利用平面拉脹性超穎材料進行可調式聲波傳遞

Tunable Acoustic Wave Propagation using Plane Auxetic Metamaterial

10.6342/NTU201602850

林詩珊

聲學超穎材料 ； 拉脹性 ； 頻散關係 ； 能帶結構 ； 波傳行為 ； 可調頻 ； Acoustic metamaterial ； Auxetic ； Dispersion relation ； Band structure ； Wave propagation ； Tunable

國立臺灣大學工程科學及海洋工程學系學位論文

2016年

碩士

黃心豪

繁體中文

本文主要探討可調頻平面超穎材料之聲波傳遞行為。首先透過商用有限元素分析軟體進行分析模擬，針對一具拉脹性薄膜結構之超穎材料作週期性排列設定，分析其單元之能帶結構，因其結構拉脹特性，利用幾何變形將可能阻擋某些特定頻率下聲波通過，達到可調頻的效果。另外，亦透過聲學實驗觀察該特定頻率下的波傳衰減行為，並與模擬進行比較與相互映證，結果顯示該結構將能阻隔特定頻率範圍內的聲波傳遞。

A tunable planar auxetic metamaterial for controlling and filtering acoustic waves was investigated. In the study, the commercial finite element software package was utilized for numerical simulations. A planar auxetic structure was placed periodically, and its acoustic band structure was obtained. It was found that the bandages may appear in certain frequency range because of the geometric deformation of the auxetic structure. In addition, the wave attenuation behavior at a specific frequency was investigated experimentally, and the experimental results were compared with those obtained from numerical simulations. Both the numerical and experimental results showed that the planar auxetic structure is tunable for controlling the sound wave propagation and filtering the waves within a specific frequency range.

1. [1] 行政院勞工委員會勞工安全衛生研究所, 防護具選用技術手冊－防音防護具, 行政院勞工委員會勞工安全衛生研究所, 台北, 1995.
   連結：
2. [2] 林俊德, "噪音與健康," 工業安全衛生, p. 52-55, 1991.
   連結：
3. [3] V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Physics-Uspekhi, vol. 10, p. 509-514, 1968.
   連結：
4. [4] J. B. Pendry, "Negative refraction makes a perfect lens," Physical review letters, vol. 85, p. 3966, 2000.
   連結：
5. [6] D. R. Smith, J. B. Pendry, and M. C. Wiltshire, "Metamaterials and negative refractive index," Science, vol. 305, p. 788-792, 2004.
   連結：
6. [7] J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature, vol. 455, p. 376-379, 2008.
   連結：
7. [8] J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, vol. 312, p. 1780-1782, 2006.
   連結：
8. [9] L. Brillouin, Wave propagation in periodic structures: electric filters and crystal lattices, Courier Corporation, New York, 2003.
   連結：
9. [10] J. Li and C. T. Chan, "Double-negative acoustic metamaterial," Physical Review E, vol. 70, p. 055602, 2004.
   連結：
10. [11] C. T. Chan, J. Li, and K. H. Fung, "On extending the concept of double negativity to acoustic waves," Journal of Zhejiang University SCIENCE A, vol. 7, p. 24-28, 2006.
    連結：
11. [12] Y. Ding, Z. Liu, C. Qiu, and J. Shi, "Metamaterial with simultaneously negative bulk modulus and mass density," Physical Review Letters, vol. 99, p. 093904, 2007.
    連結：
12. [14] Z. Liu, C. T. Chan, and P. Sheng, "Analytic model of phononic crystals with local resonances," Physical Review B, vol. 71, p. 014103, 2005.
    連結：
13. [15] G. W. Milton and J. R. Willis, "On modifications of Newton's second law and linear continuum elastodynamics," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 463, p. 855-880, 2007.
    連結：
14. [16] H. H. Huang, C. T. Sun, and G. L. Huang, "On the negative effective mass density in acoustic metamaterials," International Journal of Engineering Science, vol. 47, p. 610-617, 2009.
    連結：
15. [17] H. H. Huang and C. T. Sun, "Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density," New Journal of Physics, vol. 11, p. 013003, 2009.
    連結：
16. [18] G. L. Huang and C. T. Sun, "Band gaps in a multiresonator acoustic metamaterial," Journal of Vibration and Acoustics, vol. 132, p. 031003, 2010.
    連結：
17. [19] K. T. Tan, H. H. Huang, and C. T. Sun, "Negative effective mass density of acoustic metamaterial using dual-resonator spring-mass model," Mechanical Engineering Faculty Research, p. 28-31, 2012.
    連結：
18. [20] K. T. Tan, H. H. Huang, and C. T. Sun, "Blast-wave impact mitigation using negative effective mass density concept of elastic metamaterials," International Journal of Impact Engineering, vol. 64, p. 20-29, 2014.
    連結：
19. [21] R. Zhu, G. L. Huang, H. H. Huang, and C. T. Sun, "Experimental and numerical study of guided wave propagation in a thin metamaterial plate," Physics Letters A, vol. 375, p. 2863-2867, 2011.
    連結：
20. [22] J.-S. Chen and C. T. Sun, "Dynamic behavior of a sandwich beam with internal resonators," Journal of Sandwich Structures and Materials, p. 2519-2529, 2011.
    連結：
21. [23] H. H. Huang and C. T. Sun, "Locally resonant acoustic metamaterials with 2D anisotropic effective mass density," Philosophical Magazine, vol. 91, p. 981-996, 2011.
    連結：
22. [24] R. Zhu, X. N. Liu, G. L. Huang, H.-H. Huang, and C. T. Sun, "Microstructural design and experimental validation of elastic metamaterial plates with anisotropic mass density," Physical Review B, vol. 86, p. 144307, 2012.
    連結：
23. [25] A. P. Liu, R. Zhu, X. N. Liu, G. K. Hu, and G. L. Huang, "Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials," Wave Motion, vol. 49, p. 411-426, 2012.
    連結：
24. [26] H. H. Huang and C. T. Sun, "Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus," Journal of the Mechanics and Physics of Solids, vol. 59, p. 2070-2081, 2011.
    連結：
25. [27] 尤建勳, "彈性超穎材料 (負楊氏模數模型) 波傳行為探討與實驗分析," 碩士論文, 工程科學及海洋工程學研究所, 國立臺灣大學, 台北, 2014.
    連結：
26. [28] X. N. Liu, G. K. Hu, G. L. Huang, and C. T. Sun, "An elastic metamaterial with simultaneously negative mass density and bulk modulus," Applied Physics Letters, vol. 98, p. 251907, 2011.
    連結：
27. [29] X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, "Wave propagation characterization and design of two-dimensional elastic chiral metacomposite," Journal of Sound and Vibration, vol. 330, p. 2536-2553, 2011.
    連結：
28. [30] R. Zhu, X. Liu, G. Hu, C. Sun, and G. Huang, "A chiral elastic metamaterial beam for broadband vibration suppression," Journal of Sound and Vibration, vol. 333, p. 2759-2773, 2014.
    連結：
29. [31] E. Baravelli and M. Ruzzene, "Internally resonating lattices for bandgap generation and low-frequency vibration control," Journal of Sound and Vibration, vol. 332, p. 6562-6579, 2013.
    連結：
30. [32] R. Zhu, X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, "Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial," Nature Communications, vol. 5, p. 1-8, 2014.
    連結：
31. [34] C. N. Weng, P. W. Chang, and T. Chen, "Numerical simulation of broadband bi-negative elastic metamaterials and wave transmission properties," Procedia Engineering, vol. 79, p. 622-630, 2014.
    連結：
32. [35] Y. Cheng, X. J. Liu, and D. J. Wu, "Band structure of a phononic crystal plate in the form of a staggered-layer structure," Journal of Applied Physics, vol. 109, p. 064904, 2011.
    連結：
33. [36] P. Wang, F. Casadei, S. Shan, J. C. Weaver, and K. Bertoldi, "Harnessing buckling to design tunable locally resonant acoustic metamaterials," Physical Review Letters, vol. 113, p. 014301, 2014.
    連結：
34. [37] S. Babaee, N. Viard, P. Wang, N. X. Fang, and K. Bertoldi, "Harnessing deformation to switch on and off the propagation of sound," Advanced Materials, p. 1631-1635, 2015.
    連結：
35. [38] J. N. Grima, R. Gatt, and P. S. Farrugia, "On the properties of auxetic meta‐tetrachiral structures," Physica Status Solidi (b), vol. 245, p. 511-520, 2008.
    連結：
36. [39] J. T. B. Overvelde and K. Bertoldi, "Relating pore shape to the non-linear response of periodic elastomeric structures," Journal of the Mechanics and Physics of Solids, vol. 64, p. 351-366, 2014.
    連結：
37. [40] B. Ungureanu, Y. Achaoui, S. Enoch, S. Brûlé, and S. Guenneau, "Auxetic-like metamaterials as novel earthquake protections," EPJ Applied Metamaterials, vol. 2, p. 17, 2015.
    連結：
38. [41] A. Bacigalupo and M. L. De Bellis, "Auxetic anti-tetrachiral materials: equivalent elastic properties and frequency band-gaps," Composite Structures, vol. 131, p. 530-544, 2015.
    連結：
39. [42] I. Vendik and O. Vendik, "Metamaterials and their application in microwaves: A review," Technical Physics, vol. 58, p. 1-24, 2013.
    連結：
40. [43] F. Casadei, B. S. Beck, K. A. Cunefare, and M. Ruzzene, "Vibration control of plates through hybrid configurations of periodic piezoelectric shunts," Journal of Intelligent Material Systems and Structures, vol. 23, p. 1169-1177, 2012.
    連結：
41. [44] A. Khelif, A. Choujaa, S. Benchabane, B. Djafari-Rouhani, and V. Laude, "Guiding and bending of acoustic waves in highly confined phononic crystal waveguides," Applied Physics Letters, vol. 84, p. 4400-4402, 2004.
    連結：
42. [45] F. Casadei, L. Dozio, M. Ruzzene, and K. A. Cunefare, "Periodic shunted arrays for the control of noise radiation in an enclosure," Journal of Sound and Vibration, vol. 329, p. 3632-3646, 2010.
    連結：
43. [47] B. L. Davis and M. I. Hussein, "Nanophononic metamaterial: Thermal conductivity reduction by local resonance," Physical Review Letters, vol. 112, p. 055505, 2014.
    連結：
44. [48] F. Bloch, "Über die quantenmechanik der elektronen in kristallgittern," Zeitschrift für Physik, vol. 52, p. 555-600, 1929.
    連結：
45. [49] L. Y. Wu and L. W. Chen, "Acoustic band gaps of the woodpile sonic crystal with the simple cubic lattice," Journal of Physics D: Applied Physics, vol. 44, p. 045402, 2011.
    連結：
46. [5] R. M. Walser, "Metamaterials: What are they? What are they good for?," APS March Meeting Abstracts, vol. 1, p. 5001, 2000.
47. [13] Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally resonant sonic materials," Science, vol. 289, p. 1734-1736, 2000.
48. [33] Y. Lai, Y. Wu, P. Sheng, and Z.-Q. Zhang, "Hybrid elastic solids," Nature Materials, vol. 10, p. 620-624, 2011.
49. [46] S. A. Cummer and D. Schurig, "One path to acoustic cloaking," New Journal of Physics, vol. 9, p. 45, 2007.
50. [50] 蔡國隆, 王光賢, and 涂聰賢, 聲學原理與噪音量測控制, 全華圖書, 台北, 2013.