Fononik Kristal Kaplama ile Gösteri Salonlarında Akustik Yalıtımın Sayısal İncelenmesi

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.

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.

Kaynakça

[1] Mehta, M., Johnson, J., Rocafort, J. 1999. Architectural acoustics: Principles and Design, Prentice Hall.

[2] Maldovan, M. 2013. Sound and heat revolutions in phononics, Nature, Cilt. 503, No. 7475, s. 209-217. Doi:10.1038/nature12608

[3] Kushwaha, M.S., Halevi, P., Dobrzynski, L., Djafari-Rouhani, B. 1993. Acoustic band structure of periodic elastic composites, Physical Review Letters, Cilt. 71, No. 13, s. 2022. DOI: https://doi.org/10.1103/PhysRevLett. 71.2022

[4] Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzynski, L., DjafariRouhani, B. 1994. Theory of acoustic band structure of periodic elastic composites, Physical Review B, Cilt. 49, No. 4, s.2313. DOI: https://doi.org/10.1103/PhysRevB.49 .2313

[5] 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

[6] Vasseur, J., Deymier, P.A., DjafariRouhani, B., Pennec, Y., HladkyHennion, A. 2008. Absolute forbidden bands and waveguiding in twodimensional phononic crystal plates, Physical Review B, Cilt. 77, No.8, s. 085415. DOI: https://doi.org/10.1103/PhysRevB.77 .085415

[7] Martínez-Sala, R., Rubio, C., GarcíaRaffi, 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. 05.030

[8] 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. 111902. DOI: 10.1063/1.2970992

[9] Tanaka, Y., Tomoyasu, Y., Tamura, S.I. 2000. Band structure of acoustic waves in phononic lattices: Twodimensional composites with large acoustic mismatch, Physical Review B, Cilt. 62, No. 11, s. 7387. DOI: https://doi.org/10.1103/PhysRevB.62 .7387

[10] Gorishnyy, T., Ullal, C.K., Maldovan, M., Fytas, G., Thomas, E. 2005. Hypersonic phononic crystals, Physical Review Letters, Cilt. 94, No. 11, s. 115501. DOI: https://doi.org/10.1103/PhysRevLett. 94.115501

[11] 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: 10.1021/nl903959r

[12] Maldovan M, Narrow lowfrequency spectrum and heat management by thermocrystals, Physical Review Letters, Cilt. 110, No. 2, 2013, s.025902.

[13] Palucka T, Nano Focus: Theoretical thermocrystals control heat like sound, MRS Bulletin, Cilt. 38, No. 03, 2013, s.200.

[14] Lacatena, V., Haras, M., Robillard. J. F., Monfray, S., Skotnicki, T., Dubois, E. 2015. Toward quantitative modeling of silicon phononic thermocrystals, Applied Physics Letters, Cilt. 106, No. 11, s.114104. DOI: http://dx.doi.org/10.1063/1.4915619

[15] Miyashita, T., Inoue, C. 2001. Numerical investigations of transmission and waveguide properties of sonic crystals by finitedifference time-domain method, Japanese Journal of Applied Physics, Cilt. 40, No. 5S, s.3488. DOI: http://dx.doi.org/10.1143/JJAP.40.34 88

[16] Miyashita, T. 2005. Sonic crystals and sonic wave-guides, Measurement Science and Technology, Cilt. 16, No. 5, s. R47. DOI: http://dx.doi.org/10.1088/0957- 0233/16/5/R01

[17] Hsiao, F.L., Khelif, A., Moubchir, H., Choujaa, A., Chen, C.C., Laude, V. 2007. Waveguiding inside the complete band gap of a phononic crystal slab, Physical Review E, Cilt. 76, No. 5, s.056601. DOI: https://doi.org/10.1103/PhysRevE.76 .056601

[18] Vasseur, J., Hladky-Hennion, A. C., Djafari-Rouhani, B., Duval, F., Dubus, B., Pennec, Y., Deymier, P.A. 2007. Waveguiding in two-dimensional piezoelectric phononic crystal plates, Journal of Applied Physics, Cilt. 101, No. 11, s.114904. DOI: http://dx.doi.org/10.1063/1.2740352

[19] Khelif, A., Choujaa, A., 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. DOI: http://dx.doi.org/10.1063/1.1757642

[20] 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- 9601(01)00800-3

[21] Wu, F., Liu, Z., Liu, Y. 2004. Splitting and tuning characteristics of the point defect modes in twodimensional phononic crystals, Physical Review E, Cilt. 69, No. 6, s.066609. DOI: 10.1103/PhysRevE.69.066609

[22] 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

[23] 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. DOI: http://dx.doi.org/10.1063/1.3200964

[24] Cicek, A., Gungor, T., Kaya, O.A., Ulug, B. 2015. Guiding airborne sound through surface modes of a twodimensional phononic crystal, Journal of Physics D: Applied Physics, Cilt. 48, No. 23, s.235303. DOI: http://dx.doi.org/10.1088/0022- 3727/48/23/235303

[25] Cicek, A., Salman, A., Kaya, O.A., Ulug, B. 2015. Sharp bends of phononic crystal surface modes, Journal of Physics: Condensed Matter, Cilt. 27, No. 47, s.475003. DOI: 10.1088/0953-8984/27/47/475003

[26] Cicek, A., Salman, A., Kaya, O.A., Ulug, B. 2016. Phononic crystal surface mode coupling and its use in acoustic Doppler velocimetry, Ultrasonics, Cilt. 65, s.78-86. DOI: 10.1016/j.ultras.2015.10.017

[27] Cicek, A., Salman, A., Kaya, O.A., Ulug, B. 2015. Evanescent coupling between surface and linear-defect guided modes in phononic crystals, Journal of Physics D: Applied Physics, Cilt. 49, No. 3, s.035103. DOI: http://dx.doi.org/10.1088/0022- 3727/49/3/035103

[28] Laude, V., Wilm, M., Benchabane, S., Khelif, A. 2005. Full band gap for surface acoustic waves in a piezoelectric phononic crystal, Physical Review E, Cilt. 71, No. 3, s.036607. DOI: https://doi.org/10.1103/PhysRevE.71 .036607

[29] Salman, A., Kaya, O.A., Cicek, A., Ulug, B. 2015. Low-concentration liquid sensing by an acoustic Mach- Zehnder interferometer in a twodimensional phononic crystal, Journal of Physics D: Applied Physics, Cilt. 48, No. 25, s.255301. DOI: http://dx.doi.org/10.1088/0022- 3727/48/25/255301

[30] Beranek, L. L. ve Hidaka, T. 1998. Sound absorption in concert halls by seats, occupied and unoccupied, and by the hall's interior surfaces, The Journal of the Acoustical Society of America, Cilt. 104, s.3169. DOI: http://dx.doi.org/10.1121/1.423957

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