超穎材料是一種特殊的人造材料，其具有特殊的物理現象，現今期刊有許多介紹及應用，多半應用於吸收振動或阻隔噪音。本論文探討內含週期薄膜及半月形質量塊之超穎材料結構樑的波傳行為，由頻散關係圖(dispersion curve)中可發現特定頻率下產生能隙，阻絕彈性波的傳遞。能隙分成兩大類，分別為布拉格散射(Bragg band gap)與局部共振能隙(Locally resonant band gap) ，可藉由調整薄膜張力或質量塊的高度、角度與位置，控制減振頻率及減振頻寬，主結構的振動可於特定頻率下被抑制。而另一種方法是將不同種質量塊薄膜結構進行週期性排列或是單層局部共振器改成多層局部共振器，可有效提高減振效能及拓寬頻寬，利用振動實驗與有限軟體(COMSOL Multiphysics)進行分析，驗證減振頻帶的位置正好對應於頻散曲線中能隙的頻率範圍。最後將壓電片黏貼於共振系統上，將能量擷取出來，獲得雙層結構壓電片並聨時具有最佳的電壓值0.73V，再對電阻匹配進行探討，於電阻200kΩ時得到最高功率1.185×〖10〗^(-6)W，達到同時具有減振與擷能的效果。

In this thesis, we explore the propagation behavior of a metamaterial beam with membrane-split-ring structures acting as local resonators. There are two kinds of bandgaps occurred in the dispersion curve. One is the Bragg bandgap; the other is the resonant-type bandgap. When the exciting force frequency is close to resonant frequency of the resonator, the flexural wave is attenuated. Bandgap frequencies can be adjusted by changing membrane tension, mass magnitude, opening angle, and the location of the mass. The finite element software (COMSOL Multiphysics) is employed to predict the dispersion relation and vibration response. It is found that the proposed membrane-split-ring metamaterial beam can perform well not only in vibration reduction but also energy harvesting.

[1] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. D. Rouhani, Acoustic band structure of periodic elastic composites, Phys Rev Lett 71(13), 2022-2025 (1993).
[2] A. J. F. Metherrll and R. M. Fisher, Consequences of Bloch´s theorem on the dynamical theory of electron diffraction contrast, Physica Status Solidi 32(2), 551-562 (1969).
[3] V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ∊ and μ., Physics-Uspekhi 10(4), 509-514 (1968).
[4] A. Selamet, M. Xu, I. J. Lee, and N. Huff, Helmholtz resonator lined with absorbing material, The Journal of the Acoustical Society of America 117(2), 725-733 (2005).
[5] H. H. Huang and C. T. Sun, Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, New Journal of Physics 11(1), 013003 (2009).
[6] 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 59(10), 2070-2081 (2011).
[7] T. Kundu, R. Zhu, G. K. Hu, M. Reynolds, and G. L. Huang, An elastic metamaterial beam for broadband vibration suppression, Proc. of SPIE 8695, 86952J (2013).
[8] T. Kundu, E. Baravelli, M. Carrara, and M. Ruzzene, High stiffness, high damping chiral metamaterial assemblies for low-frequency applications, Proc. of SPIE 8695, 86952K (2013).
[9] H. H. Huang, C. T. Sun, and G. L. Huang, On the negative effective mass density in acoustic metamaterials, International Journal of Engineering Science 47(4), 610-617 (2009).
[10] Y. Xiao, J. Wen, D. Yu, and X. Wen, Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms, Journal of Sound and Vibration 332(4), 867-893 (2013).
[11] M. Nouh, O. Aldraihem, and A. Baz, Wave propagation in metamaterial plates with periodic local resonances, Journal of Sound and Vibration 341, 53-73 (2015).
[12] 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 375(30-31), 2863-2867 (2011).
[13] H. Zhang, Y. Xiao, J. Wen, D. Yu, and X. Wen, Flexural wave band gaps in metamaterial beams with membrane-type resonators: theory and experiment, Journal of Physics D: Applied Physics 48(43), 435305 (2015).
[14] M. A. Nouh, O. J. Aldraihem, and A. Baz, Periodic metamaterial plates with smart tunable local resonators, Journal of Intelligent Material Systems and Structures 27(13), 1829-1845 (2016).
[15] J. S. Chen, Y. J. Huang, and I. T. Chien, Flexural wave propagation in metamaterial beams containing membrane-mass structures, International Journal of Mechanical Sciences 131-132, 500-506 (2017).
[16] J. S. Chen, and I. T. Chien, Dynamic behavior of a metamaterial beam with embedded membrane-mass structures, The American Society of Mechanical Engineers 84(12), 121007 (2017).
[17] C. J. Naify, C.-M. Chang, G. McKnight, and S. Nutt, Transmission loss and dynamic response of membrane-type locally resonant acoustic metamaterials, Journal of Applied Physics 108(11), 114905 (2010).
[18] C. J. Naify, C.-M. Chang, G. McKnight, and S. Nutt, Transmission loss of membrane-type acoustic metamaterials with coaxial ring masses, Journal of Applied Physics 110(12), 124903 (2011).
[19] J. S. Chen and D. W. Kao, Sound attenuation of membranes loaded with square frame-shaped masses, Mathematical Problems in Engineering 2016, 1-11 (2016).
[20] A. Leblanc and A. Lavie, Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation, J Acoust Soc Am 141(6), EL538 (2017).
[21] J. Li, X. Zhou, G. Huang, and G. Hu, Acoustic metamaterials capable of both sound insulation and energy harvesting, Smart Materials and Structures 25(4), 045013 (2016).
[22] 周卓明, 壓電力學, 台灣:全華科計圖書股份有限公司 (2003).