由兩種以上介質組成複合材料的波傳研究廣泛用於各種領域，其中就包含地震波的研究，而複合材料的交界面在現實狀況並不如數學設想般的完美，因此本文將考慮界面真實情形，分析不完美界面的波傳行為，分別推導體波通過不完美界面與表面波介質交界面為不完美界面的波傳方程，比較交界面為完美界面時的差別，藉此探討不完美界面彈性波之數學波傳結果；當彈性體波通過不完美界面時，司乃耳定律依然成立，並使折射波與反射波產生相位差，同時折射波與反射波振幅會與波傳通過完美界面時不同；HS型不完美界面從數學角度能有效的抵禦表面波傳遞，但考量真實尺度的界面材料係數與地震波的頻率，不完美界面應用於地震表面波防制的可行性偏低。

Elastic wave theory of composite materials composed of two or more kinds of materials are widely used in various studies, including the seismology. The interface of composite materials in reality may differ from that of ideal assumptions. Therefore, in this thesis, we consider actual conditions of the interface, and investigate the propagating behavior of both elastic body wave and elastic surface wave with the addition of imperfect interface. When the elastic body wave passes through the imperfect interface, Snell's law remains unchanged, which means that the direction of wave propagation is exactly the same as the direction of the wave passing through the perfect interface. However, the addition of imperfect interface can lead to the phase differences between the refracted wave, the reflected wave and the incident wave. In addition, the amplitude of the refracted and reflected waves will also be different. Moreover, the high stiffness imperfect interface can effectively resist the surface wave propagation from the mathematical point of view, but is less feasible for seismic surface waves when the real surface elastic constants and the low frequency regime of seismic waves are considered.

Achaoui, Y., T. Antonakakis, S. Brule, R. Craster, S. Enoch and S. Guenneau, Clamped seismic metamaterials: ultra-low frequency stop bands, New Journal of Physics 19(6): 063022, 2017.
Achenbach, J., Wave Propagation in Elastic Solids, 1973.
Benveniste, Y., The effective mechanical behaviour of composite materials with imperfect contact between the constituents, Mechanics of Materials 4(2): 197-208, 1985.
Benveniste, Y., A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media, Journal of the Mechanics and Physics of Solids 54(4): 708-734, 2006.
Brillouin, L., Wave Propagation in Periodic Structures: electric filters and crystal lattices, 1953.
Chen, T., M.-S. Chiu and C.-N. Weng, Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids, Journal of Applied Physics 100(7): 074308, 2006.
Chen, T., G. J. Dvorak and C. Yu, Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal–mechanical connections, International Journal of Solids and Structures 44(3-4): 941-955, 2007.
Duan, H., X. Yi, Z. Huang and J. Wang, A unified scheme for prediction of effective moduli of multiphase composites with interface effects. Part I: Theoretical framework, Mechanics of Materials 39(1): 81-93, 2007.
Golub, M. V. and A. Boström, Interface damage modeled by spring boundary conditions for in-plane elastic waves, Wave Motion 48(2): 105-115, 2011.
Graff, K., Wave Motion in Elastic Solids, 1975.
Gu, S.-T., J.-T. Liu and Q.-C. He, Size-dependent effective elastic moduli of particulate composites with interfacial displacement and traction discontinuities, International Journal of Solids and Structures 51(13): 2283-2296, 2014.
Gu, S. and Q.-C. He, Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces, Journal of the Mechanics and Physics of Solids 59(7): 1413-1426, 2011.
Gurtin, M. E. and A. I. Murdoch, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57(4): 291-323, 1975.
Gurtin, M. E. and A. I. Murdoch, Effect of surface stress on wave propagation in solids, Journal of Applied Physics 47(10): 4414-4421, 1976.
Hashin, Z., Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials 8(4): 333-348, 1990.
Hashin, Z., Thin interphase/imperfect interface in elasticity with application to coated fiber composites, Journal of the Mechanics and Physics of Solids 50(12): 2509-2537, 2002.
Huang, H.-H. and C.-T. Sun, Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus, The Journal of the Acoustical Society of America 132(4): 2887-2895, 2012.
Mei, J. and Y. Wu, Controllable transmission and total reflection through an impedance-matched acoustic metasurface, New Journal of Physics 16(12): 123007, 2014.
Miniaci, M., A. Krushynska, F. Bosia and N. M. Pugno, Large scale mechanical metamaterials as seismic shields, New Journal of Physics 18(8): 083041, 2016.
Murdoch, A., The propagation of surface waves in bodies with material boundaries, Journal of the Mechanics and Physics of Solids 24(2-3): 137-146, 1976.
Pyrak-Nolte, L. J., J. Xu and G. M. Haley, Elastic interface waves propagating in a fracture, Physical Review Letters 68(24): 3650, 1992.
Pyrak‐Nolte, L. J. and N. G. Cook, Elastic interface waves along a fracture, Geophysical Research Letters 14(11): 1107-1110, 1987.
Rokhlin, S. and Y. Wang, Analysis of boundary conditions for elastic wave interaction with an interface between two solids, The Journal of the Acoustical Society of America 89(2): 503-515, 1991.
Ru, Y., G. Wang and T. Wang, Diffractions of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect, Journal of Vibration and Acoustics 131(6): 061011, 2009.
Schoenberg, M., Elastic wave behavior across linear slip interfaces, The Journal of the Acoustical Society of America 68(5): 1516-1521, 1980.
Sharma, P. and S. Ganti, Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies, Journal of Applied Mechanics 71(5): 663-671, 2004.
Shen, X., C.-T. Sun, M. V. Barnhart and G. Huang, Elastic wave manipulation by using a phase-controlling meta-layer, Journal of Applied Physics 123(9): 091708, 2018.
Shuttleworth, R., The surface tension of solids, Proceedings of the Physical Society. Section A 63(5): 444, 1950.
Su, Y.-C. and C.-T. Sun, Wave Amplification in Double Negative Elastic Metamaterials, 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2015.
Velasco, V. and F. Garcia-Moliner, Surface effects in elastic surface waves, Physica Scripta 20(1): 111, 1979.
Wang, G., Diffraction of plane compressional wave by a nanosized spherical cavity with surface effects, Applied Physics Letters 90(21): 211907, 2007.
Wang, G., Diffraction of shear waves by a nanosized spherical cavity, Journal of Applied Physics 103(5): 053519, 2008.
Wang, G., T. Wang and X. Feng, Surface effects on the diffraction of plane compressional waves by a nanosized circular hole, Applied Physics Letters 89(23): 231923, 2006.

Yu, N., P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso and Z. Gaburro, Light propagation with phase discontinuities: generalized laws of reflection and refraction, Science 334(6054): 333-337, 2011.