İç Boşluklu Akustik Metamalzemelerin Homojenizasyonu ve İletim Kayıplarının Transfer Matris Metodu ile Belirlenmesi

Öz

Bu çalışmada, yüksek ses iletim kaybına sahip yalıtım malzemesi olarak kullanılmak üzere küresel iç boşluklu akustik metahücrelerden oluşan çeşitli akustik metamalzemeler tasarlanmıştır. Bu malzemelerin iletim kayıpları vizko-termal kayıplar ihmal edilerek transfer matris metodu (TMM) ile belirlenmiştir. Metamalzemelerin etkin empedans, kırılma indisi, yoğunluk ve sıkıştırılabilirlik (tersi Bulk modülü) gibi etkin ortam parametreleri etkin ortam homojenizasyonu ile elde edilmiştir. Metamalzemeleri oluşturan metahücrelerin sayısı, geometrik büyüklükleri, dizilim periyodikliği gibi topolojik unsurların iletim kaybı (TL) üzerindeki etkisi incelenerek metamalzemelerin frekans bölgelerine göre performansları ortaya konmuştur. Sunulan yöntemin doğruluğu sonlu elemanlar metodu (SEM) ile yapılan bir karşılaştırma ile gösterilmiştir. Çalışma ile TMM ile akustik metamalzeme tasarımı ve analizleri ve etkin ortam homojenizasyonu ile etkin parametrelerin elde edilmesi gibi konular detaylı bir şekilde sunulmuştur.

Anahtar Kelimeler

• Akustik metamalzeme,transfer matris yöntemi,etkin ortam teorisi,etkin parametreler

Homogenization of In-line Cavity Based Acoustic Metamaterials and The Determination of Transmission Losses via Transfer Matrix Method

Öz

In this study, a variety of acoustic metamaterials consisting of in-line cavity based metacells are designed, for use as insulation material with high sound transmission loss. The transmission losses of these materials were determined by the transfer matrix method (TMM) with neglecting visco-thermal losses. Effective medium parameters such as effective impedance, refractive index, density and compressibility (inverse of Bulk modulus) of the metamaterials are obtained by effective medium homogenization. The effects of number of metacells, geometric size and the periodicity of the elements on the transmission loss (TL) are examined, and the performance of the metamaterials regarding frequency domain is discussed. The accuracy of the present method is demonstrated by finite element method. In the study, the topological issues such as acoustic metamaterial design and analysis and obtaining effective parameters with effective medium homogenization using the TMM, are presented in detail.

Anahtar Kelimeler

• Acoustic metamaterials,transfer matrix method,effective medium theory,effective parameters

Kaynakça

1. Veselago, V. G. 1968. The electrodynamics of substances with simultaneously negative values of μ and ε, Soviet Physics Uspekhi, 10, 4, 509-514. DOI:10.1070/PU1968v010n04ABEH003699 Ambati, M., Fang, N., Sun, C., Zhang, X. 2007. Surface resonant states and superlensing in acoustic metamaterials, Physical Review B, 75(19), 195447. DOI: 10.1103/PhysRevB.75.195447Guenneau, S., Movchan, A., Pétursson, G., Ramakrishna, S. A. 2007. Acoustic metamaterials for sound focusing and confinement, New Journal of physics, 9(11), 399. DOI: 10.1088/1367-2630/9/11/399Popa, B. I., Zigoneanu, L., Cummer, S. A. 2011. Experimental acoustic ground cloak in air, Physical review letters, 106(25), 253901. DOI:10.1103/PhysRevLett.106.253901Cheng, Y., Yang, F., Xu, J. Y., Liu, X. J. 2008. A multilayer structured acoustic cloak with homogeneous isotropic materials, Applied Physics Letters, 92(15), 151913. DOI: 10.1063/1.2903500Cummer, S. A., Popa, B. I., Schurig, D., Smith, D. R., Pendry, J., Rahm, M., Starr, A. 2008. Scattering theory derivation of a 3D acoustic cloaking Shell, Physical review letters, 100(2), 024301. DOI: 10.1103/PhysRevLett.100.024301Farhat, M., Guenneau, S., Enoch, S., Movchan, A. B. 2009. Cloaking bending waves propagating in thin elastic plates, Physical Review B, 79(3), 033102. DOI: 10.1103/PhysRevB.79.033102Zhang, X., Liu, Z. 2004. Negative refraction of acoustic waves in two-dimensional phononic crystals, Applied Physics Letters, 85(2), 341-343. DOI: 10.1063/1.1772854Liu, Z., Zhang, X., Mao, Y., Zhu, Y. Y., Yang, Z., Chan, C. T., Sheng, P. 2000. Locally resonant sonic materials, Science, 289(5485), 1734-1736. DOI: 10.1126/science.289.5485.1734Zhao, H., Liu, Y., Wang, G., Wen, J., Yu, D., Han, X., Wen, X. 2005. Resonance modes and gap formation in a two-dimensional solid phononic crystal, Physical Review B, 72(1), 012301. DOI: 10.1103/PhysRevB.72.012301Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C., Zhang, X. 2006. Ultrasonic metamaterials with negative modulus, Nature materials, 5(6), 452-456. DOI: 10.1038/nmat1644Hu, X., Ho, K. M., Chan, C. T., Zi, J. 2008. Homogenization of acoustic metamaterials of Helmholtz resonators in fluid, Physical Review B, 77(17), 172301. DOI: 10.1103/PhysRevB.77.172301Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G., Kim, C. K. 2009. Acoustic metamaterial with negative modulus, Journal of Physics: Condensed Matter, 21(17), 175704. DOI: 10.1088/0953-8984/21/17/175704Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G., Kim, C. K. 2009. Acoustic metamaterial with negative density, Physics letters A, 373(48), 4464-4469. DOI: 10.1016/j.physleta.2009.10.013Yang, Z., Mei, J., Yang, M., Chan, N. H., Sheng, P. 2008. Membrane-type acoustic metamaterial with negative dynamic mass, Physical review letters, 101(20), 204301. DOI: 10.1103/PhysRevLett.101.204301Yao, S., Zhou, X., Hu, G. 2008. Experimental study on negative effective mass in a 1D mass–spring system, New Journal of Physics, 10(4), 043020. DOI: 10.1088/136-2630/10/4/043020Croënne, C., Lee, E. J. S., Hu, H., Page, J. H. 2011. Band gaps in phononic crystals: Generation mechanisms and interaction effects, AIP Advances, 1(4), 041401. DOI: 10.1063/1.3675797Chen, Y., Wang, L. 2014. Periodic co-continuous acoustic metamaterials with overlapping locally resonant and Bragg band gaps, Applied Physics Letters, 105(19), 191907. DOI: 10.1063/1.4902129Krushynska, A. O., Miniaci, M., Bosia, F., Pugno, N. M. 2017. Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials, Extreme Mechanics Letters, 12, 30-36. DOI: 10.1016/j.eml.2016.10.004Li, J., Chan, C. T. 2004. Double-negative acoustic metamaterial, Physical Review E, 70(5), 055602. DOI: 10.1103/PhysRevE.70.055602Ding, Y., Liu, Z., Qiu, C., Shi, J. 2007. Metamaterial with simultaneously negative bulk modulus and mass density, Physical review letters, 99(9), 093904. DOI: 10.1103/PhysRevLett.99.093904Cheng, Y., Xu, J. Y., Liu, X. J. 2008. One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus, Physical Review B, 77(4), 045134. DOI: 10.1103/PhysRevB.77.045134Bongard, F., Lissek, H., Mosig, J. R. 2010. Acoustic transmission line metamaterial with negative/zero/positive refractive index, physical Review B, 82(9), 094306. DOI: 10.1103/PhysRevB.82.094306Munjal, M.L. 1987. Acoustics of ducts and mufflers with applications to exhaust and ventilation system design, Wiley Interscience Publication, Bangolore. A.M. Nicolson, G. Ross. 1970. Measurement of intrinsic properties of materials by time domain technique, IEEE Transactions on Instrumentation and Measurement, 19 (11) 377-382. DOI: 10.1109/TIM.1970.4313932W.B. Weir. 1974. Automatic measurement of complex dielectric constant and permeability at microwave frequencies, Proceedings of the IEEE, 62(1), 33-36. DOI: 10.1109/PROC.1974.9382Szabo, Zs, Park G, Hedge R, Li E. 2010. A unique extraction of metamaterial parameters based on Kramers-Kronig relationship, IEEE Trans Microwave Theory and Technology, 58(10) 2646-2653. DOI: 10.1109/TMTT.2010.2065310Fokin, V., Ambati, M., Sun, C., Zhang, X. 2007. Method for retrieving effective properties of locally resonant acoustic metamaterials, Physical review B, 76(14), 144302. DOI: 10.1103/PhysRevB.76.144302Chen, X., Grzegorczyk, T. M., Wu, B. I., Pacheco Jr, J., Kong, J. A. 2004. Robust method to retrieve the constitutive effective parameters of metamaterials, Physical Review E, 70(1), 016608. DOI: 10.1103/PhysRevE.70.016608Theocharis G., Richoux O. Romero G.V., Merkel A, Tournat V. 2014. Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures, New Journal of Physics, 16, 093017. DOI: 10.1088/1367-2630/16/9/093017Molerón M., Serra-Garcia M., Daraio C. 2016. Visco-thermal effects in acoustic metamaterials: from total transmission to total reflection and high absorption, New Journal of Physics, 18, 033003. DOI: 10.1088/1367-2630/18/3/033003