FONONİK KRİSTAL KAPLAMA İLE GÖSTERİ SALONLARINDA AKUSTİK YALITIMIN SAYISAL İNCELENMESİ

Periyodik üçgensel ahşap çıkıntılardan oluşan fononik kristal ile duvarların kaplanmasının ses yalıtımına katkı sağlayacağı sayısal hesaplarla gösterilmiştir. Ses yalıtımı fononik kristalin yüzey kipleri ile gerçekleştirilmektedir. Sonlu Elemanlar Yöntemi ile yürütülen band yapısı hesapları fononik kristal periyodu 25 cm, ahşap et kalınlığı 15 mm ve üçgen tepe açısı 60 derece iken tepe frekansı 553 Hz olan yüzey bandını göstermektedir. Yüzey kiplerinin üçgenler arasındaki düzlüklerde yerelleştiği yüzey bandı 440 Hz frekansındaki akort notasını kapsamaktadır. Durağan Sonlu Elemanlar analizleri yaklaşık olarak 300 Hz ile 550 Hz arasında yüzey ile küçük açılar yaparak gelen düzlem dalgaların az yansıma ile ve saçılmadan yüzeyde kılavuzlanabildiğini göstermiştir. Kılavuzlama 440 Hz frekansında 30 dereceye kadar olan geliş açılarında sağlanabilmektedir

Anahtar Kelimeler:

Akustik yalıtım, Fononik kristal, Yüzey kipi, Sonlu Elemanlar Yöntemi

NUMERICAL INVESTIGATION OF ACOUSTIC ISOLATION IN PERFORMANCE HALLS THROUGH COVERING WITH PHONONIC CRYSTALS

Sound isolation via covering walls with phononic crystal composed of periodic triangular wooden protrusions is demonstrated through numerical calculations. Sound isolation is achieved by surface modes of the phononic crystal. Band structure calculations through the Finite Element Method revealed a surface band with a maximum of 553 Hz when the periodicity, wall thickness and triangle apex angle are 25 cm, 15 mm and 60 degrees, respectively. Surface band the modes of which are localized in the flat regions between triangles covers the accord frequency at 440 Hz. Stationary Finite Element analyses demonstrate that plane waves with frequency between approximately 300 Hz and 550 Hz incident at small angles with the surface can be guided over the surface with low reflection and scattering. Guiding at 440 Hz can be achieved up to 30 degrees angle of incidence

Keywords:

Acoustic isolation, Phononic crystal, surface mode,

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Mehta, M., Johnson, J., Rocafort, J. Principles and Design, Prentice Hall. Maldovan, M. 2013. Sound and heat revolutions in phononics, Nature, Cilt. , Doi:10.1038/nature12608
Kushwaha, M.S., Halevi, P., Dobrzynski, L., Djafari-Rouhani, B. Acoustic band structure of periodic elastic composites, Physical Review Letters, Cilt. 71, No. 13, s. https://doi.org/10.1103/PhysRevLett. 2022
Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzynski, L., Djafari- Rouhani, B. 1994. Theory of acoustic band structure of periodic elastic composites, Physical Review B, Cilt. , https://doi.org/10.1103/PhysRevB.49 2313
Sainidou, R., Stefanou, N., Modinos, A. 2002. Formation of absolute frequency gaps in three-dimensional solid phononic crystals, Physical
Review B, Cilt. 66, No. 21, s. 212301. DOI: https://doi.org/10.1103/PhysRevB.66 212301
Vasseur, J., Deymier, P.A., Djafari- Rouhani, B., Pennec, Y., Hladky- Hennion, A. 2008. Absolute forbidden bands and waveguiding in two- dimensional phononic crystal plates,
Physical Review B, Cilt. 77, No.8, s. https://doi.org/10.1103/PhysRevB.77 085415
Martínez-Sala, R., Rubio, C., García- Raffi, L. M., Sánchez-Pérez, J. V., Sánchez-Pérez, E.A., Llinares, J. 2006.
Control of noise by trees arranged like sonic crystals, Journal of Sound and Vibration, Cilt. 291, No. 1, s. 100-106. DOI: http://dx.doi.org/10.1016/j.jsv.2005. 030
Wu, T.T., Huang, Z.G., Tsai, T.C., Wu, T.C. 2008. Evidence of complete band gap and resonances in a plate with periodic stubbed surface, Applied
Physics Letters, Cilt. 93, No. 11, s. DOI: 10.1063/1.2970992
Tanaka, Y., Tomoyasu, Y., Tamura, S.I. 2000. Band structure of acoustic waves in phononic lattices: Two- dimensional composites with large acoustic mismatch, Physical Review B, Cilt. 62, No. 11, s. 7387. DOI: https://doi.org/10.1103/PhysRevB.62 7387
Gorishnyy, T., Ullal, C.K., Maldovan, M., Fytas, G., Thomas, E. Hypersonic phononic crystals, Physical Review Letters, Cilt. 94, No. , https://doi.org/10.1103/PhysRevLett. 115501 DOI: s. DOI:
Gomopoulos, N., Maschke, D., Koh, C., Thomas, E., Tremel, W., Butt, H.J., Fytas, G. 2010. One-dimensional hypersonic phononic crystals, Nano
Letters, Cilt. 10, No. 3, s. 980-984. DOI: 1021/nl903959r
Maldovan M, Narrow low- frequency management Physical Review Letters, Cilt. 110, No. , 2013, s.025902.
Theoretical thermocrystals control heat like sound, MRS Bulletin, Cilt. 38, No. 03, 2013, s.200.
Lacatena, V., Haras, M., Robillard. J. F., Monfray, S., Skotnicki, T., Dubois, E. 2015. Toward quantitative modeling thermocrystals, Letters, Cilt. 106, No. 11, s.114104. DOI: http://dx.doi.org/10.1063/1.4915619
Miyashita, T., Inoue, C. 2001. Numerical transmission properties of sonic crystals by finite- difference
Japanese Journal of Applied Physics, Cilt. 40, No. 5S, s.3488. DOI: http://dx.doi.org/10.1143/JJAP.40.34
Miyashita, T. 2005. Sonic crystals and sonic wave-guides, Measurement
Science and Technology, Cilt. 16, No. 5, s. http://dx.doi.org/10.1088/0957- /16/5/R01
Hsiao, F.L., Khelif, A., Moubchir, H., Choujaa, A., Chen, C.C., Laude, V. complete band gap of a phononic crystal slab, Physical Review E, Cilt. 76, No. https://doi.org/10.1103/PhysRevE.76 056601
Vasseur, J., Hladky-Hennion, A. C., Djafari-Rouhani, B., Duval, F., Dubus, B., Pennec, Y., Deymier, P.A. 2007. Waveguiding and heat thermocrystals, Palucka T, Nano Focus: of silicon Applied Physics investigations of and waveguide time-domain method, R47. DOI: Waveguiding inside the , s.056601. DOI: in two-dimensional piezoelectric phononic crystal plates,
Journal of Applied Physics, Cilt. 101, No. http://dx.doi.org/10.1063/1.2740352
Benchabane, S., Djafari-Rouhani, B., Laude, V. 2004. Guiding and bending of acoustic waves in highly confined phononic crystal waveguides, Applied
Physics Letters, Cilt. 84, No. 22, s.4400-4402. http://dx.doi.org/10.1063/1.1757642
Wu, F., Hou, Z., Liu, Z., Liu, Y. 2001.
Point defect states in two-dimensional phononic crystals, Physics Letters A, Cilt. 292, No. 3, s.198-202. DOI: http://dx.doi.org/10.1016/S0375- (01)00800-3 Wu, F., Liu, Z., Liu, Y. 2004.
Splitting and tuning characteristics of the point defect modes in two- dimensional Physical Review E, Cilt. 69, No. 6, s.066609. 1103/PhysRevE.69.066609
Zhao, D., Liu, Z., Qiu, C., He, Z., Cai, F., Ke, M. 2007. Surface acoustic waves in two-dimensional phononic crystals:
Dispersion relation and the eigenfield distribution of surface modes, Physical Review B, Cilt. 76, No. 14, s.144301. DOI: https://doi.org/10.1103/PhysRevB.76 144301 DOI: Khelif, A., Choujaa, A., DOI: phononic crystals, DOI:
Jia, H., Ke, M., He, Z., Peng, S., Liu, G., Mei, X., Liu, Z. 2009. Experimental demonstration of surface acoustic waves in two-dimensional phononic crystals with fluid background, Journal of Applied Physics, Cilt. 106, No. 4, s.044512. http://dx.doi.org/10.1063/1.3200964
Cicek, A., Gungor, T., Kaya, O.A., Ulug, B. 2015. Guiding airborne sound through surface modes of a two- dimensional phononic crystal, Journal of Physics D: Applied Physics, Cilt. 48, No. DOI: , s.235303. DOI: s.78-86. DOI: acoustic waves in crystal, phononic DOI: , s.255301. DOI: