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研究生：	王家豪 Wang, JIA-HAO
論文名稱：	具不完美界面之兩相圓柱超材料動態波動行為探討 Investigation on the Dynamic Wave Behaviors of Two-Phase Cylindrical Metamaterials with Imperfect Interfaces
指導教授：	陳東陽 Chen, Tungyang
學位類別：	碩士 Master
系所名稱：	工學院 - 土木工程學系 Department of Civil Engineering
論文出版年：	2026
畢業學年度：	114
語文別：	英文
論文頁數：	123
中文關鍵詞：	地震超材料、兩相圓柱超材料、不完美界面、動態有效參數、現地試驗
外文關鍵詞：	Seismic Metamaterials, Two-Phase Cylindrical Metamaterials, Imperfect Interfaces, Dynamic Effective Parameters, Field Experiment
相關次數：	點閱：66 下載：1
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本研究建構二維地下地震超材料之彈性動力學均質化理論。相較於傳統完美黏著界面假設，本研究立足於非連續微觀力學，打破過往限制，針對圓柱拓撲分別定義兩種不完美界面模型：其一為允許介質間產生法切向滑移之「位移跳躍模型」，調控位移場之不連續性；其二為引進表面彈性膜理論之「應力跳躍模型」，描述交介面之應力跳躍特徵。研究將上述界面本構與多極矩 Mie 散射理論及相干勢能近似法（CPA）全盤耦合，在長波長極限下，通過波動勢函數邊界條件之移項與齊次化矩陣解耦，成功推導出地下圓柱超材料的五個獨立動態有效常數: 面內單極矩（n=0）平面應變體積模數 kappa^ast、面內偶極矩（n=1）橫向質量密度 rho_T^ast 及面內四極矩（n=2）橫向剪切模數mu_T^ast 、面外單極矩（n=0）軸向質量密度 rho_A^ast、面外偶極矩（n=1）軸向剪切模數 mu_A^ast 分析揭示，當微觀界面弱化效應與高體積占比進行同步調控時，系統能有效瓦解縱橫波模式間的頻率排斥瓶頸，成功於 0sim20mathrm{ Hz} 之極低頻工程微震範圍內誘發局部共振，開啟全方位阻擋表面波與體波能量之「共頻雙負（Full-DNG）」完全帶隙。
為驗證理論，本研究初步探討如何把這套均質化理論轉化成一套具體可行的實體現地試驗方法論。規劃於國立成功大學土木系館北側草地進行縮尺現地試驗。試驗透過低頻穩態波包激發與感測採集，並採用振幅折減因子（ARF）與分貝傳輸損失（dB）作為減震成效之逆向驗證指標。此微觀界面理論與現地實證架構，兼有力學理論自恰性與工程實踐度，未來可為高科技廠房精密微震抑制與國家級耐震減災工程提供新一代的防禦技術。

This study proposes a comprehensive theoretical framework to analyze and design seismic metamaterials for effective seismic wave mitigation. Departing from idealized perfect-bonding assumptions, this research explicitly incorporates two engineering-realistic boundaries for two-phase cylindrical metamaterials: the displacement-jump model for micro-slip, and the stress-jump model for surface tension. Integrating these with elastodynamics, multipole Mie scattering, and the coherent potential approximation (CPA), we derive five independent dynamic effective parameters in the long-wavelength limit. The findings demonstrate that coupling imperfect interface manipulation with a high volume fraction overcomes modal antagonism, successfully opening a common-frequency double-negative complete bandgap within the ultra-low frequency range of 0–20 Hz.
To validate the theory, a scaled field test was envisaged at the NCKU Civil Engineering Building site. Using steady-state wave packets for harmonic excitation and wavefield acquisition, the amplitude reduction factor (ARF) and transmission loss (dB) were adopted to verify wave attenuation. Fusing micromechanical theory with empirical evidence, this self-consistent framework provides a next-generation defense technology for precision micro-vibration suppression and seismic disaster mitigation.

中文摘要 i
Abstract ii
Acknowledgements iii
Table of contents iv
List of contents vii
Table of Figures viii
Chapter 1. Introduction	1
1 Theoretical background 1
2 Literature Review 2
3 Motivation 8
4 Outline 8
Chapter 2. Effective Medium Theory for Generalized Imperfect Interfaces: Displacement Jump Model 11
1 Microscopic Physical Model and Wave Potential Function Expansion 12
1.1 In-Plane Scattering Model 13
1.2 Out-of-Plane Scattering Model 15
1.3 Physical Mapping of Azimuthal Modes 16
2 Derivation of Analytical Solutions 17
2.1 Imperfect Boundary Conditions 18
2.2 In-Plane Generalized Scattering Matrix: 19
2.3 Out-of-Plane Generalized Scattering Coefficient 23
2.4 Physical Significance of Matrix Element Reconstruction 25
3 Asymptotic Derivation of Generalized Effective Moduli and Limit Verification 26
3.1 Analytical Solutions for the effective medium parameters 30
3.2 Physical Implications and Asymptotic Limit Verification 32
Chapter 3. Effective Medium Theory for Generalized Imperfect Interfaces: Stress Jump Model 37
1 Derivation of Analytical Solutions 37
1.1 Imperfect Boundary Conditions 38
1.2 In-Plane Scattering Matrix: 39
1.3 Out-of-Plane Generalized Scattering Coefficient: 41
2 Asymptotic Derivation of Generalized Effective Moduli and Limit Verification 43
Chapter 4. Numerical Analysis and Validation of Metamaterial Arrays 49
1 Introduction and Material Properties 49
2 Influence of Interfacial Stiffness and Surface Elastic Moduli 51
3 Size Effect 69
4 Investigation of Multi-Negative Properties 81
Chapter 5. Experimental Program and Methodology 85
1 Experimental Setup and Instrumentation 85
2 Materials Characterization and Specimen Preparation 87
2.1 Material Selection and Properties 87
2.2 Specimen Design and Geometric Layout 88
3 Experimental Setup and Instrumentation 89
3.1 Experimental Site and Spatial Zonation 89
3.2 Instrumentation and Sensor Array 91
4 Signal Processing and Verification Methodology 94
4.1 Quantification via Amplitude Reduction Factor (ARF) 94
4.2 Evaluation of Vibration Transmission Magnitude (dB) 94
4.3 Verification of Macroscopic Effective Properties 95
5 Practical Implementation and Future Experimental Validation 97
Chapter 6. Conclusion and Future Work 99
References 101
Appendix A ：Calculation of Scattering Coefficients\ D_n^{\alpha\beta}\left(f,m\right) (Perfect Interface) 105
                                    

Bruch, M. J., Hansen, F. Y., & Ibsen, L. B.Evaluation of low-frequency seismic wave attenuation in geotechnical metasolids embedded in a dense sand matrix. Soil Dynamics and Earthquake Engineering, 142, 106530. (2021).

Chen, T., Chiu, M. S., & Weng, C. N. Derivations of the generalized Young–Laplace equations of surface elasticity for anisotropic interfaces and their applications. Journal of Applied Physics, 100(7), 074308. (2006).

Chen, T., Dvorak, G. J., & Yu, C. C. Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mechanica, 188(1-2), 39–54.(2007).

Christensen, R. M., & 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).

Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C., & Zhang, X. Ultrasonic metamaterials with negative modulus. Nature Materials, 5(6), 452–456. (2006).

Favier, E., Nemati, N., & Perrot, C. Two-component versus three-component metasolids. The Journal of the Acoustical Society of America, 148(5), 3065-3074. (2020).

Favier, E., Nemati, N., Perrot, C., & He, Q. C. Generalized analytic model for rotational and anisotropic metasolids. Journal of Physics Communications, 2(3), 035035. (2018).

Garcia, N., & Nieto-Vesperinas, M. Left-handed materials do not make a perfect lens. Physical Review Letters, 88(20), 207403. (2002).

Graff, K. F. Wave motion in elastic solids. Ohio State University Press. (1975).

Gu, B., & Rokhlin, S. I. Characterization of interfacial properties in fluid-loaded membrane structures using ultrasonic waves. The Journal of the Acoustical Society of America, 92(2), 929–937. (1992).

Hashin, Z., & Rosen, B. W.Elastic moduli of fiber-reinforced materials. Journal of Applied Mechanics, 31(2), 223–232. (1964).
Hashin, Z. Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials, 8, 333-348. (1990).

Hill, R. Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour. Journal of the Mechanics and Physics of Solids, 12(4), 199–212. (1964).

Hung, Y. C., & Chen, T. Local resonance behavior of two-phase cylindrical composites. Journal of Mechanics, 41, 494–509. (2025).

Kolinko, P., & Smith, D. R. Numerical study of a matched left-handed material slab. Optics Express, 11(7), 640–648. (2003).

Koschny, T., Kafesaki, M., Economou, E. N., & Soukoulis, C. M. Effective medium theory of left-handed materials. Physical Review Letters, 93(10), 107402. (2004).

Lagarkov, A. N., Sarychev, A. K., Smychkovich, Y. R., & Vinogradov, A. P. Effective medium theory for microwave composite materials. Journal of Electromagnetic Waves and Applications, 6(9), 1159–1177. (1992).

Lewin, L. The electrical properties of a semi-solid dielectric containing a mixture of solids. Proceedings of the Institution of Electrical Engineers, 94(27), 65–68. (1947).

Liu, Z., Chan, C. T., & 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. Y., Yang, Z., Chan, C. T., & Sheng, P. Locally Resonant Sonic Materials. Science, 289(5485), 1734-1736. (2000).

Maxwell-Garnett, J. C. 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), 385–420. (1904).

Mal, A. K., & Bose, S. K. Dynamic elastic moduli of a suspension of imperfectly bonded spheres. Mathematical Proceedings of the Cambridge Philosophical Society, 78(3), 547-558. (1975).

Mie, G. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik, 330(3), 377–445. (1908).

Pendry, J. B., Holden, A. J., Robbins, D. J., & 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. Negative refraction makes a perfect lens. Physical Review Letters, 85(18), 3966–3969. (2000).

Sarychev, A. K., McPhedran, R. C., & V. M. Shalaev. Electrodynamics of metal-dielectric composites in a magnetic field. Physical Review B, 62(12), 8531–8539. (2000).

Shelby, R. A., Smith, D. R., Nemat-Nasser, S. C., & Schultz, S. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial. Applied Physics Letters, 78(4), 489–491. (2001).

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

Shen, J. T., & Platzman, P. M. Near field imaging with negative dielectric constant materials. Applied Physics Letters, 80(18), 3286–3288. (2002).

Sheng, P. Introduction to wave scattering, localization and mesoscopic phenomena. Springer. (2006).

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

Smith, D. R., Schurig, D., Rosenbluth, M., Schultz, S., Ramakrishna, S. A., & Pendry, J. B. Limitations on subdiffraction imaging with a mu= -1 right-handed lens. Applied Physics Letters, 82(10), 1506–1508. (2003).

Smith, D. R., & Pendry, J. B. Homogenization of metamaterials by field averaging. Journal of the Optical Society of America B, 23(3), 391–403. (2006).

Smith, D. R., Pendry, J. B., & Wiltshire, M. Metamaterials and negative refractive index. Science, 305(5685), 788–792. (2004).

Veselago, V. G. The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ. Soviet Physics Uspekhi, 10(4), 509–514. (1968).

Willis, J. R. Effective constitutive relations for waves in composites and metamaterials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467(2135), 3465-3479. (2011)

Wu, Y., Li, J., Zhang, Z. Q., & Chan, C. T. Effective medium theory for phononic crystals. Physical Review B, 74(8), 085111. (2006).

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

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

Zhou, M. Y., & Sheng, P. First-principles criterion for effective-medium theories. Physical Review B, 43(10), 8460–8467, (1992).

簡廷宇，具帶隙效應之層狀基礎於隔減震之應，成功大學土木工程學系碩士論文(2019)。

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