現今世界上越來越多國家開始關注噪音污染的問題近年來，聲學超穎材料(MAMs)被發現可以有效的阻隔低頻範圍中波的傳遞。本文中將對一些我們設計的結構進行探討，在特定頻率下當聲音穿過結構物時會造成穿透損失，藉此來抑制噪音的傳遞。我們利用有限元素多物理耦合的分析軟體 COMSOL Multiphysics 5.0 對附加半環形質量與穿孔薄膜來進行聲音穿透損失的研究。透過許多物理現象的分析，包含:共振時的模態圖、有效質量密度、空氣的速度場…等，來了解聲音穿透損失的形成原因。此外也特別的對附著半環形質量的偏心率，孔半徑和薄膜預應力等微觀結構的影響因素進行參數研究，並且用阻抗管進行聲音損失實驗，將模擬與實驗結果相互比對及驗證。

Noise pollution is an issue of growing concern in the world. Acoustic membrane type metamaterials (MAMs) has been proven useful in blocking sound waves in the low frequency regime. In this thesis, I present some new designs of acoustic metamaterials. The finite element software COMSOL Multiphysics 5.0 is used to study sound transmission loss of the proposed structures (membrane with semi-ring masses and a perforated membrane-ring structure). To understand the physics behind the transport properties, resonance mode shape, effective mass density, air velocity field are also investigated. Moreover, parameter studies including eccentricity of the attached ring masses, orifice radius and pre-tension of the membrane on sound transmission loss are examined. It is found that FE results are in good agreement with the experimental results.

References

[1] H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak", Phys. Rev. Lett. 99, 063903 (2007).
[2] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity", Phys. Rev. Lett. 84, 4184-4187 (2000).
[3] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures", Phys. Rev. Lett. 76, 4773-4776 (1996).
[4] R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction", Sci. 292, 77-79 (2001).
[5] J. B. Pendry, "Negative refraction makes a perfect lens", Phys. Rev. Lett. 85, 3966-3969 (2000).
[6] J. B. Pendry, "Negative refraction", Contem. Phys. 45, 191-202 (2004).
[7] Z. Liu, C. T. Chan, and P. Sheng, "Analytic model of phononic crystals with local resonances", Phys. Rev. B. 71, 014103 (2005).
[8] J. S. Chen, Y. B. Chen, H. W. Chen, and Y. C. Yeh, "Bandwidth broadening for transmission loss of acoustic waves using coupled membrane-ring structure," Mater. Res. Express. 3, 105801 (2016).
[9] M. Yang, G. Ma, Z. Yang, and P. Sheng, "Coupled membranes with doubly negative mass density and bulk modulus", Phys. Rev. Lett. 110, 134301 (2013).
[10] Z. Yang, J. Mei, M. Yang, N. H. Chan, and P. Sheng, "Membrane-type acoustic metamaterial with negative dynamic mass", Phys. Rev. Lett. 101, 204301 (2008).
[11] C. J. Naify, C. M. Chang, G. McKnight, F. Scheulen, and S. Nutt, "Membrane-type metamaterials: Transmission loss of multi-celled arrays", J. Appl. Phys. 109, 104902 (2011).
[12] Z. Y. Liu, X. X. Zhang, Y. W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan, and P. Sheng, "Locally resonant sonic materials", Sci. 289, 1734-1736 (2000).
[13] M. Yang, G. Ma, Z. Yang, and P. Sheng, "Coupled membranes with doubly negative mass density and bulk modulus," Phys. Rev. Lett. 110, 134301 (2013).
[14] S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, "Acoustic metamaterial with negative modulus" J. Phys. Condens. Matter. 21, 175704 (2009).
[15] G. Ma, M. Yang, Z. Yang, and P. Sheng, "Acoustic double negativity with coupled-membrane metamaterial", Proc. Mtgs. Acoustic. 19, 065039-065039 (2013).
[16] Y. Zhang, J. Wen, Y. Xiao, X. Wen, and J. Wang, "Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials", Phys. Rev. A. 376, 1489-1494 (2012).
[17] Z. Yang, J. Mei, M. Yang, N. H. Chan, and P. Sheng, "Membrane-type acoustic metamaterial with negative dynamic mass", Phys. Rev. Lett. 101, 204301 (2008).
[18] C. J. Naify, C.M. Chang, G. McKnight, and S. Nutt, "Transmission loss and dynamic response of membrane-type locally resonant acoustic metamaterials", J. Appl. Phys.108, 114905 (2010).
[19] H. Tian, X. Wang, and Y. h. Zhou, "Theoretical model and analytical approach for a circular membrane–ring structure of locally resonant acoustic metamaterial", Appl. phys. A. 114, 985-990 (2013).
[20] C. J. Naify, C.M. Chang, G. McKnight, and S. Nutt, "Transmission loss of membrane-type acoustic metamaterials with coaxial ring masses", J. Appl. Phys. 110, 124903 (2011).
[21] C. J. Naify, C.M. Chang, G. McKnight, F. Scheulen, and S. Nutt, "Membrane-type metamaterials: Transmission loss of multi-celled arrays", J. Appl. Phys. 109, 104902 (2011).
[22] C. J. Naify, C. M. Chang, G. McKnight, and S. R. Nutt, "Scaling of membrane-type locally resonant acoustic metamaterial arrays", J. Acoust. Soc. Am. 132, 2784-2792 (2012).
[23] Y. Y. Chen, G. L. Huang, X. M. Zhou, G. K. Hu, and C. T. Sun, "Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: Plate model", J. Acoust. Soc. Am. 136, 2926-2934 (2014).
[24] Y. Y. Chen, G. L. Huang, X. M. Zhou, G. K. Hu, and C. T. Sun, "Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: Membrane model", J. Acoust. Soc. Am. 136, 969-979 (2014).
[25] J. Mei, G. Ma, M. Yang, Z. Yang, W. Wen, and P. Sheng, "Dark acoustic metamaterials as super absorbers for low-frequency sound", Nat. Commun. 3, 756 (2012).
[26] F. Langfeldt, H. Kemsies, W. Gleine, and O. von. Estorff, "Perforated membrane-type acoustic metamaterials", Phy. Let. A. 381, 1457-1462 (2017).
[27] M. Oudich, X. Zhou, and M. B. Assouar, "General analytical approach for sound transmission loss analysis through a thick metamaterial plate", J. Appl. Phys. 116, 193509 (2014).
[28] Y. H. Kim, “Sound propagation”, Wiley (2010).
[29] C. E. Wilson, “Noise control: measurement, analysis, and control of sound and vibration”, Krieger (1994).
[30] M. L. Dong, “The research on sound transmission loss measuring system of acoustic material”, thesis, Shanghai Jiao Tong University, Shanghai, China (2008).
[31] ASTM E2611-09, “Standard test method for measurement of normal incidence sound transmission of acoustical materials based on the transfer matrix method”, American Society for Testing and Materials (2009).

[32]M. Suhanek, K. Jambrosic, and H. Domitrovic, “Student project of building an impedance tube”, J. Acoust. Soc. Am. 123, 3616 (2008).
[33] COMSOL, “Acoustics Module Model Library Manual,” COMSOL 5.0 (2014).
[34] H. W. Chen, “Sound Transmission of Coupled Membrane-Ring Structure: FE Analysis,” M. S. Thesis, National Cheng Kung University, Tainan, Taiwan (2016).
[35] Y. C. Yeh, “Sound Transmission of Coupled Membrane-Ring Structure: Experiment Analysis,” M. S. Thesis, National Cheng Kung University, Tainan, Taiwan (2016).