. F., Matsumoto, T., Takahashi, T., and Isakari, H., “Analysis of Band Structure for 2D Acoustic Phononic Structure by BEM and the Block SS Method”, CMES: Computer Modeling in Engineering & Sciences, Vol. 90, No. 4, pp. 283-301, 2013.
18. Kafesaki, M.; and Economou, E. N., “Multiple-Scattering Theory for Three Dimensional Periodic Acoustic Composites”, Physical Review B, Vol. 60, pp. 11993, 1999.
19. Yan, Z. Z.; and Wang, Y. S., “Wavelet-Based Method for Calculating Elastic Band Gaps of Two-Dimensional Phononic Crystals”, Journal of Computational Physics, Vol. 74, pp. 224303, 2006.
20. Djafari-Rouhani, B., Vasseur, J. O., Hladky-Hennion, A. C., Deymier, P., Duval, F., Dubus, B., and Pennec, Y., “Absolute Band Gaps and Waveguiding in Free Standing and Supported Phononic Crystal Slabs”, Photonics and Nanostructures Fundamentals and Applications, Vol. 6, pp. 32-37, 2008.
21. Chew, W. C., and Liu, Q. H., “Perfectly Matched Layers for Elastodynamics: A New Absorbing Boundary Condition”, Journal of Computational Acoustics, Vol. 4, pp. 341-359, 1996.
22. Sun, J. H., and Wu, T. T., “Guided Surface Acoustic Waves in Phononic Crystal Waveguides”, IEEE Ultrasonics Symposium, pp. 673-676, 2006.
23. Tanaka, Y., Yano, T., and Tamura, S., “Surface Guided Waves in Two-Dimensional Phononic Crystals”, Wave Motion, Vol. 44, pp. 501-512, 2007.
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