Dönen Kare Çubuklu İki Boyutlu Fononik Kristalin Dispersiyon Özellikleri

Yıl 2019, Cilt: 19 Sayı: 3, 536 - 543, 31.12.2019

Selami Palaz , Oral Oltulu , Amirullah M. Mamedov

https://doi.org/10.35414/akufemubid.577855

Öz

Bu çalışmada, bir kare
örgülü hava matrisinde yer alan kare şekilli saçılardan oluşan iki boyutlu
fononik kristallerin bant yapısı çalışıldı. Bant yapısı hesaplamaları için, bir
hava matrisindeki kare LiNbO₃ çubuklarından oluşan iki boyutlu bir
fononik kristal dikkate alındı. Kare çubukların yönelimlerinin akustik bant
aralıkları üzerindeki etkisi, iletim kaybı spektrumları, basınç alanı haritası
ve dağılım ilişkileri sonlu elemanlar yöntemi ve Bloch teoremi kullanılarak
hesaplandı. Bu yapı için maksimum bant aralığı 45° dönme açısında bulundu.
Sayısal sonuçlar, bant aralıklarının kare çubukların dönüş açısını değiştirerek
ayarlanabileceğini göstermektedir.

Anahtar Kelimeler

Akustik Dalgalar, Fononik Kristaller, Metamateryaller, Bant Aralıkları

Kaynakça

• Ang, L.Y.L., Koh, Y. K. and Lee, H.,2016. A potential for cabin noise control in automobiles and armored vehicles. International Journal of Applied Mechanics , 8(5), 1650072.
• Chen, A.L., Wang, Y.S., Guo, Y.F. and Wang, Z.D., 2008. Band structures of Fibonacci phononic quasicrystals. Solid State Communications, 145, 103-108.
• COMSOL AB, Stockholm, Sweden. COMSOL Multiphysics® v. 5.2. www.comsol.com.
• El-Naggar, S.A., Mostafa, S.I. and Rafat, N.H., 2011. Complete band gaps of phononic crystal plates with square rods. Ultrasonics, 52(4), 536-542.
• Haberman, M.R. and Guild, M.D., 2016. Acoustic Metamaterials. Physics Today, 69(6), 42–48.Haberman, M.R. and Norris, A.N., 2016. Acoustic Metamaterials. Acoustics Today, 12(3), 31–41.
• Hsu, J.C. and Wu, T.T., 2017. Lamb waves in binary locally resonant phononic plates with two dimensional lattices. Applied Physics Letters, 90, 201904.
• Kafesaki, M. and Economou, E.N., 1999. Multiple-scattering theory for three-dimensional periodic acoustic composites. Physical Review B, 60, 11993-12001.
• Khelif, A., Choujaa, A., Benchabane, S., Djafari-Rouhani, B. and Laude, V., 2004. Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. Applied Physics Letters, 84(22), 4400-4402.
• Kushwaha, M.S. and Halevi, P., 1994. Band-gap engineering in periodic elastic composites. Applied Physics Letters, 64(9), 1085–1087.
• Kushwaha, M.S., Halevi, P., Dobrzynski, L. and Djafari-Rouhani, B., 1993. Acoustic band structure of periodic elastic composites. Physical Review Letters, 71(13), 2022–2025.
• Kushwaha, M.S., 2016. The Phononic Crystals: An unending quest for tailoring acoustics. Modern Physics Letters B, 30(19), 1630004
• Li, F-L., Wang, Y-S., Zhang, C., “Bandgap calculation of two-dimensional mixed solid–fluid phononic crystals by Dirichlet-to-Neumann maps”, Physica Scripta, vol. 84, pp. 055402, 2011.
• Li, J., Zhang, Y.S. and Zhang, C., 2008. Finite element method for analysis of band structures of three dimensonal phononic crystals. 2008 IEEE International Ultrasonics Symposium Proceedings, vol. 1-4, 1468-1471.
• Li, X., Wu, F., Hu, H., Zhong, S. and Liu, Y., 2003. Large acoustic band gaps created by rotating square rods in two-dimensional periodic composites. Journal of Physics D: Applied Physics,m36, L15-L17.
• Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T. and Sheng, P., 2000. Locally resonant sonic materials. Science, 289(5485), 1734-1736.
• Lu, M.H., Feng, L. and Chen, Y.F., 2009. Phononic crystals and acoustic metamaterials. Materials Today, 12(12), 34-42.
• Júnior, E.J.P. de M. and Santos, J.M.C.D., 2017. Band Structure in Carbon Nanostructure Phononic Crystals. Materials Research, 20(2), 555-571.
• Meseguer, F., Holgado, M., Caballero, D., Benaches, N., Sánchez-Dehesa, J., López, C. And Llinares, J., 1999. Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal. Physical Review B, 59, 12169–12172.
• Montero de Espinosa, F.R., Jiménez, E. and Torres, M., 1998. Ultrasonic band gap in a periodic two-dimensional composite. Physical Review Letters, 80, 1208-1211.
• Pennec, Y., Rouhani, B.D., El Boudouti, E., Li, C., El Hassouani, Y., Vasseur et al, J.O., 2011. Band gaps and waveguiding in phoxonic silicon crystal slabs. Chinese Journal of Physics, 49, 100–110.
• Pennec, Y., Vasseur, J.O., Djafari-Rouhani, B., Dobrzyński, L. and Deymier, P.A., 2010. Two-dimensional phononic crystals: Examples and applications. Surface Science Reports, 65, 229-291.
• Sainidou, R., Stefanou, N. and Modinos, A., 2002. Formation of absolute frequency gaps in three-dimensional solid phononic crystals. Physical Review B, 66(21), 2012301.
• Sigalas, M.M. and Economou, E.N., 1992. Elastic and acoustic-wave band-structure. Journal of Sound and Vibration ,158(2), 377–382.
• Tanaka, Y., Tomoyasu, Y. and Tamura, S., 2000. Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch. Journal of Sound and Vibration, 62, 7387-7392.
• Vasseur, J. O., Deymier, P.A., Frantziskonis, G., Hong, G., DRouhani, B. and Dobrzynski, L., 1998. Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media. Journal of Physics: Condensed Matter, 10, 6051–6064.
• Wang, J., Xu ,X., Liu ,X. and Xu ,G., 2009. A tunable acoustic filter made by periodical structured materials. Applied Physics Letters, 94(18), 181908.
• Wang, X.H., Gu, B. Y., Li, Z.Y. and Yang, G.Z., 1999. Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices. Physical Review B, 60(16), 11417-11411.
• Wang, Y.Z., Li, F.M., Huang, W.H. and Wang, Y.S., 2007. Effects of inclusion shapes on the band gaps in two-dimensional piezoelectric phononic crystals. Journal of Physics: Condensed Matter, 19, 496204.
• Wilm, M., Khelif, A., Laude, V. and Ballandras, S., 2007. Design guidelines of 1-3 piezoelectric composites dedicated to ultrasound imaging transducers, based on frequency band-gap considerations. The Journal of the Acoustical Society of America, 122(2), 786-793.
• Wu, T.T., Wu, L.C. and Huang, Z.G., 2005. Frequency band-gap measurement of two-dimensional air/silicon phononic crystals using layered slanted finger interdigital transducers. Journal of Applied Physics, 97(9), 94916.
• Yu, D., Wen, J., Zhao, H., Liu, Y. and Wen, X., 2008. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. Journal of Sound and Vibration, 318(1-2), 193-205.