近年來不少學者投入於地震超材料(seismic metamaterial)設計與應用之相關研究，其概念為透過超材料具帶隙(band gap)的特殊現象，在地震波衝擊結構物前，先過濾最具傷害性的低頻地震波，達到抗震的效果。有別於大多數文獻將地震超材料設置於結構外部，本文則是將地震超材料放置於結構物基礎，採用橡膠版與混凝土版兩種常見的工程材料交互排列成之層狀結構(layered structure)作為我們的抗震基礎。利用一維彈性層版理論分析其頻散關係(dispersion relation)，透過調整材料與尺寸兩種參數來預測帶隙發生的頻率區間，並使用有限元素軟體模擬連體模型受波傳行為後，驗證能量衰減的趨勢是否符合帶隙的預測。最後考慮橡膠為黏彈性材料以廣義馬克士威模型(generalized Maxwell model)並進行分析，透過黏彈性材料具阻尼消能的特性，給定合理的材料參數後，同樣透過有限元素軟體進行連體模型分析，觀察其於帶隙外消能的效果。

Seismic metamaterials have been widely studied in recent years. The concept of seismic metamaterials is to filter the most harmful low-frequency seismic waves within band gap to protect buildings from seismic waves. In distinct to most studies, in which seismic metamaterials are placed outside the protected targets. In this thesis, seismic metamaterials are served as the foundation of structural system. The foundation is a layered medium, consisting of rubber and concrete. Based on the theory of elastodynamics and Bloch’s theorem, we analyze the dispersion relation for the layered foundation. The frequency interval of the band gap is calculated by adjusting material parameters, and finite element method is used to simulate the wave propagation in continuum model, which will provide a verification of the trend of wave attenuation and the prediction of the band gap. Since rubber has a characteristic of damping energy dissipation, we also consider that rubber is viscoelastic. Numerical method based on finite element is adopted the generalized Maxwell model. Finally, we conclude that the energy dissipation mechanism is controlled mostly by band gap rather than damping, and the enhanced response due to resonance outside the band gap can be reduced.

Achaoui, Y., Antonakakis, T., Brûlé, S., Craster, R. V., Enoch, S. and Guenneau, S., Clamped seismic metamaterials: ultra-low frequency stop bands, New Journal of Physics 19(6) (2017).

Achenbach, J., Wave Propagation in Elastic Solids. (Elsevier, 2012).

Auld, B. A., Acoustic Fields and Waves in Solids. (Рипол Классик, 1973).

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

Brillouin, L., Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. (Courier Corporation, 2003).

Cheng, Z. and Shi, Z., Composite periodic foundation and its application for seismic isolation, Earthquake Engineering & Structural Dynamics 47(4): 925-944 (2018).

Cheng, Z., Shi, Z., Mo, Y. and Xiang, H., Locally resonant periodic structures with low-frequency band gaps, Journal of Applied Physics 114(3): 033532 (2013).

Christensen, R. M., Theory of Viscoelasticity: An Introduction. (Elsevier, 2012a).

Christensen, R. M., Mechanics of Composite Materials. (Courier Corporation, 2012b).

Delph, T., Herrmann, G. and Kaul, R., Harmonic wave propagation in a periodically layered, infinite elastic body: Antiplane strain, Journal of Applied Mechanics 45(2): 343-349 (1978).

Delph, T., Herrmann, G. and Kaul, R., Harmonic wave propagation in a periodically layered, infinite elastic body: plane strain, analytical results, Journal of Applied Mechanics 46(1): 113-119 (1979).

Delph, T., Herrmann, G. and Kaul, R., Harmonic Wave propagation in a periodically layered, infinite elastic body: Plane strain, Numerical results, Journal of Applied Mechanics 47(3): 531-537 (1980).

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).

Ferry, J. D., Viscoelastic Properties of Polymers. (John Wiley & Sons, 1980).

Geng, Q., Zhu, S. and Chong, K. P., Issues in design of one-dimensional metamaterials for seismic protection, Soil Dynamics and Earthquake Engineering 107(1): 264-278 (2018).

Graff, K. F., Wave Motion in Elastic Solids. (Courier Corporation, 1975).

Huang, H. and Sun, C., Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, New Journal of Physics 11(1): 013003 (2009).

Huang, H. and Sun, C., Locally resonant acoustic metamaterials with 2D anisotropic effective mass density, Philosophical Magazine 91(6): 981-996 (2011).

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).

Huang, J. and Shi, Z., Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves, Journal of Sound and Vibration 332(19): 4423-4439 (2013).

Ibrahim, R., Recent advances in nonlinear passive vibration isolators, Journal of Sound and Vibration 314(3-5): 371-452 (2008).

Jones, R. M., Mechanics of Composite Materials. (CRC press, 2014).

Kelly, J. M., Aseismic base isolation: review and bibliography, Soil Dynamics and Earthquake Engineering 5(4): 202-216 (1986).

Kim, S.-H. and Das, M. P., Seismic waveguide of metamaterials, Modern Physics Letters B 26(17): 1250105 (2012).

Kittel, C., McEuen, P. and McEuen, P., Introduction to Solid State Physics. (Wiley New York, 1996).

Krödel, S., Thomé, N. and Daraio, C., Wide band-gap seismic metastructures, Extreme Mechanics Letters 4: 111-117 (2015).

Krushynska, A., Kouznetsova, V. and Geers, M., Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials, Journal of the Mechanics and Physics of Solids 96: 29-47 (2016).

Lai, Y., Wu, Y., Sheng, P. and Zhang, Z.-Q., Hybrid elastic solids, Nature Materials 10(8): 620 (2011).

Lakes, R., Viscoelastic Materials. (Cambridge University Press, 2009).

Lewińska, M., Kouznetsova, V., van Dommelen, J., Krushynska, A. and Geers, M., The attenuation performance of locally resonant acoustic metamaterials based on generalised viscoelastic modelling, International Journal of Solids and Structures 126: 163-174 (2017).

Liu, X., Huang, G. and Hu, G., Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices, Journal of the Mechanics and Physics of Solids 60(11): 1907-1921 (2012).

Liu, X., Shi, Z., Xiang, H. and Mo, Y., Attenuation zones of periodic pile barriers with initial stress, Soil Dynamics and Earthquake Engineering 77: 381-390 (2015).

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).

Meseguer, F., Holgado, M., Caballero, D., Benaches, N., Sánchez-Dehesa, J., López, C. and Llinares, J., Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal, Physical Review B 59(19): 12169 (1999).

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).

Naeim, F. and Kelly, J. M., Design of Seismic Isolated Structures: From Theory to Practice. (John Wiley & Sons, 1999).

Nayfeh, A. H., Wave Propagation in Layered Anisotropic Media: With Application to Composites. (Elsevier, 1995).

Palermo, A., Krodel, S., Marzani, A. and Daraio, C., Engineered metabarrier as shield from seismic surface waves, Scientific Reports 6: 39356 (2016).

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

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

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

Royer, D. and Dieulesaint, E., Elastic Waves in Solids I: Free and Guided Propagation. (Springer Science & Business Media, 1999).

Sakoda, K., Optical Properties of Photonic Crystals. (Springer Science & Business Media, 2004).

Skrzypek, J. and Ganczarski, A., Mechanics of Anisotropic Materials. (Springer, 2015).

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

Sun, C., Achenbach, J. and Herrmann, G., Time-harmonic waves in a stratified medium propagating in the direction of the layering, Journal of Applied Mechanics, Transactions ASME 35(2): 408-410 (1964).

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

Wang, Y.-F., Wang, Y.-S. and Laude, V., Wave propagation in two-dimensional viscoelastic metamaterials, Physical Review B 92(10): 104110 (2015).

Witarto, W., Wang, S., Yang, C., Nie, X., Mo, Y., Chang, K., Tang, Y. and Kassawara, R., Seismic isolation of small modular reactors using metamaterials, AIP Advances 8(4): 045307 (2018).

Xiang, H., Shi, Z., Wang, S. and Mo, Y., Periodic materials-based vibration attenuation in layered foundations: experimental validation, Smart Materials and Structures 21(11): 112003 (2012).

Yan, Y., Cheng, Z., Menq, F., Mo, Y., Tang, Y. and Shi, Z., Three dimensional periodic foundations for base seismic isolation, Smart Materials and Structures 24(7): 075006 (2015).

Yan, Y., Laskar, A., Cheng, Z., Menq, F., Tang, Y., Mo, Y. L. and Shi, Z., Seismic isolation of two dimensional periodic foundations, Journal of Applied Physics 116(4) (2014).

Zhu, R., Huang, H., Huang, G. and Sun, C., Microstructure continuum modeling of an elastic metamaterial, International Journal of Engineering Science 49(12): 1477-1485 (2011).

寧彥傑，具負等效質量慣性矩之微極彈模型設計，成功大學土木工程研究所碩士論文 (2016)。