超穎材料為一種具有獨特性質的人造材料，是藉由週期性的局部結構排列而成，並透過設計局部結構的幾何形狀或尺寸來改變其振動傳遞特性，而創造出非傳統之物理現象，如負質量、負泊松比以及負剛度效應。超穎材料的概念一開始被應用在電磁波，後來逐漸發展到聲波以及彈性波領域，使得噪音和振動可以更有選擇性地傳遞或隔絕在目標頻率範圍內。
本研究提出的超穎結構模型，是由每個單元主結構樑的兩側各別接上局部懸臂樑。首先研究彈性波在有限長的主樑中減振效果，利用有限元素軟體COMSOL分析主結構的頻率響應，並且藉由振動實驗比較減振區的位置及範圍，驗證所提出的超穎結構振動衰減性能。為了確認局部共振帶隙(或稱能隙)的機制，擾動頻率與局部共振器的共振頻率匹配時，諧波沿著主結構的波傳方向其振幅會出現顯著的衰減。可以得出局部共振器可以抑制主結構的撓曲運動結論。後來通過改變局部共振器末端的質量塊厚度或不同質量組成的雙共振器結構可以輕易地調控減振區位置。在本篇後來還提出了一種同時減振和擷能的模型，係將PVDF壓電片貼在局部共振器上，利用壓電的正壓電效應將形變能進一步轉換成電能為其他裝置供電。經過壓電實驗和振動響應的模擬比對，其最大電壓輸出之位置與振動頻率響應的波谷位置一致。

關鍵字：超穎材料、帶隙、壓電。

In this thesis, the locally resonant beam consists of nine cantilever-type resonators. Each local resonator is modeled by a pair of cantilevers with tip masses. The finite element (FE) software COMSOL is used to analyze the frequency response of the beam structure. The vibration experiment is used to verify the position and range of the attenuation zone predicted by FE method. When the excitation force frequency is close to the resonant frequency of the resonator, the bending wave amplitude shows exponential attenuation. It can be concluded that the local resonator can suppress the flexural motion of the host structure. The attenuation region can be easily adjusted by the magnitude of the tip mass. The proposed model can not only reduce vibration but also energy harvesting. The PVDF piezoelectric film is attached to the local resonator, and the harvested electric energy might be used to supply other devices.

Keywords: metamaterial, bandgap, piezoelectric material.

[1] V. G. Veselago, The Electrodynamics of Substances with Simultaneously Negative Values of ϵ and μ, Physics-Uspekhi 10(4), 509-514(1968).
[2] J. B. Pendry, Negative refraction makes a perfect lens,Physical review letters 85(18), 3966(2000).
[3] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites, Physical review letters,71(13), 2022(1993).
[4] H. Huang, C. Sun, and G. Huang, On the negative effective mass density in acoustic metamaterials, International Journal of Engineering Science, 47(4), 610-617(2009).
[5] H. Huang and C. Sun, Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, New Journal of Physics,11(1), 013003(2009).
[6] R. Zhu, G. Huang, H. Huang, and C. Sun, Experimental and numerical study of guided wave propagation in a thin metamaterial plate, Physics Letters A,375(30-31),2863-2867(2011).
[7] G. Gantzounis, M. Serra-Garcia, K. Homma, J. Mendoza, and C. Daraio,Granular metamaterials for vibration mitigation, Journal of Applied Physics, 114(9),093514(2013).
[8] 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).
[9] 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).
[10] N. S. Shenck and J. A. Paradiso,Energy scavenging with shoe-mounted piezoelectrics,IEEE micro, 21(3),30-42(2001).
[11] C. Pan and T. Wu, "Development of a rotary electromagnetic microgenerator," Journal of Micromechanics and Microengineering,17(1),120(2006).
[12] S. Roundy, P. K. Wright, and K. S. Pister, Micro-electrostatic vibration-to-electricity converters, in ASME 2002 International Mechanical Engineering Congress and Exposition, 17-22,487-496(2002).
[13] 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).
[14] W. G. Li, S. He, and S. Yu, Improving power density of a cantilever piezoelectric power harvester through a curved L-shaped proof mass, IEEE Transactions On Industrial Electronics,57(3),868-876(2009).
[15] COMSOL, What Is Mode Superposition?, (2018).
[16] 林永盛, 基礎結構動力, 台灣:文笙圖書有限公司 (1992).
[17] 周卓明, 壓電力學, 台灣:全華科技圖書股份有限公司 (2003).