進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-2208201812282600
論文名稱(中文) 利用等效介質理論探討超材料在不同物理模式之尺度關聯
論文名稱(英文) Metamaterials for different physical phenomena and their corresponding length scales based on effective medium concept
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 106
學期 2
出版年 107
研究生(中文) 黃瑜琛
研究生(英文) Yu-Chen Huang
學號 N66051118
學位類別 碩士
語文別 中文
論文頁數 82頁
口試委員 指導教授-陳東陽
口試委員-葉超雄
口試委員-吳光鐘
口試委員-馬劍清
口試委員-汪向榮
中文關鍵字 超材料  等效介質理論  等效材料係數  帶隙 
英文關鍵字 metamaterials  effective medium theory  effective material parameters  band gap 
學科別分類
中文摘要 超材料為經過特殊設計的複合材料,與波場間的交互作用能產生自然材料所沒有的現象,如負折射、負材料係數等,透過適當的運用可達到控制波動傳播的效果,在光學、電磁學、聲學、彈性波傳等領域上皆有豐碩的研究成果。從文獻中可以發現,超材料在不同物理模式之間的尺度與應用頻率上具有相當的差異性,為了瞭解不同系統間是否存在著尺度上的關連,本文探討超材料應用在聲波、平面電磁波、反平面剪力波等物理模式的尺度問題。首先藉由等效介質理論求取不同系統的等效材料係數,以此建構超材料的頻散關係。接著以該頻散關係為基礎,探討等效係數與波傳行為間的關係,並分析超材料在晶格常數、材料係數等因子的影響下帶隙頻率變化,進而找出在尺度上的關連性。最後整合這三種系統的分析結果,藉由物理模式間的類比性質及晶格常數與波長間的關係說明不同物理模式下超材料的尺度關連。
英文摘要 Metamaterials have properties that are not found in natural materials, such as negative refraction and negative parameters. There are abundant research in different areas, including electromagnetism, acoustics and elastodynamics. It can be found from the literature that the length scale and the corresponding frequency of metamaterials have disparity in different physical phenomena. In order to understand whether they are scale correlated among different systems, this thesis discusses the length scale of metamaterials in acoustic waves, plane electromagnetic waves, and anti-plane shear waves. First, we construct the dispersion relation of the metamaterials by the effective medium theory. Based on this dispersion relation, the influence of the lattice constant and the material parameters on the band gap frequency is discussed, from which the connection with the length scale is found. Finally, comparing the results of the three physical modes, the analogy of different systems and the relationship between the lattice constant and the wavelength are identified to illustrate the scale correlation of the metamaterials in different physical modes.
論文目次 中文摘要 I
Abstract II
誌謝 VIII
目錄 IX
表目錄 XI
圖目錄 XII
符號表 XIV
第一章 緒論 1
1.1 超材料的歷史沿革與相關文獻回顧 1
1.2 研究動機 8
1.3 論文簡介 9
第二章 聲波超材料的尺度分析 11
2.1 聲波簡介 11
2.2 聲波方程式 12
2.3 二維聲波超材料的等效係數 14
2.4 聲波等效係數與波傳特性探討 22
2.5 聲波超材料的尺度分析與探討 25
2.5.1 晶格常數的影響 25
2.5.2 材料係數的影響 28
2.5.3 內含物與基材之體積比的影響 29
2.5.4 綜合分析與探討 30
第三章 電磁超材料的尺度分析 34
3.1 電磁波(electromagnetic waves) 34
3.2 電磁波方程式 36
3.3 二維電磁超材料的等效係數 38
3.4 電磁波等效係數與波傳特性探討 42
3.5 電磁超材料的尺度分析與探討 45
3.5.1 晶格常數的影響 46
3.5.2 材料係數的影響 47
3.5.3 內含物與基材之體積比的影響 49
3.5.4 綜合分析與探討 49
第四章 彈性超材料的尺度分析 54
4.1 彈性波簡介 54
4.2 彈性波方程式 55
4.3 二維彈性波超材料的等效係數 57
4.4 彈性波等效係數與波傳特性探討 62
4.5 彈性超材料的尺度分析與探討 65
4.5.1 晶格常數的影響 65
4.5.2 材料係數的影響 67
4.5.3 內含物與基材之體積比的影響 68
4.5.4 綜合分析與探討 69
第五章 綜合討論與結論 71
5.1 物理模式間的尺度關連與綜合討論 71
5.2 結論與未來展望 76
參考文獻 79
參考文獻 Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Dover Publications, 1965.

Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland Publishing Company, 1975.

Balanis, C. A., Advanced Engineering Electromagnetics, Wiley-India, 1999.

Bolt, B. A., Earthquakes, W.H. Freeman, 1993.

Brûlé, S., Javelaud, E., Enoch, S. and Guenneau, S., Experiments on seismic metamaterials: Molding surface waves, Physical Review Letters 112(13): 133901, 2014.

Chen, H. and Chan, C. T., Acoustic cloaking in three dimensions using acoustic metamaterials, Applied Physics Letters 91(18): 183518, 2007.

Chen, T., Weng, C.-N. and Chen, J.-S., Cloak for curvilinearly anisotropic media in conduction, Applied Physics Letters 93(11): 114103, 2008.

Cheng, Y., Xu, J. Y. and Liu, X. J., One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus, Physical Review B 77(4): 045134, 2008.

Christensen, R. M. and Lo, K. H., Solutions for effective shear properties in three phase sphere and cylinder models, Journal of the Mechanics and Physics of Solids 27(4): 315-330, 1979.

Ding, C., Hao, L. and Zhao, X., Two-dimensional acoustic metamaterial with negative modulus, Journal of Applied Physics 108(7): 074911, 2010.

Ding, Y., Liu, Z., Qiu, C. and Shi, J., Metamaterial with simultaneously negative bulk modulus and mass density, Physical Review Letters 99(9): 093904, 2007.

Du, Q., Zeng, Y., Huang, G. and Yang, H., Elastic metamaterial-based seismic shield for both lamb and surface waves, AIP Advances 7(7): 075015, 2017.

Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 241(1226): 376-396, 1957.

Fang, N., Lee, H., Sun, C. and Zhang, X., Sub–diffraction-limited optical imaging with a silver superlens, Science 308(5721): 534-537, 2005.

Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C. and Zhang, X., Ultrasonic metamaterials with negative modulus, Nature Materials 5: 452, 2006.

Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C. and Zhang, X., Ultrasonic metamaterials with negative modulus, Nature Materials 5(6): 452, 2006.

Garnett, J. C. M., Xii. Colours in metal glasses and in metallic films, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 203(359-371): 385, 1904.

Graff, K. F., Wave Motion in Elastic Solids, Dover Publications, 1991.

Hashin, Z., The elastic moduli of heterogeneous materials, Journal of Applied Mechanics 29(1): 143-150, 1962.

Huang, G. L. and Sun, C. T., Band gaps in a multiresonator acoustic metamaterial, Journal of Vibration and Acoustics 132(3): 031003-031003-031006, 2010.

Huang, H., Sun, C. and Huang, G., On the negative effective mass density in acoustic metamaterials, International Journal of Engineering Science 47(4): 610-617, 2009.

Hussein, M. I., Leamy, M. J. and Ruzzene, M., Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook, Applied Mechanics Reviews 66(4): 040802, 2014.

Joannopoulos, J. D., Villeneuve, P. R. and Fan, S., Photonic crystals: Putting a new twist on light, Nature 386(6621): 143, 1997.

John, S., Strong localization of photons in certain disordered dielectric superlattices, Physical Review Letters 58(23): 2486, 1987.

Kadic, M., Bückmann, T., Schittny, R. and Wegener, M., Metamaterials beyond electromagnetism, Reports on Progress in Physics 76(12): 126501, 2013.

Kinsler, L. E., Fundamentals of Acoustics, Wiley, 1982.

Knott, E. F., Schaeffer, J. F. and Tulley, M. T., Radar Cross Section, Institution of Engineering and Technology, 2004.

Lai, Y., Wu, Y., Sheng, P. and Zhang, Z.-Q., Hybrid elastic solids, Nature Materials 10: 620, 2011.

Lamb, W., Wood, D. M. and Ashcroft, N. W., Long-wavelength electromagnetic propagation in heterogeneous media, Physical Review B 21(6): 2248-2266, 1980.

Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G. and Kim, C. K., Composite acoustic medium with simultaneously negative density and modulus, Physical Review Letters 104(5): 054301, 2010.

Leonhardt, U., Optical conformal mapping, Science 312(5781): 1777-1780, 2006.

Li, J. and Chan, C. T., Double-negative acoustic metamaterial, Physical Review E 70(5): 055602, 2004.

Liu, Z., Chan, C. T. and Sheng, P., Analytic model of phononic crystals with local resonances, Physical Review B 71(1): 014103, 2005.

Liu, Z., Zhang, X., Mao, Y., Zhu, Y., Yang, Z., Chan, C. T. and Sheng, P., Locally resonant sonic materials, Science 289(5485): 1734-1736, 2000.

Lu, M.-H., Feng, L. and Chen, Y.-F., Phononic crystals and acoustic metamaterials, Materials Today 12(12): 34-42, 2009.

Maldovan, M., Sound and heat revolutions in phononics, Nature 503(7475): 209, 2013.

Mansfield, E., Neutral holes in plane sheet—reinforced holes which are elastically equivalent to the uncut sheet, The Quarterly Journal of Mechanics and Applied Mathematics 6(3): 370-378, 1953.

Marco, M., Anastasiia, K., Federico, B. and Nicola, M. P., Large scale mechanical metamaterials as seismic shields, New Journal of Physics 18(8): 083041, 2016.

Mei, J., Liu, Z., Wen, W. and Sheng, P., Effective dynamic mass density of composites, Physical Review B 76(13): 134205, 2007.

Milton, G. W., Briane, M. and Willis, J. R., On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics 8(10): 248, 2006.

Miniaci, M., Krushynska, A., Bosia, F. and Pugno, N. M., Large scale mechanical metamaterials as seismic shields, New Journal of Physics 18(8): 083041, 2016.

Mow, C. C. and Pao, Y., Diffraction of Elastic Waves and Dynamic Stress concentrations, Crane, Russak, 1973.

O’Brien, S., McPeake, D., Ramakrishna, S. A. and Pendry, J. B., Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials, Physical Review B 69(24): 241101, 2004.

Pendry, J. B., Negative refraction makes a perfect lens, Physical Review Letters 85(18): 3966, 2000.

Pendry, J. B., Holden, A. J., Robbins, D. J. and Stewart, W. J., Magnetism from conductors and enhanced nonlinear phenomena, IEEE Transactions on Microwave Theory and Techniques 47(11): 2075-2084, 1999.

Pendry, J. B., Holden, A. J., Stewart, W. J. and Youngs, I., Extremely low frequency plasmons in metallic mesostructures, Physical Review Letters 76(25): 4773-4776, 1996.

Pendry, J. B., Schurig, D. and Smith, D. R., Controlling electromagnetic fields, Science 312(5781): 1780-1782, 2006.

Sadd, M. H., Elasticity: Theory, Applications, and Numerics, Elsevier Butterworth Heinemann, 2005.

Schurig, D., Mock, J. J., Justice, B. J., Cummer, S. A., Pendry, J. B., Starr, A. F. and Smith, D. R., Metamaterial electromagnetic cloak at microwave frequencies, Science 314(5801): 977-980, 2006.

Shelby, R. A., Smith, D. R. and Schultz, S., Experimental verification of a negative index of refraction, Science 292(5514): 77-79, 2001.

Sheng, P., Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, Springer Berlin Heidelberg, 2006.

Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. and Schultz, S., Composite medium with simultaneously negative permeability and permittivity, Physical Review Letters 84(18): 4184-4187, 2000.

Soukoulis, C. M. and Wegener, M., Past achievements and future challenges in the development of three-dimensional photonic metamaterials, Nature Photonics 5: 523, 2011.

Veselago, V. G., The electrodynamics of substances with simultaneously negative values of ε and μ, Soviet Physics Uspekhi 10(4): 509, 1968.

Wu, Y., Lai, Y. and Zhang, Z.-Q., Effective medium theory for elastic metamaterials in two dimensions, Physical Review B 76(20): 205313, 2007.

Wu, Y., Lai, Y. and Zhang, Z.-Q., Elastic metamaterials with simultaneously negative effective shear modulus and mass density, Physical Review Letters 107(10): 105506, 2011.

Wu, Y., Li, J., Zhang, Z.-Q. and Chan, C. T., Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit, Physical Review B 74(8): 085111, 2006.

Wu, Y. and Zhang, Z.-Q., Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions, Physical Review B 79(19): 195111, 2009.

Yablonovitch, E., Inhibited spontaneous emission in solid-state physics and electronics, Physical Review Letters 58(20): 2059-2062, 1987.

Yablonovitch, E., Photonic crystals: Semiconductors of light, Scientific American 285(6): 46-55, 2001.

Yang, Z., Mei, J., Yang, M., Chan, N. H. and Sheng, P., Membrane-type acoustic metamaterial with negative dynamic mass, Physical Review Letters 101(20): 204301, 2008.

Yao, S., Zhou, X. and Hu, G., Experimental study on negative effective mass in a 1d mass–spring system, New Journal of Physics 10(4): 043020, 2008.

翁崇寧,轉換材料在不同物理與彈性問題之理論及等效行為探討,國立成功大學土木所博士論文,2010。

陳盈豪,轉換介質的聲波解析與數值模擬,國立成功大學土木所碩士論文,2011。
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2021-09-01起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2021-09-01起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw