Skip to main content Accessibility help
×
Home

Propagation of Lamb Waves in Phononic-Crystal Plates

  • J.-C. Hsu (a1) and T.-T. Wu (a1)

Abstract

In this paper, the band structures of Lamb waves in the two-dimensional phononic-crystal plates are calculated and analyzed based on the plane wave expansion method. The phononic-crystal plates are composed of an array of circular crystalline iron cylinders embedded in the epoxy matrix. Square lattice and triangular lattice are analyzed and discussed, respectively. For the square lattice, two complete band gaps exist, and a narrow pass band between the complete band gaps separates them apart. For the triangular lattice, a wide complete band gap existing with the ratio of gap width to midgap frequency Δω/ωm equal to 72% is found. Furthermore, the influence of the plate thickness is crucial for band structures of Lamb waves. Tuning plate thickness can shift the pass bands effectively, and band shifting causes the variation of the width of complete band gap and its opening and closure.

Copyright

Corresponding author

*Postdoctoral Researcher
**Professor

References

Hide All
1.Kushwaha, M. S., Halevi, P., Dobrzynski, L. and Djafari-Rouhani, B., “Acoustic Band Structure of Periodic Elastic Composite,” Phys. Rev. Lett., 71, pp. 20222025 (1993).
2.Sigalas, M. M. and Economou, E. N., “Elastic and Acoustic Band Structure,” J. Sound Vib., 158, pp. 377382 (1992).
3.Bria, D. and Djafari-Rouhani, B., “Omnidirectional Elastic Band Gap in Finite Lamellar Structure,” Phys. Rev. E 66, pp. 056609:18(2002).
4.Torres, M., Montero de Espinosa, F. R., García-Pablos, D. and García, N., “Sonic Band Gaps in Finite Elastic Media: Surface States and Localization Phenomena in Linear and Point Defects,” Phys. Rev. Lett., 82, pp. 30543057 (1999).
5.Tanaka, Y. and Tamura, S., “Surface Acoustic Waves in Two-Dimensional Periodic Elastic Structures,” Phys. Rev. B, 58, pp. 79587965(1998).
6.Psarobas, I. E., Stefanou, N. and Modinos, A., “Scattering of Elastic Waves by Periodic Arrays of Spherical Bodies,” Phys. Rev. B 62, pp. 278291 (2000).
7.Tanaka, Y., Tomoyasu, Y. and Tamura, S., “Band Structure of Acoustic Waves in Phononic Lattices: Two Dimensional Composites with Large Acoustic Mismatch,” Phys. Rev. B, 62, pp. 73877392 (2000).
8.Torres, M., Montero de Espinosa, F. R., García-Pablos, D. and García, N., “Sonic Band Gaps in Finite Elastic Media: Surface States and Localization Phenomena in Linear and Point Defects,” Phys. Rev. Lett., 82, pp. 30543057 (1999).
9.Vasseur, J. O., Deymier, P. A., Chenni, B., Djafari-Rouhani, B., Dobrzynski, L. and Prevost, D., “Experimental and Theoretical Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Solid Phononic Crystals,”Phys. Rev. Lett., 86, pp. 30123015 (2001).
10.Gorishnyy, T., Ullal, C. K., Maldovan, M., Fytas, G. and Thomas, E. L., “Hypersonic Phononic Crystals,” Phys. Rev. Lett., 94, pp. 115501:14 (2005).
11.Cervera, F., Sanchis, L., Sanchez-Perez, J. V., Martinez-Sala, R., Rubio, C. and Mesegure, F., “Refraction Acoustic Device for Airborne Sound,” Phys. Rev. Lett., 88, pp. 023902:14 (2002).
12.Sun, J.-H. and Wu, T.-T., “Analyses of Mode Coupling in Joined Parallel Phononic Crystal Waveguides,” Phys. Rev. B, 71, pp. 174303:18 (2005).
13.Laude, V., Khelif, A., Benchabane, S. and Wilm, M., “Phononic Band-Gap Guidance of Acoustic Modes in Photonic Crystal Fiber,” Phys. Rev. B, 71, pp. 045107:16, (2005).
14.Wu, T.-T. and Chen, Y.-Y., “Analysis of Surface Acoustic Waves in Layered Piezoelectric Media and Its Applications to the Design of SAW Devices,” The Chinese Journal of Mechanics —Series A, 19, pp. 225232 (2003).
15.Wu, T.-T., Hsu, J.-C. and Huang, Z.-G., “Band Gaps and the Electromechanical Coupling Coefficient of a Surface Acoustic Wave in a Two-Dimensional Piezoelectric Phononic Crystal,” Phys. Rev. B, 71, pp. 064303:15 (2005).
16.Wu, T.-T., Huang, Z.-G. and Lin, S., “Surface and Bulk Acoustic Waves in Two-Dimensional Phononic Crystal Consisting of Materials with General Anisotropy,” Phys. Rev. B, 69, pp. 094301:110 (2004).
17.Hsu, J.-C. and Wu, T.-T., “Bleustein-Gulyaev-Shimizu Surface Acoustic Waves in Two-Dimensional Piezoelectric Phononic Crystals,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., 53, pp. 11691176 (2006).
18.Wu, C. Y., Chang, J. S. and Wu, K. C., “Analysis of Wave Propagation in Infinite Piezoelectric Plates,” Journal of Mechanics, 21, pp. 103108 (2005).
19.Wilm, M., Ballandras, S., Laude, V. and Pastureaud, T., “A Full 3D Plane-Wave-Expansion Model for 1–3 Piezoelectric Composite Structures,” J. Acoust. Soc. Am., 119, pp. 943952 (2002).
20.Sainidou, R. and Stefanou, N., “Guided and Quasiguided Elastic Waves in Phononic Crystal Slabs,” Phys. Rev. B, 73, pp. 184301:17 (2006).
21.Ashcroft, N. W. and Mermin, N. D., Solid State Physics, 1st Ed., Thomson, Learning, Brooks/Cole, United States, pp. 131145 (1976).
22.Cao, Y., Hou, Z. and Liu, Y., “Convergence Problem of Plane-Wave Expansion Method for Phononic Crystal,” Phys. Lett. A, 327, pp. 247253 (2004).
23.Li, L., “Use of Fourier Series in Analysis Discontinuous Periodic Structures,” J. Opt. Soc. Am., 13, pp. 18701876 (1996).
24.Shen, L. and He, S., “Analysis for the Convergence Problem of the Plane-Wave Expansion Method for Photonic Crystals,” J. Opt. Soc. Am. A, 19, pp. 10211024 (2002).
25.Lalanne, P., “Effective Properties and Band Structures of Lamellar Subwavelength Crystals: Plane-Wave Method Revisited,” Phys. Rev. B, 58, pp. 98019807 (1998).
26.Auld, B. A., Acoustic Fields and Waves in Solids. 2nd Ed., Krieger, , Malbar, FL, pp. 366379 (1990).
27.Sainidou, R., Stefanou, N. and Modinos, A., “Formation of Absolute Frequency Gaps in Three-Dimensional Solid Phononic Crystals,” Phys. Rev. B, 66, pp. 212301:14 (2002).
28.Zhao, H., Liu, Y., Wang, G., Wen, J., Yu, D., Han, X. and Wen, X., “Resonance Modes and Gap Formation in Two-Dimensional Solid Phononic Crystal,” Phys. Rev. B, 72, pp. 012301:14 (2005).

Keywords

Propagation of Lamb Waves in Phononic-Crystal Plates

  • J.-C. Hsu (a1) and T.-T. Wu (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed