本研究分為兩個部分，分別為對聲子晶體共振腔與具減振結構之細長樑的分析。聲子晶體具有能隙現象，可延伸應用於諸多聲學裝置計，如共振腔、感測器及能量擷取裝置等等，而具減振結構之細長樑則結合聲學黑洞效應以及阻尼層，具有良好的寬頻減振特性。
本文第一部分研究三組由壓克力與空氣兩種材料組成的聲子晶體共振腔，分別為點缺陷聲子晶體、圓形共振腔以及環之共振腔，藉由特徵模態與色散曲線的計算討論不同共振腔內的缺陷模態形式與特性。接著由聲強的計算可得到缺陷模態之品質因子，儘管未考慮黏滯與摩擦熱影響，但仍可比較各個聲子晶體共振腔其缺陷模態的能量集中能力。而後設計一套實驗流程以量測所分析的聲子晶體共振腔之缺陷模態及缺陷頻率，討論實驗結果以及實驗結果與模擬的差異。
第二部分則討論具減振設計的細長樑，基於學者們對彎曲波中的聲學黑洞效應與自由層阻尼處理的研究基礎，利用Oberst's equation對貼覆阻尼層之細長樑分析，探討其等效撓曲剛性與等效損失係數如何受阻尼層楊氏模數與厚度的影響。接著以幾何聲學近似和有限元素法計算具聲學黑洞結構之細長樑的反射係數，藉此討論聲學黑洞效應與阻尼層結合的減振特性，並比較兩種反射係數計算方法的差別。最後量測具聲學黑洞效應之細長樑樣品的反射係數，討論實驗結果以及實驗與理論的差異。

In this study, our work is divided into two different parts, which are the analysis of phononic crystal cavities and Euler–Bernoulli beam with vibration reduction structure. The first part is that we analyze three kinds of phononic crystal cavities that are composed of acrylic and air. They are phononic crystals with a point defect phononic crystal, phononic crystals with a round cavity and phononic crystals with an annular cavity. By means of calculating eigenmodes and dispersion curves of them, we discuss types and characteristics of their defect modes We also calculate the quality factor of their defect modes to compare the energy-gathering properties in spite of neglecting the effect of friction and viscosity. Finally, create the measurement method to measure defect modes and defect frequencies of the round cavity, and discuss the difference between experimental results and numerical calculation. The second part is to study in Euler–Bernoulli beams with vibration reduction structure. We first analyze Euler beams with a damping later by using Oberst's equation to understand how effective flexural rigidity is affected by the property of a damping layer. Next, we calculate the reflection coefficient of ABH beams with a damping layer to explore the vibration reduction properties about the combination of ABH effect and damping layer. At last, we measure the simple of ABH beam with damping layer and discuss the experimental results and the dissimilarity between experiments and numerical simulations.

[1] L. Brillouin, Wave propagation in periodic structures: electric filters and crystal lattices: Courier Corporation, 2003.
[2] E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys Rev Lett, vol. 58, pp. 2059-2062, May 18 1987.
[3] Z. Liu, "Locally Resonant Sonic Materials," Science, vol. 289, pp. 1734-1736, 2000.
[4] L.-Y. Wu, L.-W. Chen, and C.-M. Liu, "Experimental investigation of the acoustic pressure in cavity of a two-dimensional sonic crystal," Physica B: Condensed Matter, vol. 404, pp. 1766-1770, 2009.
[5] A. Khelif, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Dobrzynski, "Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency," Journal of Applied Physics, vol. 94, pp. 1308-1311, 2003.
[6] Y.-n. Zhang, Y. Zhao, and R.-q. Lv, "A review for optical sensors based on photonic crystal cavities," Sensors and Actuators A: Physical, vol. 233, pp. 374-389, 2015.
[7] H. Lv, X. Tian, M. Y. Wang, and D. Li, "Vibration energy harvesting using a phononic crystal with point defect states," Applied Physics Letters, vol. 102, p. 034103, 2013.
[8] 吳亮諭, "聲子晶體共振腔之分析與聲能能量擷取," 成功大學機械工程學系學位論文, pp. 1-121, 2010.
[9] J. W. S. B. Rayleigh, The theory of sound vol. 2: Macmillan, 1896.
[10] H.-Y. Ryu, M. Notomi, G.-H. Kim, and Y.-H. Lee, "High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity," Optics express, vol. 12, pp. 1708-1719, 2004.
[11] G. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, et al., "Whispering gallery mode microresonators: fundamentals and applications," Rivista del Nuovo Cimento, vol. 34, pp. 435-488, 2011.
[12] H. Kudo, R. Suzuki, and T. Tanabe, "Whispering gallery modes in hexagonal microcavities," Physical Review A, vol. 88, 2013.
[13] V. V. Krylov, "Wedge acoustic waves: New theoretical and experimental results," 1990.
[14] V. Krylov and D. Parker, "Harmonic generation and parametric mixing in wedge acoustic waves," Wave Motion, vol. 15, pp. 185-200, 1992.
[15] M. Mironov, "Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval," vol. 34, ed: AMER INST PHYSICS CIRCULATION FULFILLMENT DIV, 500 SUNNYSIDE BLVD, WOODBURY, NY 11797-2999, 1988, pp. 318-319.
[16] V. V. Krylov and F. J. B. S. Tilman, "Acoustic ‘black holes’ for flexural waves as effective vibration dampers," Journal of Sound and Vibration, vol. 274, pp. 605-619, 2004.
[17] P. A. Feurtado, S. C. Conlon, and F. Semperlotti, "A normalized wave number variation parameter for acoustic black hole design," J Acoust Soc Am, vol. 136, pp. EL148-52, Aug 2014.
[18] V. V. Krylov and R. E. T. B. Winward, "Experimental investigation of the acoustic black hole effect for flexural waves in tapered plates," Journal of Sound and Vibration, vol. 300, pp. 43-49, 2007.
[19] V. V. Krylov, "Propagation of plate bending waves in the vicinity of one-and two-dimensional acoustic ‘black holes’," 2007.
[20] L. Zhao, S. C. Conlon, and F. Semperlotti, "Broadband energy harvesting using acoustic black hole structural tailoring," Smart Materials and Structures, vol. 23, p. 065021, 2014.
[21] L. Zhao, S. C. Conlon, and F. Semperlotti, "An experimental study of vibration based energy harvesting in dynamically tailored structures with embedded acoustic black holes," Smart Materials and Structures, vol. 24, p. 065039, 2015.
[22] V. Denis, F. Gautier, A. Pelat, and J. Poittevin, "Measurement and modelling of the reflection coefficient of an Acoustic Black Hole termination," Journal of Sound and Vibration, vol. 349, pp. 67-79, 2015.
[23] V. Denis, A. Pelat, and F. Gautier, "Scattering effects induced by imperfections on an acoustic black hole placed at a structural waveguide termination," Journal of Sound and Vibration, vol. 362, pp. 56-71, 2016.
[24] D. I. Jones, Handbook of viscoelastic vibration damping: John Wiley & Sons, 2001.
[25] F. Cortés and M. J. Elejabarrieta, "Structural vibration of flexural beams with thick unconstrained layer damping," International Journal of Solids and Structures, vol. 45, pp. 5805-5813, 2008.
[26] R. Hibbeler, "Mechanics of Materials, 1997," ed: Prentice Hall.
[27] L. Ziomek, Fundamentals of acoustic field theory and space-time signal processing: CRC press, 1994.
[28] 赵寰宇, 何存富, 吴斌, and 汪越胜, "二维正方晶格多点缺陷声子晶体实验研究," 物理学报, vol. 62, pp. 301-310, 2013.
[29] W. Heylen and P. Sas, Modal analysis theory and testing: Katholieke Universteit Leuven, Departement Werktuigkunde, 2005.
[30] M. J. Moloney, "Quality factors and conductances in Helmholtz resonators," American Journal of Physics, vol. 72, pp. 1035-1039, Aug 2004.
[31] M. J. Moloney and D. L. Hatten, "Acoustic quality factor and energy losses in cylindrical pipes," American Journal of Physics, vol. 69, pp. 311-314, 2001.
[32] Y. Mitsuoka and T. Fujii, "Vibration damping sheet," ed: Google Patents, 2008.