超穎材料為一種具有獨特性質的人造材料，因具有自然界不存在的物理特性，廣泛應用在不同領域當中，大部分是由週期性的局部共振結構排列而成，並透過設計局部結構的幾何形狀或尺寸，改變其物理特性。本研究提出週期性雙螺旋超穎結構梁，是由框型梁架結構附加多個雙螺旋型局部共振器組成，使用COMSOL有限元素軟體做模擬分析，首先對其局部共振器做共振頻率預測，發現在205Hz其局部結構會呈現共振現象，而後運算與繪製頻散關係曲線圖，觀察帶隙形成的位置及模態。模擬穩態分析在有限長度主梁的波傳行為，由頻率響應圖中發現205Hz到251Hz的區間有一個減振區間，與頻散曲線中帶隙的位置相同，表示在此頻率範圍因局部共振器帶隙造成波傳行為受到阻絕。選擇與局部共振器頻率相近的頻率進行暫態分析，檢測在各個位置超穎結構梁振幅衰減的情況，可以發現波沿著主結構的波傳方向其振幅會出現顯著的衰減，並藉由調整局部共振器之幾何結構，探討其對於帶隙位置及頻率響應的影響。從振動實驗結果與模擬結果相互對照，振動衰減的位置十分吻合，在暫態實驗中，隨著量測位置距離激振端越遠，波的衰減幅度增加，實驗結果與模擬預測的結果相符。最後，提出了一種同時減振和擷能的模型，利用PVDF壓電片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，經由模擬PVDF壓電片貼在局部共振器上，預測壓電片產電的頻率位置與電壓，且藉由阻抗匹配進行探討，當外接電阻300kΩ時得到最高功率 。經過實驗認證在外接電阻300kΩ會有最佳功率，且經由並聯壓電片後實際量測電壓約有0.38V，由結果可知，所提出的超穎結構模型可同時達到減振與擷能效果。

This thesis presents a novel metastructure with a double-spiral local resonator for vibration suppression and energy harvesting. The metamaterial beam consists of nine cells. Each cell is divided into two parts: a host beam with a central hole and a double-spiral type of local resonator embedded in it. The double-spiral type of local resonator is comprised of fourteen beams with a central mass. The finite element (FE) software COMSOL Multiphysics 5.3 is used to obtain dispersion curves and frequency response analyses. The vibration experiment is used to verify FE results. Comparing the simulations with experimental results, attenuation zones obtained by two methods match quite well. In transient analysis, it is observed that as the excitation force frequency is close to the natural frequencies of the resonator, wave is attenuated. It can be concluded that the proposed structure can suppress the flexural motion of the host structure. Furthermore, the attenuation region can be easily turned by adjusting the number of beams, the thickness of central mass or subordinate beams. The proposed model can not only suppress the vibration amplitude but also harvest the vibration energy. The PVDF piezoelectric films are attached to the local resonator, and the harvested electric energy can be used for operating other devices.

[1] V. G.Veselago, "The electrodynamics of substances with simultaneously negative value of ε and μ", Physics (College. Park. Md)., vol. 10, no. 4, 1968.
[2] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, "Acoustic band structure of periodic elastic composites", Phys Rev Lett 71(13), 2022-2025, 1993.
[3] Z. Liu, X. Zhang, Y. Mao, Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally resonant sonic materials", Science 289(5485), 1734-1736, 2000.
[4] J. Li and C. T. Chan, "Double-negative acoustic metamaterial", Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top., vol. 70, no. 5, p. 4, 2004.
[5] H. Huang and C. 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.
[6] J. B.Pendry, "Negative refraction makes a perfect lens", Phys. Rev. Lett., vol. 85, no. 18, pp. 3966–3969, 2000.
[7] R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction", science, vol. 292, no. 5514, pp. 77-79, 2001.
[8] J. S. Chen and C. T. Sun, "Dynamic behavior of a sandwich beam with internal resonators", Journal of Sandwich Structures & Materials, vol. 13, no. 4, pp. 391-408, 2011.
[9] S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, "Acoustic metamaterial with negative modulus", Journal of Physics: Condensed Matter 21(17), 175704, 2009.
[10] C. Ding, L. Hao, and X. Zhao, "Two-dimensional acoustic metamaterial with negative modulus", Journal of Applied Physics 108(7), 074911, 2010.
 
[11] S. Zhai, H. Chen, C. Ding, and X. Zhao, "Double-negative acoustic metamaterial based on meta-molecule", J. Phys. D. Appl. Phys., vol. 46, no. 47, 2013.
[12] V. E. Gusev and O. B. Wright, "Double-negative flexural acoustic metamaterial", New J. Phys., vol. 16, 2014.
[13] 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.
[14] I. L. Chang, Z. X. Liang, H. W. Kao, S. H. Chang, and C. Y. Yang, "The wave attenuation mechanism of the periodic local resonant metamaterial", Journal of Sound and Vibration 412, 349-359, 2018.
[15] Y. Xiao, J. Wen, D. Yu, and X. Wen, "Flexural wave propagation in beams with periodically attachedvibration absorbers: Band-gap behavior and bandformation mechanisms", Journal of Sound and Vibration 332(4), 867-893, 2003.
[16] J. Ma, M. Sheng, Z. Guo and Q. Qin, "Dynamic analysis of periodic vibration suppressors with multiple secondary oscillators", Journal of Sound and Vibration, vol. 424, pp. 94-111, 2018.
[17] Z. Yang, H. M. Dai, N. H. Chan, G. C. Ma and P. Sheng, "Acoustic metamaterial panels for sound attenuation in the 50-1000 Hz regime", Applied Physics Letters, vol. 96, no. 4, 041906, 2010.
[18] 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, vol. 48, no. 43, 435305, 2015.
[19] 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, vol. 131-132, pp. 500-506, 2017.
 
[20] Y. Xiao, J. Wen, G. Wang, and X. Wen, "Theoretical and experimental study of locally resonant and Bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators", Journal of Vibration and Acoustics, vol. 135, no. 4, 041006, 2013.
[21] 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, vol. 375, no. 30-31, pp. 2863-2867, 2011.
[22] A. A. Santos, J. D. Hobeck, and D. J. Inman, "Analytical modeling of orthogonal spiral structures", Smart Mater. Struct., vol. 25, no. 11, 2016.
[23] T. Dong, E. Halvorsen and Z. Yang, "A MEMS-based spiral piezoelectric energy harvester", PowerMEMS, pp. 77-80, 2008.
[24] X. Bai, Y. Wen, P. Li, J. Yang, X. Peng and X. Yue, "Multi-modal vibration energy harvesting utilizing spiral cantilever with magnetic coupling", Sensors and Actuators A: Physical, vol. 209, pp. 78-86, 2014.
[25] K. S. M. Murthy, L. M. Kakarla, S. R. Tejeswi, S. Vamsi and M. Reddy, "Fem simulation of ultra low resonant piezoelectric spiral energy harvester", Journal of Advanced Research in Dynamical and Control Systems, vol. 9, pp. 2313-2319, 2017.
[26] F. Lu, H. P. Lee, andS. P. Lim, "Modeling and analysis of micro piezoelectric power generators for micro-electromechanical-systems applications", Smart Mater. Struct., vol. 13, no. 1, pp. 57-63, 2004.
[27] M. Fakhzan and A. G. Muthalif, "Vibration based energy harvesting using piezoelectric material", IEEE, pp. 1-7, 2011.
[28] J. E. Kim and Y. Y. Kim, "Analysis of piezoelectric energy harvesters of a moderate aspect ratio with a distributed tip mass", Journal of Vibration and Acoustics, vol. 133, no. 4, 041010, 2011.
[29] M. Fakhzan and A. G. Muthalif, "Harvesting vibration energy using piezoelectric material: Modeling, simulation and experimental verifications", Mechatronics, vol. 23, no. 1, pp. 61-66, 2013.
[30] G. Hu, L. Tang, and R. Das, "Internally coupled metamaterial beam for simultaneous vibration suppression and low frequency energy harvesting", Journal of Applied Physics, vol. 123, no. 5, 055107, 2018.
[31] L. Wang, L. Zhao, Z. Jiang, G. Luo, P. Yang, X. Han, X. Li, and R. Maeda, "High accuracy comsol simulation method of bimorph cantilever for piezoelectric vibration energy harvesting", AIP Advances 9(9), 095067, 2019.
[32] S. J. Rupitsch, "Piezoelectric sensors and actuators: fundamentals and applications", Springer, Berlin, 2019.
[33] 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.
[34] L. Meirovitch, "Fundamentals of vibrations", Waveland Press Inc., 2010.
[35] N. Seera, "Viscoelastic damping of hexagonal honeycomb sandwich panels", Master thesis, 2011.