Analysis of Wave Propagation in Two-dimensional Phononic Crystals with Hollow Cylinders
Large full frequency band gaps of surface and bulk
acoustic waves in two-dimensional phononic band structures with
hollow cylinders are addressed in this paper. It is well-known that
absolute frequency band gaps are difficultly obtained in a band
structure consisted of low-acoustic-impedance cylinders in
high-acoustic-impedance host materials such as PMMA/Ni band
structures. Phononic band structures with hollow cylinders are
analyzed and discussed to obtain large full frequency band gaps not
only for bulk modes but also for surface modes. The tendency of
absolute frequency band gaps of surface and bulk acoustic waves is
also addressed by changing the inner radius of hollow cylinders in this
paper. The technique and this kind of band structure are useful for
tuning the frequency band gaps and the design of acoustic waveguides.
[1] S. G. Johnson and J. D. Joannopoulos, PHOTONIC CRYSTALS: The
road from theory to practice, Kluwer academic publishers, Boston, 2003.
[2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:
Molding the flow of light, Princeton University Press, Princeton, NJ,
1995.
[3] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani,
"Acoustic Band Structure of Periodic Elastic Composites," Phys. Rev.
Lett. 71, 2022, 1993.
[4] J. O. Vasseur, P. A. Deymier, G. Frantziskonis, G. Hong, B.
Djafari-Rouhani, and L. J. Dobrzynski, "Experimental evidence for the
existence of absolute acoustic band gaps in two-dimensional periodic
composite media," J. Phys.: Condens. Matter 10, 6051, 1998.
[5] C. Goffaux and J. P. Vigneron, "Theoretical study of a tunable phononic
band gap system," Phys. Rev. B 64, 075118, 2001.
[6] M. Kafesaki and E. N. Economou, "Multiple-scattering theory for
three-dimensional periodic acoustic composites," Phys. Rev. B 60, 11993,
1999.
[7] I. E. Psarobas and N. Stefanou, "Scattering of elastic waves by periodic
arrays of spherical bodies," Phys. Rev. B 62, 278, 2000.
[8] Z. Liu, C. T. Chan, and P. Sheng, "Elastic wave scattering by periodic
structures of spherical objects: Theory and experiment," Phys. Rev. B 62,
2446, 2000.
[9] D. Garica-Pablos, M. Sigalas, F. R. Montero de Espinosa, M. Torres, M.
Kafesaki, and N. Garcia, "Theory and Experiments on Elastic Band gaps,"
Phys. Rev. Lett. 84, 4349, 2000.
[10] J. H. Sun and T.-T. Wu, "Analyses of mode coupling in joined parallel
phononic crystal waveguides," Phys. Rev. B 71, 174303, 2005.
[11] Y. Tanaka and S. Tamura, "Surface acoustic waves in two-dimensional
periodic elastic structures," Phys. Rev. B 58, 7958, 1998.
[12] T.-T. Wu, Z. G. Huang, and S. Lin, "Surface and bulk acoustic waves in
two-dimensional phononic crystals consisting of materials with general
anisotropy," Phys. Rev. B 69, 094301, 2004.
[13] Z. G. Huang and T.-T. Wu, "Temperature effects on bandgaps of surface
and bulk acoustic waves in two-dimensional phononic crystals," IEEE
Trans. Ultrason. Ferroelectr. Freq. Control 52, 365, 2005.
[14] T.-T. Wu and Z. G. Huang, "Level repulsion of bulk acoustic waves in
composite materials," Phys. Rev. B 70, 214304, 2004.
[15] T.-T. Wu, Z. C. Hsu, and Z. G. Huang, "Band gaps and the
Electromechanical coupling coefficient of a surface acoustic wave in a
two-dimensional piezoelectric phononic crystal," Phys. Rev. B 71,
064303, 2005.
[16] V. Laude, M. Wilm, S. Benchabane, A. Khelif, "Full band gap for surface
acoustic waves in a piezoelectric phononic crystal," Phys. Rev. E 71,
036607, 2005.
[1] S. G. Johnson and J. D. Joannopoulos, PHOTONIC CRYSTALS: The
road from theory to practice, Kluwer academic publishers, Boston, 2003.
[2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals:
Molding the flow of light, Princeton University Press, Princeton, NJ,
1995.
[3] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani,
"Acoustic Band Structure of Periodic Elastic Composites," Phys. Rev.
Lett. 71, 2022, 1993.
[4] J. O. Vasseur, P. A. Deymier, G. Frantziskonis, G. Hong, B.
Djafari-Rouhani, and L. J. Dobrzynski, "Experimental evidence for the
existence of absolute acoustic band gaps in two-dimensional periodic
composite media," J. Phys.: Condens. Matter 10, 6051, 1998.
[5] C. Goffaux and J. P. Vigneron, "Theoretical study of a tunable phononic
band gap system," Phys. Rev. B 64, 075118, 2001.
[6] M. Kafesaki and E. N. Economou, "Multiple-scattering theory for
three-dimensional periodic acoustic composites," Phys. Rev. B 60, 11993,
1999.
[7] I. E. Psarobas and N. Stefanou, "Scattering of elastic waves by periodic
arrays of spherical bodies," Phys. Rev. B 62, 278, 2000.
[8] Z. Liu, C. T. Chan, and P. Sheng, "Elastic wave scattering by periodic
structures of spherical objects: Theory and experiment," Phys. Rev. B 62,
2446, 2000.
[9] D. Garica-Pablos, M. Sigalas, F. R. Montero de Espinosa, M. Torres, M.
Kafesaki, and N. Garcia, "Theory and Experiments on Elastic Band gaps,"
Phys. Rev. Lett. 84, 4349, 2000.
[10] J. H. Sun and T.-T. Wu, "Analyses of mode coupling in joined parallel
phononic crystal waveguides," Phys. Rev. B 71, 174303, 2005.
[11] Y. Tanaka and S. Tamura, "Surface acoustic waves in two-dimensional
periodic elastic structures," Phys. Rev. B 58, 7958, 1998.
[12] T.-T. Wu, Z. G. Huang, and S. Lin, "Surface and bulk acoustic waves in
two-dimensional phononic crystals consisting of materials with general
anisotropy," Phys. Rev. B 69, 094301, 2004.
[13] Z. G. Huang and T.-T. Wu, "Temperature effects on bandgaps of surface
and bulk acoustic waves in two-dimensional phononic crystals," IEEE
Trans. Ultrason. Ferroelectr. Freq. Control 52, 365, 2005.
[14] T.-T. Wu and Z. G. Huang, "Level repulsion of bulk acoustic waves in
composite materials," Phys. Rev. B 70, 214304, 2004.
[15] T.-T. Wu, Z. C. Hsu, and Z. G. Huang, "Band gaps and the
Electromechanical coupling coefficient of a surface acoustic wave in a
two-dimensional piezoelectric phononic crystal," Phys. Rev. B 71,
064303, 2005.
[16] V. Laude, M. Wilm, S. Benchabane, A. Khelif, "Full band gap for surface
acoustic waves in a piezoelectric phononic crystal," Phys. Rev. E 71,
036607, 2005.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:59664", author = "Zi-Gui Huang and Tsung-Tsong Wu", title = "Analysis of Wave Propagation in Two-dimensional Phononic Crystals with Hollow Cylinders", abstract = "Large full frequency band gaps of surface and bulk
acoustic waves in two-dimensional phononic band structures with
hollow cylinders are addressed in this paper. It is well-known that
absolute frequency band gaps are difficultly obtained in a band
structure consisted of low-acoustic-impedance cylinders in
high-acoustic-impedance host materials such as PMMA/Ni band
structures. Phononic band structures with hollow cylinders are
analyzed and discussed to obtain large full frequency band gaps not
only for bulk modes but also for surface modes. The tendency of
absolute frequency band gaps of surface and bulk acoustic waves is
also addressed by changing the inner radius of hollow cylinders in this
paper. The technique and this kind of band structure are useful for
tuning the frequency band gaps and the design of acoustic waveguides.", keywords = "Phononic crystals, Band gap, SAW, BAW.", volume = "3", number = "5", pages = "578-5", }