Band Structures in Two-Dimensional Phononic Crystals with Periodic S-Shaped Slot

Hirsekorn, M.: Small-size sonic crystals with strong attenuation bands in the audible frequency range. Appl. Phys. Lett. 84, 3364–3366 (2004)

Qiu, C., Liu, Z., Shi, J., Chan, C.T.: Directional acoustic source based on the resonant cavity of two-dimensional phononic crystals. Appl. Phys. Lett. 86, 224105 (2005)

Mohammadi, S., Eftekhar, A.A., Khelif, A., Hunt, W.D., Adibi, A.: Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates. Appl. Phys. Lett. 92, 221905 (2008)

Wu, T.-T., Chen, Y.-T., Sun, J.-H., Lin, S.-C.S., Huang, T.J.: Focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal plate. Appl. Phys. Lett. 98, 171911 (2011)

Leamy, M.J.: Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices. J. Sound. Vib. 331, 1580–1596 (2012)

Larabi, H., Pennec, Y., Djafari-Rouhani, B., Vasseur, J.O.: Multicoaxial cylindrical inclusions in locally resonant phononic crystals. Phys. Rev. E 75, 066601 (2007)

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

Vasseur, J.O., Morvan, B., Tinel, A., Swinteck, N., Hladky-Hennion, A.C., Deymier, P.A.: Experimental evidence of zero-angle refraction and acoustic wave-phase control in a two-dimensional solid/solid phononic crystal. Phys. Rev. B 86, 134305 (2012)

Lai, Y., Wu, Y., Sheng, P., Zhang, Z.-Q.: Hybrid elastic solids. Nat Mater. 10, 620–624 (2011)

Yu, K., Chen, T., Wang, X.: Large band gaps in two-dimensional phononic crystals with neck structures. J. Appl. Phys. 113, 134901 (2013)

Qiu, C., Liu, Z., Mei, J., Shi, J.: Mode-selecting acoustic filter by using resonant tunneling of two-dimensional double phononic crystals. Appl. Phys. Lett. 87, 104101 (2005)

Khelif, A., Choujaa, A., Benchabane, S., Djafari-Rouhani, B., Laude, V.: Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. Appl. Phys. Lett. 84, 4400–4402 (2004)

Lee, C.-Y., Leamy, M.J., Nadler, J.H.: Frequency band structure and absorption predictions for multi-periodic acoustic composites. J. Sound Vib. 329, 1809–1822 (2010)

Xiao, Y., Wen, J., Wen, X.: Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators. J. Sound Vib. 331, 5408–5423 (2012)

Xiao, Y., Wen, J., Yu, D., Wen, X.: Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. J. Sound Vib. 332, 867–893 (2013)

Yudistira, D., Boes, A., Djafari-Rouhani, B., Pennec, Y., Yeo, L.Y., Mitchell, A., Friend, J.R.: Monolithic phononic crystals with a surface acoustic band gap from surface Phonon-Polariton coupling. Phys. Rev. Lett. 113, 215503 (2014)

Tanaka, Y., Tomoyasu, Y., Tamura, S.I.: Band structure of acoustic waves in phononic lattices: two-dimensional composites with large acoustic mismatch. Phys. Rev. B 62, 7387–7392 (2000)

Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. Science 289, 1734–1736 (2000)

Wang, G., Wen, X., Wen, J., Shao, L., Liu, Y.: Two-dimensional locally resonant phononic crystals with binary structures. Phys. Rev. Lett. 93, 154302 (2004)

Charles, C., Bonello, B., Ganot, F.: Propagation of guided elastic waves in 2D phononic crystals. Ultrasonics 44, e1209–e1213 (2006)

Cui, Z.Y., Chen, T.N., Chen, H.L., Su, Y.P.: Experimental and calculated research on a large band gap constituting of tubes with periodic narrow slits. Appl. Acoust. 70, 1087–1093 (2009)

Yu, K.P., Chen, T.N., Wang, X.P., Zhou, A.A.: Effect of the internal rib structure of the inclusions on the two-dimensional phononic crystal composed of periodic slotted tubes in air. Phys. B 407, 4287–4292 (2012)

Xu, Y.L., Tian, X.G., Chen, C.Q.: Band structures of two dimensional solid/air hierarchical phononic crystals. Phys. B 407, 1995–2001 (2012)

Gao, N., Wu, J.H., Yu, L.: Research on bandgaps in two-dimensional phononic crystal with two resonators. Ultrasonics 56, 287–293 (2015)

Li, Y., Chen, T., Wang, X., Yu, K., Song, R.: Band structures in two-dimensional phononic crystals with periodic Jerusalem cross slot. Phys. B 456, 261–266 (2015)

Qin, Q.-H.: Trefftz finite element method and its applications. Appl. Mech. Rev. 58, 316–337 (2005)

Qin, Q.H.: The Trefftz finite and boundary element method. WIT Press, Southampton (2000)