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摘要: 声学黑洞(acoustic black hole, ABH) 效应是利用薄壁结构几何参数或者材料特性参数的梯度变化, 使波在结构中的传播速度逐渐减小, 理想情况下波速减小至零从而不发生反射的现象.实现声学黑洞效应的主要方法是将薄板结构的厚度按照一定规律裁剪, 利用声学黑洞可以将结构中传播的波动能量聚集在特定的位置.声学黑洞对波的聚集具有宽频高效、实现方法简单灵活等特点, 在薄壁结构的减振降噪、能量回收等应用中具有明显的优势.本文介绍声学黑洞效应的基本原理、相关力学问题的研究进展和有待进一步探究的问题, 包括声学黑洞结构的建模与分析方法、实验研究方法及进展、声学黑洞结构中波的传播与操控, 以及声学黑洞在工程应用中的相关问题.Abstract: Acoustic black hole (ABH) efiect utilizes the gradient variance of the structural conflguration or material properties to diminish wave velocity in the structure. The wave velocity decreases to zero in an ideal scenario, resulting in zero reflection. The mainstream method to realize ABH efiect is to tailor the structure thickness properly, such that energy is captured in a certain area. Great advantages and potential in applications for flexural wave manipulation in thin-walled structure result from its high e-ciency, broadband characteristics and flexible implementation. We introduce basic principles of ABH efiect, recent progress of related mechanical problems, and problems to be further explored. We describe the modeling and analysis method of ABH structure, the method and progress of experimental studies, manipulation and propagation of waves in ABH structures, and related issues in engineering applications of ABH structures.
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图 9 反射系数R1与激励频率之间的关系(实线:厚度700 μm的阻尼层; 点虚线:厚度10 μm的阻尼层; 虚线:黑洞区域不贴阻尼层; 点线:无声学黑洞的均匀梁结构粘贴厚度700 μm的阻尼层) (Georgiev et al. 2011)
图 11 厚度变化的阻尼材料对系统阻尼损失因子的影响, 厚度均匀的阻尼材料对应厚度为hd=0.005 cm, 阻尼材料分布的位置为xd=1~2 cm (Tang et al. 2016)
图 17 特定频率下的位移响应. (a) f=0.22 kHz, (b) f=1.85 kHz, (c) f=3.74 kHz, (d) f=0.49 kHz, (e) f=1.20 kHz, (f) f=2.20 kHz, (g) f=0.98 kHz, (h) f=1.90 kHz, (i) f=3.10 kHz (O'Boy & Krylov 2011)
图 18 带黑洞的圆板和不带黑洞环板在同一点处的机械导纳w˙ (Rm, θ=0, ω)/p (Rf) 的比较(O'Boy & Krylov 2011)
图 19 (a) 辐射声功率在频域上的幅值, (b) 对应的结构表面加速度(其中黑色实线表示均匀板, 红色虚线为25个周期排布声学黑洞的板结构) (声学黑洞由于截断会在中心形成小孔) (Conlon et al. 2015b)
图 20 (a) 模态损失因子, (b) 周期排布25个声学黑洞时板结构辐射声功率的幅频特性(其中黑色实线表示声学黑洞中心圆孔较大的情况, 红色虚线表示声学黑洞中心圆孔(ABH-SH) 较小的情况) (Conlon et al. 2015)
图 21 (a) 数值仿真模型: (a1) 声学黑洞结构, (a2) 声学黑洞与阻尼材料(ABH-Damp) 结合, (a3) 声学黑洞与阻尼材料和动力吸振器(ABH-DVA) 结合; (b) 数值仿真结果(Jia et al. 2015)
图 26 实验测量所得椭圆形板的点导纳对比图, 实线表示含声学黑洞并粘贴阻尼材料, 虚线表示不含声学黑洞但在同一位置粘贴同样面积的阻尼材料, 点划线表示不含声学黑洞但在整个试件上粘贴阻尼材料(Georgiev et al. 2011)
图 27 结构的机械导纳. (a) 不含声学黑洞的结构, (b) 含有声学黑洞的结构(O'Boy & Krylov 2011)
图 35 四种涡轮叶片试件上的流动显示图. (a) 未扭曲的参考叶片, (b) 未扭曲含有一维声学黑洞边缘的叶片, (c) 未扭曲含有一维声学黑洞边缘的叶片边缘粘贴普通阻尼材料, (d) 未扭曲含有一维声学黑洞边缘的叶片边缘粘贴阻尼材料(该材料还原了参考叶片的几何外形)
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[1] 阚君武, 唐可洪, 王淑云, 杨志刚, 贾杰, 曾平. 2008.压电悬臂梁发电装置的建模与仿真分析.光学精密工程, 16: 71 http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200801015.htmKan J W, Tang K H, Wang S Y, Yang Z G, Jia J, Zeng P. 2008. Modeling and siulation of piezoelectric cantilever generators. Optics and Precision Engineering, 16: 71. http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM200801015.htm [2] 赵娟, 刘伟群, 刘永斌, 冯志华. 2010.压电等应变梁能量回收装置研究.压电与声光, 32: 406-409 http://www.cnki.com.cn/Article/CJFDTOTAL-YDSG201003021.htmZhao J, Liu W Q, Liu Y B, Feng Z H. 2010. Research on uniform-stain piezoelectric energy harvesting mechanicsm. Piezoelectrics & Acoustooptics, 32: 406-409. http://www.cnki.com.cn/Article/CJFDTOTAL-YDSG201003021.htm [3] Bailey C D. 1978. Direct analytical solutions to non-uniform beam problems. Journal of Sound and Vibration, 56: 501-507. doi: 10.1016/0022-460X(78)90292-4 [4] Bayod J J. 2011. Experimental study of vibration damping in a modifled elastic wedge of power-law proflle. Journal of Vibration and Acoustics, 133: 061003. doi: 10.1115/1.4003591 [5] Bowyer E P, Krylov V V. 2012. Sound radiation of rectangular plates containing tapered indentations of power-law proflle//Proceedings of Meetings on Acoustics. Kansas City, Missouri, Acoustical Society of America through the American Institute of Physics, 18: 030002-030002. [6] Bowyer E P, Krylov V V. 2014a. Damping of flexural vibrations in turbofan blades using the acoustic black hole efiect. Applied Acoustics, 76: 359-365. doi: 10.1016/j.apacoust.2013.09.009 [7] Bowyer E P, Krylov V V. 2014b. Experimental investigation of damping flexural vibrations in glass flbre composite plates containing one-and two-dimensional acoustic black holes. Composite Structures, 107: 406-415. doi: 10.1016/j.compstruct.2013.08.011 [8] Bowyer E P, Krylov V V. 2015a. Experimental study of sound radiation by plates containing circular indentations of power-law proflle. Applied Acoustics, 88: 30-37. doi: 10.1016/j.apacoust.2014.07.014 [9] Bowyer E P, Krylov V V. 2015b. A review of experimental investigations into the acoustic black hole efiect and its applications for reduction of flexural vibrations and structure-borne sound. [10] Bowyer E P, Krylov V V, O'Boy D J. 2012a. Damping of flexural vibrations in rectangular plates by slots of power-law froflle//Proceedings of the Acoustics 2012 Nantes Conference. Nantes, France: 2187-2192. [11] Bowyer E P, Krylov V V, O'Boy D J. 2012b. Damping of flexural vibrations in rectangular plates by slots of power-law proflle//Acoustics 2012. [12] Bowyer E P, Lister J, Krylov V V, O'Boy D J. 2012. Experimental study of damping flexural vibrations in tapered turbofan blades//Acoustics 2012. [13] Bowyer E P, Nash P, Krylov V V. 2013. Damping of flexural vibrations in glass flbre composite plates and honeycomb sandwich panels containing indentations of power-law proflle. Acoustical Society of America, 18: 030004. [14] Bowyer E P, O'Boy D J, Krylov V V. 2012. Damping of flexural vibrations in composite plates and panels containing one-and two-dimensional acoustic black holes//Acoustics 2012. [15] Bowyer E P, O'Boy D J, Krylov V V, Gautier F. 2010. Experimental investigation of damping flexural vibrations using two-dimensional acoustic "black holes"//Proceedings of the International Conference on Noise and Vibration Engineering, Leuven, Belgium, 1181-1192. [16] Bowyer E P, O'Boy D J, Krylov V V, Gautier F. 2013. Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law proflle. Applied Acoustics, 74: 553-560. doi: 10.1016/j.apacoust.2012.10.004 [17] Bowyer E P, O'Boy D J, Krylov V V, Horner J L. 2012. Efiect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law proflle. Applied Acoustics, 73: 514-523. doi: 10.1016/j.apacoust.2011.12.010 [18] Cheng L. 1996. Vibroacoustic modeling of mechanically coupled structures: Artiflcial spring technique applied to light and heavy mediums. Shock and Vibration, 3: 193-200. doi: 10.1155/1996/343429 [19] Cheng L, Lapointe R. 1995. Vibration attenuation of panel structures by optimally shaped viscoelastic coating with added weight considerations. Thin-walled structures, 21: 307-326. doi: 10.1016/0263-8231(95)93617-U [20] Climente A, Torrent D, Sáanchez-Dehesa J. 2014. Gradient index lenses for flexural waves based on thickness variations. Applied Physics Letters, 105: 064101. doi: 10.1063/1.4893153 [21] Climente A, Torrent D, Sáanchez-Dehesa J. 2013. Omnidirectional broadband insulating device for flexural waves in thin plates. Journal of Applied Physics, 114: 214903. doi: 10.1063/1.4839375 [22] Conlon S C, Fahnline J B, Semperlotti F, Feurtado P A. 2014. Enhancing the low frequency vibration reduction performance of plates with embedded acoustic black holes. Inter-noise and Noise-con Congress and Conference Proceedings InterNoise14, Australia, 175-182. [23] Conlon S C, Fahnline J B, Semperlotti F. 2015a. Numerical analysis of the vibroacoustic properties of plates with embedded grids of acoustic black holes. J Acoust Soc Am, 137: 447-457. doi: 10.1121/1.4904501 [24] Conlon S C, Fahnline J B, Shepherd M R, Feurtado P A. 2015b. Vibration control using grids of Acoustic Black Holes: How many is enough. [25] Conway H. 1958. Some special solutions for the flexural vibration of discs of varying thickness. Archive of Applied Mechanics, 26: 408-410. [26] Cottone F, Gammaitoni L, Vocca H, Ferrari M, Ferrari V. 2012. Piezoelectric buckled beams for random vibration energy harvesting. Smart materials and structures, 21: 035021. doi: 10.1088/0964-1726/21/3/035021 [27] Denis V, Gautier F, Pelat A, Poittevin J. 2015. Measurement and modelling of the reflection coe-cient of an Acoustic Black Hole termination. Journal of Sound and Vibration, 349: 67-79. doi: 10.1016/j.jsv.2015.03.043 [28] Denis V, Pelat A, Gautier F, Elie B. 2014. Modal Overlap Factor of a beam with an acoustic black hole termination. Journal of Sound and Vibration, 333: 2475-2488. doi: 10.1016/j.jsv.2014.02.005 [29] Dubois M, Farhat M, Bossy E, Enoch S, Guenneau S, Sebbah P. 2013. Flat lens for pulse focusing of elastic waves in thin plates. Applied Physics Letters, 103: 071915. doi: 10.1063/1.4818716 [30] El-Ouahabi A A, Krylov V V, O'Boy D J. 2015. Investigation of the acoustic black hole termination for sound waves propagating in cylindrical waveguides//Inter-noise and Noise-con Congress and Conference Proceedings, Institute of Noise Control Engineering. [31] Elishakofi I. 2000. Axisymmetric vibration of inhomogeneous clamped circular plates: an unusual closedform solution. Journal of Sound and Vibration, 233: 723-734. doi: 10.1006/jsvi.1999.2825 [32] Erturk A, Inman D. 2011a. Broadband piezoelectric power generation on high-energy orbits of the bistable Du-ng oscillator with electromechanical coupling. Journal of Sound and Vibration, 330: 2339-2353. doi: 10.1016/j.jsv.2010.11.018 [33] Erturk A, Inman D J. 2011b. Piezoelectric Energy Harvesting. John Wiley & Sons. [34] Fíelix S, Pagneux V. 2002. Multimodal analysis of acoustic propagation in three-dimensional bends. Wave Motion, 36: 157-168. doi: 10.1016/S0165-2125(02)00009-4 [35] Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C, Zhang X. 2006. Ultrasonic metamaterials with negative modulus. Nature materials, 5: 452-456. doi: 10.1038/nmat1644 [36] Foucaud S, Michon G, Gourinat Y, Pelat A, Gautier F. 2012. Immersed acoustic black hole as a travelling wave absorber: understanding artiflcial cochlear mechanics//Acoustics 2012. [37] Gang W, Li H S, Yao Z L, Ji H W. 2006. Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals. Chinese Physics, 15: 1843. doi: 10.1088/1009-1963/15/8/036 [38] Gautier F, Moulet M H, Pascal J C. 2006. Reflection, transmission and coupling of longitudinal and flexural waves at beam junctions. Part Ⅰ: measurement methods. Acta Acustica United with Acustica, 92: 982-997. [39] Georgiev V, Cuenca J, Bermudez M M, Gautier F, Simon L. 2010. Recent progress in vibration reduction using Acoustic Black Hole efiect//10ème Congrès Françcais d'Acoustique. [40] Georgiev V B, Cuenca J, Gautier F, Simon L, Krylov V V. 2011. Damping of structural vibrations in beams and elliptical plates using the acoustic black hole efiect. Journal of Sound and Vibration, 330: 2497-2508. doi: 10.1016/j.jsv.2010.12.001 [41] Georgiev V B, Cuenca J, Moleron Bermudez M, Gautier F, Simon L, Krylov V V. 2009. Numerical and experimental investigation of the acoustic black hole efiect for vibration damping in beams and elliptical plates//Euronoise 2009, Edinburgh, Scotland. [42] Hou T, Qin H. 2012. Continuous and discrete Mexican hat wavelet transforms on manifolds. Graphical Models, 74: 221-232. doi: 10.1016/j.gmod.2012.04.010 [43] Huang W, Ji H, Qiu J, Cheng L. 2016. Wave energy focalization in a plate with imperfect two-dimensional acoustic black hole indentation. Journal of Vibration and Acoustics, 138: 061004. doi: 10.1115/1.4034080 [44] Jain R. 1972. Vibrations of circular plates of variable thickness under an inplane force. Journal of Sound and Vibration, 23: 407-414. doi: 10.1016/0022-460X(72)90499-3 [45] Jia X, Du Y, Zhao K. 2015. Vibration control of variable thickness plates with embedded acoustic black holes and dynamic vibration absorbers//ASME 2015 Noise Control and Acoustics Division Conference at InterNoise 2015, American Society of Mechanical Engineers. [46] Kobayashi H, Sonoda K. 1991. Vibration and buckling of tapered rectangular plates with two opposite edges simply supported and the other two edges elastically restrained against rotation. Journal of Sound and Vibration, 146: 323-337. doi: 10.1016/0022-460X(91)90766-D [47] Kralovic V, Bowyer E P, Krylov V V, O'Boy D J. 2009. Experimental study on damping of flexural waves in rectangular plates by means of one-dimensional acoustic "Black Holes"//14th International Acoustic Conference. [48] Kralovic V, Krylov V V. 2007. Damping of flexural vibrations in tapered rods of power-law proflle: Experimental studies. Proceeding of the Institute of Acoustics, 29: 66-73. [49] Kravchun P. 1991. Generation and Methods of Reduction of Noise and Vibration. Moscow: Moscow University Press. [50] Krvlov V V. 1990a. Localized acoustic modes of a quadratic solid wedge. Physies Billelin, 45: 65-69. [51] Krylov V V. 1989. Conditions for validity of the geometrical-acoustics approximation in application to waves in an acute-angle solid wedge. Soviet Physics -Acoustics, 35: 176-180. [52] Krylov V V. 1990b. Geometrical-acoustics approach to the description of localized vibrational modes of an elastic solid wedge. Sovjet Physics-Technical Physics, 25: 137-140. [53] Krylov V V. 1995. Surface properties of solids and surface acoustic waves: Application to chemical sensors and layer characterization. Applied Physics A, 61: 229-236. doi: 10.1007/BF01538187 [54] Krylov V V. 1997. On the velocities of localized vibration modes in immersed solid wedges. Journal of Acoustical Society of America, 103: 767. [55] Krylov V V. 1998. On the velocities of localized vibration modes in immersed solid wedges. The Journal of the Acoustical Society of America, 103: 767-770. doi: 10.1121/1.421240 [56] Krylov V V. 2004. New type of vibration dampers utilising the efiect of acoustic black holes". Acta Acustica united with Acustica, 90: 830-837. [57] Krylov V V. 2007. Propagation of plate bending waves in the vicinity of one-and two-dimensional acoustic black hole//Proceedings of the ECCOMAS International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2007). Rethymno, Crete, Greece: CD-ROM. [58] Krylov V V. 2014. Acoustic black holes: Recent developments in the theory and applications. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 61: 1296-1306. doi: 10.1109/TUFFC.2014.3036 [59] Krylov V V, Shuvalov A. 2000. Propagation of localised flexural vibrations along plate edges described by a power law. Proceedings of the Institute of Acoustics, 22: 263-270. [60] Krylov V V, Tilman F J B S. 2004. Acoustic "black holes" for flexural waves as efiective vibration dampers. Journal of Sound and Vibration, 274: 605-619. doi: 10.1016/j.jsv.2003.05.010 [61] Krylov V V, Winward E. 2005. Experimental evidence of the acoustic black hole efiect for flexural waves in tapered plates//Proceedings of the 12th International Congress on Suond and Vibration, Lisbon, Portugal. [62] Krylov V V, Winward R E T B. 2007. Experimental investigation of the acoustic black hole efiect for flexural waves in tapered plates. Journal of Sound and Vibration, 300: 43-49. doi: 10.1016/j.jsv.2006.07.035 [63] Liu H, Lee C, Kobayashi T, Tay C J, Quan C. 2012. Investigation of a MEMS piezoelectric energy harvester system with a frequency-widened-bandwidth mechanism introduced by mechanical stoppers. Smart Materials and Structures, 21: 035005. doi: 10.1088/0964-1726/21/3/035005 [64] Liu Z, Chan C, Sheng P. 2005. Analytic model of phononic crystals with local resonances. Physical Review B, 71: 014103. doi: 10.1103/PhysRevB.71.014103 [65] Liu Z, Zhang X, Mao Y, Zhu Y, Yang Z, Chan C, Sheng P. 2000. Locally resonant sonic materials. Science, 289: 1734-1736. doi: 10.1126/science.289.5485.1734 [66] Lomonosov A M, Yan S L, Han B, Zhang H C, Shen Z H. 2015. Orbital-type trapping of elastic Lamb waves. Ultrasonics, 64: 58-67. [67] Mironov M. 1988. Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a flnite interval. Amer Inst Physics Circulation Fulflllment Div, 500 Sunnyside Blvd, Woodbury, NY 11797-2999. 34: 318-319. [68] Mironov M, Pislyakov V. 2002. One-dimensional acoustic waves in retarding structures with propagation velocity tending to zero. Acoustical Physics, 48: 347-352. doi: 10.1134/1.1478121 [69] Narimanov E E, Kildishev A V. 2009. Optical black hole: Broadband omnidirectional light absorber. Applied Physics Letters, 95: 041106. doi: 10.1063/1.3184594 [70] Neu J, Krolla B, Paul O, Reinhard B, Beigang R, Rahm M. 2010. Metamaterial-based gradient index lens with strong focusing in the THz frequency range. Optics express, 18: 27748-27757. doi: 10.1364/OE.18.027748 [71] Ng S, Araar Y. 1989. Free vibration and buckling analysis of clamped rectangular plates of variable thickness by the Galerkin method. Journal of sound and vibration, 135: 263-274. doi: 10.1016/0022-460X(89)90725-6 [72] O'Boy D, Bowyer E P, Krylov V V. 2010. Damping of flexural vibrations in thin plates using one and two dimensional acoustic black hole efiect//10th International Conference on Recent Advances in Structural Dynamics, Southampton, UK, 12-14 July. [73] O'Boy D J, Krylov V V. 2011. Damping of flexural vibrations in circular plates with tapered central holes. Journal of Sound and Vibration, 330: 2220-2236. doi: 10.1016/j.jsv.2010.11.017 [74] O'Boy D J, Krylov V V, Kralovic V. 2010. Damping of flexural vibrations in rectangular plates using the acoustic black hole efiect. Journal of Sound and Vibration, 329: 4672-4688. doi: 10.1016/j.jsv.2010.05.019 [75] Pekeris C. 1946. Theory of propagation of sound in a half-space of variable sound velocity under conditions of formation of a shadow zone. The Journal of the Acoustical Society of America, 18: 295-315. doi: 10.1121/1.1916366 [76] Peng S Z, Pan J. 2004. Acoustical wave propagator for time-domain flexural waves in thin plates. The Journal of the Acoustical Society of America, 115: 467. doi: 10.1121/1.1639905 [77] Qiu J, Tan J Y, Liu L H, Hsu P f. 2011. Infrared radiative properties of two-dimensional square optical black holes. Journal of Quantitative Spectroscopy and Radiative Transfer, 112: 2584-2591. doi: 10.1016/j.jqsrt.2011.08.002 [78] Ross, D, Ungar E E, Kerwin E M Jr. 1960. Damping of Plate Flexural Vibrations by Means of Viscoelastic Laminae. Ruzicka, J.E. ed. Structural Damping, Oxford: Pergamon Press, 49-87. [79] Press, Oxford 1960, 49-87.Semperlotti F, Zhu H. 2015. Acoustic meta-structures based on periodic acoustic black holes. The Journal of the Acoustical Society of America, 137: 2265-2265. [80] Singh B, Saxena V. 1995. Axisymmetric vibration of a circular plate with double linear variable thickness. Journal of Sound and Vibration, 179: 879-897. doi: 10.1006/jsvi.1995.0059 [81] Singh B, Saxena V. 1996. Axisymmetric vibration of a circular plate with exponential thickness variation. Journal of sound and vibration, 192: 35-42. doi: 10.1006/jsvi.1996.0174 [82] Spadoni A, Ruzzene M, Cunefare K. 2009. Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches. Journal of Intelligent Material Systems and Structures, 20: 979-990. doi: 10.1177/1045389X08100041 [83] Taher H R D, Omidi M, Zadpoor A, Nikooyan A. 2006. Free vibration of circular and annular plates with variable thickness and difierent combinations of boundary conditions. Journal of Sound and Vibration, 296: 1084-1092. doi: 10.1016/j.jsv.2006.03.022 [84] Tang L, Cheng L. 2016. Loss of acoustic black hole efiect in a structure of flnite size. Applied Physics Letters, 109: 014102. doi: 10.1063/1.4955127 [85] Tang L, Yang Y, Soh C K. 2013. Broadband Vibration Energy Harvesting Techniques. Advances in Energy Harvesting Methods, Springer: 17-61. [86] Tang L, Zhang S, Ji H, Cheng L, Qiu J. 2016. Characterization of acoustic black hole efiect using a 1-D fully-coupled and wavelet-decomposed semi-analytical model. Journal of Sound and Vibration, 374: 172-184. doi: 10.1016/j.jsv.2016.03.031 [87] Torrent D, Pennec Y, Djafari-Rouhani B. 2014. Omnidirectional refractive devices for flexural waves based on graded phononic crystals. Journal of Applied Physics, 116: 224902. doi: 10.1063/1.4903972 [88] Torrent D, Sáanchez-Dehesa J. 2007. Acoustic metamaterials for new two-dimensional sonic devices. New journal of physics, 9: 323. doi: 10.1088/1367-2630/9/9/323 [89] Vocca H, Neri I, Travasso F, Gammaitoni L. 2012. Kinetic energy harvesting with bistable oscillators. Applied Energy, 97: 771-776. doi: 10.1016/j.apenergy.2011.12.087 [90] Wang G, Wang J, Chen S, Wen J. 2011. Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits. Smart Materials and Structures, 20: 125019. doi: 10.1088/0964-1726/20/12/125019 [91] Wang H, Chen L. 2011. A cylindrical optical black hole using graded index photonic crystals. Journal of Applied Physics, 109: 103104. doi: 10.1063/1.3590336 [92] Wang X, Yang J, Xiao J. 1995. On free vibration analysis of circular annular plates with non-uniform thickness by the difierential quadrature method. Journal of Sound and Vibration, 184: 547-551. doi: 10.1006/jsvi.1995.0332 [93] Wang Z, Norris A. 1995. Waves in cylindrical shells with circumferential submembers: a matrix approach. Journal of Sound and Vibration, 181: 457-484. doi: 10.1006/jsvi.1995.0152 [94] Wu X M, Lin J H, Kato S, Zhang K, Ren T, Liu L T. 2008. A frequency adjustable vibration energy harvester. Proceedings of PowerMEMS, 245-248. [95] Wu Y, Qiu J, Chao Z, Zhu K, Ji H. 2014. A Method to Improve the Visibility of the Damage-Reflected Wave. Chinese Journal of Lasers, 41: 0308001-0308020. [96] Xiao Y, Wen J, Wen X. 2012. Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators. New Journal of Physics, 14: 033042. doi: 10.1088/1367-2630/14/3/033042 [97] Yan S, Lomonosov A M, Shen Z. 2016. Numerical and experimental study of Lamb wave propagation in a two-dimensional acoustic black hole. Journal of Applied Physics, 119: 214902. doi: 10.1063/1.4953221 [98] Yang J. 1993. The vibration of a circular plate with varying thickness. Journal of Sound and Vibration, 165: 178-184. doi: 10.1006/jsvi.1993.1251 [99] Yu D, Liu Y, Wang G, Zhao H, Qiu J. 2006. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. Journal of Applied Physics, 100: 124901. doi: 10.1063/1.2400803 [100] Zhang C, Qiu J, Ji H. 2014. Laser ultrasonic imaging for impact damage visualization in composite structure//EWSHM-7th European Workshop on Structural Health Monitoring. [101] Zhang S, Yin L, Fang N. 2009. Focusing ultrasound with an acoustic metamaterial network. Phys Rev Lett, 102: 194301. doi: 10.1103/PhysRevLett.102.194301 [102] Zhao L, Conlon S, Semperlotti F. 2015. Experimental veriflcation of energy harvesting performance in plate-like structures with embedded acoustic black holes//INTER-NOISE and NOISE-CON Congress and Conference Proceedings, Institute of Noise Control Engineering. [103] Zhao L, Conlon S C, Semperlotti F. 2014. Broadband energy harvesting using acoustic black hole structural tailoring. Smart Materials and Structures, 23: 065021. doi: 10.1088/0964-1726/23/6/065021 [104] Zhu H, Semperlotti F. 2015. Phononic thin plates with embedded acoustic black holes. Physical Review B, 91: 39-43. -
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