基于颤振机理的微型压电风致振动能量收集器基础理论与关键技术
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摘要
微能源具有体积小、功率密度高、寿命长、绿色环保等优点，是解决微型器件与系统的电源问题的有效途径，受到了国内外研究者的广泛关注。目前微能源的研究主要针对环境中的动能、热能、太阳能等方面的收集与转化，而对于风能收集的微能源研究较少。基于风致振动机理的微型风能收集器具有体积小、结构简单等优点，是微型风能收集器的主要研究方向。
论文针对环境中广泛存在的风能，提出了一种基于颤振机理的微型压电风致振动能量收集器。基于压电效应，建立了微型压电风致振动能量收集器的单向耦合集总参数模型、单向耦合分布参数模型和双向耦合分布参数模型，完成了模型的修正；提出了压电梁与柔性梁复合的颤振新结构，建立了微型风致振动能量收集器在轴向风中的线性颤振模型和非线性颤振模型；研究了微型压电风致振动能量收集器的设计方法，提出了T型柔性梁结构、非流线体结构、逆风颤振结构等优化结构；完成了微型压电风致振动能量收集器可靠性封装设计和器件的加工，研制出了原理验证样机；搭建了测试分析平台，完成了原理样机的性能测试与分析。研制出的原理样机体积0.1cm3，在风速12.2m/s时，开路电压有效值为16.4V、输出功率为3.1mW。
论文主要工作是：
①研究分析了微型风能收集器的国内外研究现状以及存在的科学与技术问题，提出了基于颤振机理的微型压电风致振动能量收集器研究方案；
②基于Euler悬臂梁理论，建立了微型压电风致振动能量收集器单向耦合的集总参数模型与分布参数模型，研究了不同激励下的输出性能；基于双向压电耦合效应，建立了双向耦合分布参数模型，修正了单向耦合模型；采用有限元分析方法对理论模型进行了验证；
③提出基于颤振机理的压电梁与柔性梁复合的新结构，基于非定常流气动理论方程、Euler悬臂梁理论建立了颤振机理的线性理论模型，采用切比雪夫配点法完成了数值求解；基于Lighthill气动力学模型、悬臂梁的不可拉伸条件建立了非线性颤振理论模型，采用Galerkin模态叠加方法和Houbolt方法完成了非线性颤振模型的数值化求解；
④确定了微型风致振动能量收集器工作风速范围的设计要求；采用颤振理论模型分析了柔性梁尺寸等因素对颤振临界风速等性能的影响，确定了柔性梁尺寸范围；研究了降低临界风速的方法，提出了T型柔性梁、非流线体和逆风颤振结构等三个优化设计方案；开展了微型风致振动能量收集器可靠性封装设计；
⑤完成了微型风致振动能量收集器的加工与组装，研制出了原理样机；搭建了小型风洞测试平台和振动测试平台；分析了微型风致振动能量收集器的颤振过程，完成了顺风结构、T型柔性梁结构、非流线体结构和逆风结构等器件的性能测试与分析；研究了环境风的变化对微型风致振动能量收集器性能的影响，完成了器件的过载保护与封装。
The micro power is an effective approach for the micro devices and systemsbecause of small sizes, larger power density, long lifetime and green. And micro powerhas being paid attention to at home and abroad. Recently, lots of researches about themicro power sources focus on harvesting the vibration energy, temperature difference,solar and so on from ambient. However, micro power harvesting wind energy is lessreported. Micro wind energy harvester based on wind-induced vibration has become amajor thrust of research because of simple structure and small size.
This paper proposes a micro wind-induced vibration (WIV) energy harvester basedon fluttering. Based on the piezoelectric effect, the oneway coupled lumped parametermodel, oneway coupled distributed parameter model and twoway coupled distributedparameter model about the vibration energy energy harvester were developed andmodified. A new fluttering composite structure consisting of piezoelectric beam andflexible beam was proposed. The linear flutter model and nonlinear flutter model of theWIV energy harvester in axial wind flow were established. The WIV energy harvesterswere designed and three optimized flutter structures were presented: T shape flexiblebeam, blunt structure and upwind structure. The reliability and packaging technologiesabout the WIV energy harvester were studied, and the WIV harvester prototypes weredeveloped. An experimental test platform was built up and the characteristics of theWIV harvester prototypes were measured and analyzed. The RMS output voltage of thedevice is16.4V, the power is3.1mW.
The main contributions of this work are listed as follows:
①The state of the art about the wind energy harvester was analyzed and thechallenges about the device were developed. A wind-induced vibration energy harvesterusing the fluttering mechanism was proposed.
②Using Euler-Bernoulli beam theory, the oneway coupled lumped parametermodel and distributed parameter model were developed for the micro piezoelectricvibration energy harvester. The output performance response was analyzed underdifferent excitation conditions. Using the double piezoelectric effect, the twowaycoupled distributed parameter model was developed and the oneway coupled modelswere modified. The micro piezoelectric vibration energy harvester models were verifiedusing finite element method.
③A new fluttering composite structure consisting of piezoelectric beam andflexible beam was proposed for wind energy harvesting. A linear fluttering model of thecomposite structure in axial flow was developed using unsteady Bernoulli aerodynamictheory and Euler-Bernoulli beam theory, and numerically calculated using Chebyshevcollocation method. Meanwhile a nonlinear fluttering model was developed usingLighthill theory and inextensibility condition, and numerically calculated usingGalerkin method and Houbolt method.
④The working wind speed rang was determined. The performance of the WIVharvester, such as fluttering critical wind speed, was studied as a function of flexiblebeam size, and flexible beam size range was determined. The critical wind speeddecreasing method was researched, and three optimized structures were proposed: Tshape flexible beam, blunt structure and upwind structure. The reliability and packagingtechnologies about the WIV energy harvester were studied.
⑤The WIV energy harvester prototypes were fabricated and assembled. A smallwind tunnel and a vibration test system were built up. The motion state of the WIVenergy harvester was observe and studied. The prototypes using downwind structure, Tshape flexible beam, blunt structure and upwind structure were measured and resultswere analyzed. The performances of the WIV harvester were measured in differentambient wind.
论文针对环境中广泛存在的风能，提出了一种基于颤振机理的微型压电风致振动能量收集器。基于压电效应，建立了微型压电风致振动能量收集器的单向耦合集总参数模型、单向耦合分布参数模型和双向耦合分布参数模型，完成了模型的修正；提出了压电梁与柔性梁复合的颤振新结构，建立了微型风致振动能量收集器在轴向风中的线性颤振模型和非线性颤振模型；研究了微型压电风致振动能量收集器的设计方法，提出了T型柔性梁结构、非流线体结构、逆风颤振结构等优化结构；完成了微型压电风致振动能量收集器可靠性封装设计和器件的加工，研制出了原理验证样机；搭建了测试分析平台，完成了原理样机的性能测试与分析。研制出的原理样机体积0.1cm3，在风速12.2m/s时，开路电压有效值为16.4V、输出功率为3.1mW。
论文主要工作是：
①研究分析了微型风能收集器的国内外研究现状以及存在的科学与技术问题，提出了基于颤振机理的微型压电风致振动能量收集器研究方案；
②基于Euler悬臂梁理论，建立了微型压电风致振动能量收集器单向耦合的集总参数模型与分布参数模型，研究了不同激励下的输出性能；基于双向压电耦合效应，建立了双向耦合分布参数模型，修正了单向耦合模型；采用有限元分析方法对理论模型进行了验证；
③提出基于颤振机理的压电梁与柔性梁复合的新结构，基于非定常流气动理论方程、Euler悬臂梁理论建立了颤振机理的线性理论模型，采用切比雪夫配点法完成了数值求解；基于Lighthill气动力学模型、悬臂梁的不可拉伸条件建立了非线性颤振理论模型，采用Galerkin模态叠加方法和Houbolt方法完成了非线性颤振模型的数值化求解；
④确定了微型风致振动能量收集器工作风速范围的设计要求；采用颤振理论模型分析了柔性梁尺寸等因素对颤振临界风速等性能的影响，确定了柔性梁尺寸范围；研究了降低临界风速的方法，提出了T型柔性梁、非流线体和逆风颤振结构等三个优化设计方案；开展了微型风致振动能量收集器可靠性封装设计；
⑤完成了微型风致振动能量收集器的加工与组装，研制出了原理样机；搭建了小型风洞测试平台和振动测试平台；分析了微型风致振动能量收集器的颤振过程，完成了顺风结构、T型柔性梁结构、非流线体结构和逆风结构等器件的性能测试与分析；研究了环境风的变化对微型风致振动能量收集器性能的影响，完成了器件的过载保护与封装。
The micro power is an effective approach for the micro devices and systemsbecause of small sizes, larger power density, long lifetime and green. And micro powerhas being paid attention to at home and abroad. Recently, lots of researches about themicro power sources focus on harvesting the vibration energy, temperature difference,solar and so on from ambient. However, micro power harvesting wind energy is lessreported. Micro wind energy harvester based on wind-induced vibration has become amajor thrust of research because of simple structure and small size.
This paper proposes a micro wind-induced vibration (WIV) energy harvester basedon fluttering. Based on the piezoelectric effect, the oneway coupled lumped parametermodel, oneway coupled distributed parameter model and twoway coupled distributedparameter model about the vibration energy energy harvester were developed andmodified. A new fluttering composite structure consisting of piezoelectric beam andflexible beam was proposed. The linear flutter model and nonlinear flutter model of theWIV energy harvester in axial wind flow were established. The WIV energy harvesterswere designed and three optimized flutter structures were presented: T shape flexiblebeam, blunt structure and upwind structure. The reliability and packaging technologiesabout the WIV energy harvester were studied, and the WIV harvester prototypes weredeveloped. An experimental test platform was built up and the characteristics of theWIV harvester prototypes were measured and analyzed. The RMS output voltage of thedevice is16.4V, the power is3.1mW.
The main contributions of this work are listed as follows:
①The state of the art about the wind energy harvester was analyzed and thechallenges about the device were developed. A wind-induced vibration energy harvesterusing the fluttering mechanism was proposed.
②Using Euler-Bernoulli beam theory, the oneway coupled lumped parametermodel and distributed parameter model were developed for the micro piezoelectricvibration energy harvester. The output performance response was analyzed underdifferent excitation conditions. Using the double piezoelectric effect, the twowaycoupled distributed parameter model was developed and the oneway coupled modelswere modified. The micro piezoelectric vibration energy harvester models were verifiedusing finite element method.
③A new fluttering composite structure consisting of piezoelectric beam andflexible beam was proposed for wind energy harvesting. A linear fluttering model of thecomposite structure in axial flow was developed using unsteady Bernoulli aerodynamictheory and Euler-Bernoulli beam theory, and numerically calculated using Chebyshevcollocation method. Meanwhile a nonlinear fluttering model was developed usingLighthill theory and inextensibility condition, and numerically calculated usingGalerkin method and Houbolt method.
④The working wind speed rang was determined. The performance of the WIVharvester, such as fluttering critical wind speed, was studied as a function of flexiblebeam size, and flexible beam size range was determined. The critical wind speeddecreasing method was researched, and three optimized structures were proposed: Tshape flexible beam, blunt structure and upwind structure. The reliability and packagingtechnologies about the WIV energy harvester were studied.
⑤The WIV energy harvester prototypes were fabricated and assembled. A smallwind tunnel and a vibration test system were built up. The motion state of the WIVenergy harvester was observe and studied. The prototypes using downwind structure, Tshape flexible beam, blunt structure and upwind structure were measured and resultswere analyzed. The performances of the WIV harvester were measured in differentambient wind.
引文
[1]李林．基于MEMS的振动能量采集及其器件设计[D]．杭州：浙江大学，2008：1-11.
[2]刘路，解晶莹．微能源[J]．电源技术，2002，26（6）：470-474．
[3]秦冲，苑伟政，孙磊，乔大勇．微能源发展概述[J]．光电子技术，2005，25（4）：218-221．
[4] P. B. Koeneman，I. J. Busch-Vishniac，K. L. Wood．Feasibility of micro power supplies forMEMS[J]．Journal of Microelectromechanical Systems，1997，6（4）：355-362．
[5] A. P. Chandrakasan，D. C. Daly，J. Kwong，Y. K. Ramadass．Next generation micro-powersystems[C]．VLSI Circuits,2008IEEE Symposium on，Honolulu，USA，2008：2-5．
[6] S. R. Anton，H. A. Sodano．A review of power harvesting using piezoelectric materials (2003–2006)[J]．Smart Materials and Structures，2007，16（3）：R1-R21．
[7] K. A. Cook-Chennault，N. Thambi，A. M. Sastry．Powering MEMS portable devices—a reviewof non-regenerative and regenerative power supply systems with special emphasis onpiezoelectric energy harvesting systems[J]．Smart Materials and Structures，2008，17（4）：43001．
[8] S. P. Beeby，M. J. Tudor，N. M. White．Energy harvesting vibration sources for microsystemsapplications[J]．Measurement science and technology，2006，17（12）：R175-R195．
[9] N. E. DuToit， B. L. Wardle． Experimental verification of models for microfabricatedpiezoelectric vibration energy harvesters[J]．AIAA journal，2007，45（5）：1126-1137．
[10] N. E. DuToit，L. W. BRIAN，K. Sang-Gook．Design considerations for MEMS-scalepiezoelectric mechanical vibration energy harvesters[J]．Integrated Ferroelectrics，2005，71（1）：121-160．
[11] E. E. Aktakka，R. L. Peterson，K. Najafi．Multi-layer PZT stacking process for piezoelectricbimorph energy harvesters[C]．11th International Conference on Micro and Nanotechnologyfor Power Generation and Energy Conversion Applications (PowerMEMS'11)，Seoul，Republic of Korea，2011：139-142．
[12] A. Erturk，D. J. Inman．On mechanical modeling of cantilevered piezoelectric vibration energyharvesters[J]．Journal of Intelligent Material Systems and Structures，2008，19（11）：1311-1325．
[13] H. Liu，C. J. Tay，C. Quan，T. Kobayashi，C. Lee．Piezoelectric MEMS energy harvester forlow-frequency vibrations with wideband operation range and steadily increased outputpower[J]．Journal Microelectromechanical Systems，2011，20（5）：1131-1142．
[14] R. Vullers，M. Renaud，R. Elfrink，R. van Schaijk．MEMS based vibration harvesting: Facingthe ugly facts[C]．The17th International Conference on Solid-State Sensors, Actuators andMicrosystems，Barcelona，Spain，2013：685-688．
[15] J. C. Park，J. Y. Park．Asymmetric PZT bimorph cantilever for multi-dimensional ambientvibration harvesting[J]．Ceramics International，2013，39（1）：S653-S657．
[16] W. Yang，J. Chen，G. Zhu，X. Wen，P. Bai，Y. Su，Y. Lin，Z. Wang．Harvesting vibrationenergy by a triple-cantilever based triboelectric nanogenerator[J]．Nano Research，2013，1-7．
[17] Y. Y. Tao， Z. R. Li， G. Q. Shang， C. H. Sun． On Piezoelectric HarvestingTechnology[J]．Advanced Materials Research，2012，516：1496-1499.
[18] A. Harb．Energy harvesting: State-of-the-art[J]．Renewable Energy，2011，36（10）：2641-2654．
[19] T. Kim． Fully-integrated micro PEM fuel cell system with NaBH4hydrogengenerator[J]．International Journal of Hydrogen Energy，2012，37（3）：2440-2446．
[20] T. Kim．Hydrogen generation from sodium borohydride using microreactor for micro fuelcells[J]．International Journal of Hydrogen Energy，2011，36（2）：1404-1410．
[21] P. Su， F. B. Prinz． Nanoscale membrane electrolyte array for solid oxide fuelcells[J]．Electrochemistry Communications，2012，16（1）：77-79．
[22] B. C. Yen，F. Herrault，K. J. Hillman，M. G. Allen，F. F. Ehrich，S. Jacobson，C. Ji，J. H.Lang，H. Li，Z. S. Spakovszky．Characterization of a fully-integrated permanent-magnetturbine generator[C]．the8th International Workshop on Micro and Nanotechnology forPower Generation and Energy Conversion Applications (PowerMEMS2008)，Sendai，Japan，2008：121-124．
[23] A. Iizuka，M. Takato，M. Kaneko，T. Nishi，K. Saito，F. Uchikoba．Millimeter Scale MEMSAir Turbine Generator by Winding Wire and Multilayer Magnetic CeramicCircuit[J]．Modern Mechanical Engineering，2012，2（2）：41-46．
[24] C. Pan，T. Wu．Development of a Rotary Electro-magnetic Microgenerator[J]．Journal ofMicromechanics and Microengineering，2007，17（1）：120-128．
[25] A. S. Holmes，G. Hong，K. R. Pullen．Axial-flux permanent magnet machines for micropowergeneration[J]．Journal of microelectromechanical systems，2005，14（1）：54-62．
[26] A. S. Holmes，G. Hong，K. R. Pullen，K. R. Buffard．Axial-flow microturbine withelectromagnetic generator: design, CFD simulation, and prototype demonstration[C]．MicroElectro Mechanical Systems,2004.17th IEEE International Conference on.(MEMS)，Maastricht，The Netherlands，2004：568-571．
[27] S. Roundy， P. K. Wright． A piezoelectric vibration based generator for wirelesselectronics[J]．Smart Materials and Structures，2004，13（5）：1131．
[28] S. Roundy，P. K. Wright，J. Rabaey．A study of low level vibrations as a power source forwireless sensor nodes[J]．Computer Communications，2003，26（11）：1131-1144．
[29] S. Priya．Modeling of electric energy harvesting using piezoelectric windmill[J]．AppliedPhysics Letters，2005，87（18）：184101．
[30] S. Priya，C. Chen，D. Fye，J. Zahnd．Piezoelectric windmill: a novel solution to remotesensing[J]．Japanese Journal of Applied Physics，2005，44（3）：104-107．
[31] H. Chang，D. Kim，J. Park．Design and analysis of portable loadless wind power source forubiquitous sensor network[C]．Computer and Automation Engineering (ICCAE),2010The2nd International Conference on，Singapore，2010：93-96．
[32]孙加存，陈荷娟．风动压电发电机的结构设计及实验研究[J]．压电与声光，2012，34（6）：860-863．
[33]宋久振，赵劲草，庄静，冯玮，尤云祥．均匀粘性流体中截断直立圆柱体受迫振荡的三维数值模拟[J]．舰船科学技术，2012，34（8）：12-17．
[34] W. P. Robbins，I. Marusic，D. Morris，T. O. Novak．Wind-generated electrical energy usingflexible piezoelectric materials[C]．International Mechanical Engineering Congress andExposition，Chicago，United States，2006：1-9．
[35] H. D. Akayd n，N. Elvin，Y. Andreopoulos．Wake of a cylinder: a paradigm for energyharvesting with piezoelectric materials[J]．Experiments in Fluids，2010，49（1）：291-304．
[36] S. Pobering，S. Ebermeyer，N. Schwesinger．Generation of electrical energy using shortpiezoelectric cantilevers in flowing media[C]．Proc. SPIE7288, Active and Passive SmartStructures and Integrated Systems2009，San Diego, California，USA，2009：728801-728807．
[37] W. B. Hobbs．Piezoelectric energy harvesting: vortex induced vibrations in plants, soap films,and arrays of cylinders[D]．Atlanta, USA：Georgia Institute of Technology，2010：7-58.
[38] J. Hwang，K. Yang，S. Sun．Reduction of flow-induced forces on a circular cylinder using adetached splitter plate[J]．Physics of Fluids，2003，15（8）：2433-2436．
[39] S. Ozono．Flow control of vortex shedding by a short splitter plate asymmetrically arrangeddownstream of a cylinder[J]．Physics of Fluids，1999，11（10）：2928-2934．
[40] B. G. Dehkordi，H. H. Jafari．On the suppression of vortex shedding from circular cylindersusing detached short splitter-plates[J]．Journal of fluids engineering，2010，132（4）：44501．
[41] J. J. Allen，A. J. Smits．Energy harvesting eel[J]．Journal of Fluids and Structures，2001，15（3）：629-640．
[42] S. Kwon．A T-shaped piezoelectric cantilever for fluid energy harvesting[J]．Applied PhysicsLetters，2010，97（16）：164102．
[43] L. Tang，M. P. Pa doussis．On the instability and the post-critical behaviour of two-dimensionalcantilevered flexible plates in axial flow[J]．Journal of Sound and Vibration，2007，305（1）：97-115．
[44] S. Michelin， O. Doaré． Energy harvesting efficiency of piezoelectric flags in axialflows[J]．Journal of Fluid Mechanics，2013，714：489-504.
[45] L. Tang，M. P. Pa doussis，J. Jiang．Cantilevered flexible plates in axial flow: Energy transferand the concept of flutter-mill[J]．Journal of Sound and Vibration，2009，326（1）：263-276．
[46] S. M. Frayne．Fluid-induced energy converter with curved parts[P]．US，7772712，2010-08-10．
[47] S. M. Frayne． Generator utilizing fluid-induced oscillations[P]． US，20090309362，2009-12-17．
[48] S. Li， H. Lipson． Vertical-stalk flapping-leaf generator for wind energyharvesting[C]．Conference on Smart Materials, Adaptive Structures and Intelligent Systems(SMASIS2009)，Oxnard，California，USA，2009：1-9．
[49] S. Li， J. Yuan， H. Lipson． Ambient wind energy harvesting using cross-flowfluttering[J]．Journal of Applied Physics，2011，109（2）：26104．
[50] M. Bryant，E. Wolff，E. Garcia．Aeroelastic flutter energy harvester design: the sensitivity of thedriving instability to system parameters[J]．Smart Materials and Structures，2011，20（12）：125017．
[51] M. Bryant， E. Garcia． Modeling and testing of a novel aeroelastic flutter energyharvester[J]．Journal of vibration and acoustics，2011，133（1）：11010．
[52]雷军命．引信气流谐振压电发电机[J]．探测与控制学报，2009，23（1）：23-26．
[53]杨芳，隋丽，石庚辰．气动柔性带压电发电机[J]．探测与控制学报，2013，35（1）：1-5．
[54] D. St Clair，A. Bibo，V. R. Sennakesavababu，M. F. Daqaq，G. Li．A scalable concept formicropower generation using flow-induced self-excited oscillations[J]．Applied PhysicsLetters，2010，96（14）：144103．
[55]季军．基于谐振腔和簧片阀结构的风能回收装置[D]．合肥：中国科学技术大学，2010：1-47．
[56]杜志刚，贺学锋．带谐振腔的微型压电风能采集器[J]．传感技术学报，2012，25（6）：748-750．
[57] J. Sirohi，R. Mahadik．Harvesting wind energy using a galloping piezoelectric beam[J]．Journalof vibration and acoustics，2012，134（1）：11009．
[58] H. Jung，I. Kim，S. Jang．An energy harvesting system using the wind-induced vibration of astay cable for powering a wireless sensor node[J]．Smart Materials and Structures，2011，20（7）：75001．
[59] H. Liu，S. Zhang，R. Kathiresan，T. Kobayashi，C. Lee．Development of piezoelectricmicrocantilever flow sensor with wind-driven energy harvesting capability[J]．AppliedPhysics Letters，2012，100（22）：223905．
[60] D. Zhu，S. Beeby，J. Tudor，N. White，N. Harris．A novel miniature wind generator for wirelesssensing applications[C]．Sensors,2010IEEE，Waikoloa, Hawaii，USA，2010：1415-1418．
[61] Y. B. Jeon，R. Sood，J. H. Jeong，S. G. Kim．MEMS power generator with transverse mode thinfilm PZT[J]．Sensors and Actuators A: Physical，2005，122（1）：16-22．
[62] L. Zhou，J. Sun，X. J. Zheng，S. F. Deng，J. H. Zhao，S. T. Peng，Y. Zhang，X. Y. Wang，H. B. Cheng．A model for the energy harvesting performance of shear mode piezoelectriccantilever[J]．Sensors and Actuators A: Physical，2012，179：185-192.
[63] C. B. Williams， R. B. Yates． Analysis of a micro-electric generator formicrosystems[J]．Sensors and Actuators A: Physical，1996，52（1）：8-11．
[64] Y. B. Jeon，R. Sood，J. Jeong，S. Kim．MEMS power generator with transverse mode thin filmPZT[J]．Sensors and Actuators A: Physical，2005，122（1）：16-22．
[65] H. Fang，J. Liu，Z. Xu，L. Dong，D. Chen，B. Cai，Y. Liu．A MEMS-based piezoelectric powergenerator for low frequency vibration energy harvesting[J]．Chinese Physics Letters，2006，23（3）：732-734．
[66] D. Shen，J. Park，J. Ajitsaria，S. Choe，C. W. Howard III，D. Kim．The design, fabricationand evaluation of a MEMS PZT cantilever with an integrated Si proof mass for vibrationenergy harvesting[J]．Journal of Micromechanics and Microengineering，2008，18（5）：55017．
[67] N. E. du Toit，L. W. Brian，K. Sang-Gook．Design considerations for MEMS-scale piezoelectricmechanical vibration energy harvesters[J]．Integrated Ferroelectrics，2005，71（1）：121-160．
[68] S. Chen，G. Wang，M. Chien．Analytical modeling of piezoelectric vibration-induced micropower generator[J]．Mechatronics，2006，16（7）：379-387．
[69] F. Lu，H. P. Lee，S. P. Lim．Modeling and analysis of micro piezoelectric power generators formicro-electromechanical-systems applications[J]．Smart Materials and Structures，2004，13（1）：57-63．
[70] A. Erturk，D. J. Inman．An experimentally validated bimorph cantilever model for piezoelectricenergy harvesting from base excitations[J]．Smart Materials and Structures，2009，18（2）：25009．
[71] A. Erturk，D. J. Inman．A distributed parameter electromechanical model for cantileveredpiezoelectric energy harvesters[J]．Journal of Vibration and Acoustics，2008，130（4）：41002．
[72] S. Priya，D. J. Inman．Energy harvesting technologies[M]．New York, USA：Springer，2008：41-128.
[73]克拉夫，彭津，王光远．结构动力学[M]．北京：高等教育出版社，2006：195-227．
[74]倪振华．振动力学[M]．西安：西安交通大学出版社，1989：338-429．
[75] K. D. Hjelmstad．Fundamentals of Structural Mechanics[M]．New York, USA：Springer-VerlagNew York Inc.，2005：34-75.
[76]王喆垚．微系统设计与制造[M]．北京：清华大学出版社，2008：32-78．
[77] R. Andosca，T. G. McDonald，V. Genova，S. Rosenberg，J. Keating，C. Benedixen，J.Wu． Experimental and theoretical studies on MEMS piezoelectric vibrational energyharvesters with mass loading[J]．Sensors and Actuators A: Physical，2012，178：76-87.
[78]贺学锋，温志渝，温中泉，尚正国，刘海涛，廖海洋．振动式压电发电机的理论模型与实验[J]．纳米技术与精密工程，2007，5（4）：307-310．
[79] Y. C. Shu，I. C. Lien．Analysis of power output for piezoelectric energy harvestingsystems[J]．Smart materials and structures，2006，15（6）：1499．
[80]张福学，王丽坤．现代压电学[M]．北京：科学出版社，2002：84-100．
[81]栾桂冬，张金铎，王仁乾．压电换能器和换能器阵[M]．北京：北京大学出版社，1990：99-183．
[82]党沙沙，许洋，张红松．ANSYS12.0多物理耦合场有限元分析从入门到精通[M]．北京：机械工业出版社，2010：1-91．
[83]白莱文斯R. D.，吴恕三，王觉．流体诱发振动[M]．北京：机械工业出版社，1981：9-49．
[84]道尔E. H.，小柯蒂斯H. C.，斯坎伦R. H.，西斯托F.，陈文俊，尹传家．气动弹性力学现代教程[M]．北京：中国宇航出版社，1991：78-101．
[85]黄本才．结构抗风分析原理及应用[M]．上海：同济大学出版社，2001：64-134．
[86]项海帆．现代桥梁抗风理论与实践[M]．北京：人民交通出版社，2005：50-109．
[87]克莱斯·迪尔比耶，斯文·奥勒·汉森．结构风荷载作用[M]．北京：中国建筑工业出版社，2006：135-166．
[88] K. Y. Billah，R. H. Scanlan．Resonance, Tacoma Narrows bridge failure, and undergraduatephysics textbooks[J]．American Journal of Physics，1991，59（2）：118-124．
[89] H. Petroski，H. Petroski，H. Petroski．To engineer is human: The role of failure in successfuldesign[M]．New York, USA：Vintage books New York，1992：1-27.
[90] A. Erturk，W. Vieira，C. De Marqui，D. J. Inman．On the energy harvesting potential ofpiezoaeroelastic systems[J]．Applied Physics Letters，2010，96（18）：184103．
[91] L. Huang．Flutter of cantilevered plates in axial flow[J]．Journal of Fluids and Structures，1995，9（2）：127-147．
[92] C. Q. Guo，M. P. Paidoussis．Stability of rectangular plates with free side-edges intwo-dimensional inviscid channel flow[J]．Journal of Applied Mechanics，2000，67（1）：171-176．
[93] C. Eloy，C. Souilliez，L. Schouveiler．Flutter of a rectangular plate[J]．Journal of fluids andstructures，2007，23（6）：904-919．
[94] C. Eloy，R. Lagrange，C. Souilliez，L. Schouveiler．Aeroelastic instability of cantileveredflexible plates in uniform flow[J]．Journal of Fluid Mechanics，2008，611（1）：97-106．
[95] T. S. Balint，A. D. Lucey．Instability of a cantilevered flexible plate in viscous channelflow[J]．Journal of Fluids and Structures，2005，20（7）：893-912．
[96] M. Argentina，L. Mahadevan．Fluid-flow-induced flutter of a flag[J]．Proceedings of theNational academy of Sciences of the United States of America，2005，102（6）：1829-1834．
[97] D. M. Tang， H. Yamamoto， E. H Dowell． Flutter and limit cycle oscillations oftwo-dimensional panels in three-dimensional axial flow[J]．Journal of Fluids and Structures，2003，17（2）：225-242．
[98]赵文胜．轴向流中板结构流固耦合动力学研究[D]．武汉：武汉大学，2011：1-97．
[99] K. Singh，S. Michelin，E. De Langre．The effect of non-uniform damping on flutter in axial flowand energy-harvesting strategies[J]．Proceedings of the Royal Society A: Mathematical,Physical and Engineering Science，2012，468（2147）：3620-3635．
[100] A. Kornecki，E. H. Dowell，J. O'Brien．On the aeroelastic instability of two-dimensional panesin uniform incompressible flow[J]．Journal of Sound and Vibration，1976，47（2）：163-178．
[101] S. Michelin，S. G. L. Smith．Linear stability analysis of coupled parallel flexible plates in anaxial flow[J]．Journal of Fluids and Structures，2009，25（7）：1136-1157．
[102] M. J. Lighthill．Large-amplitude elongated-body theory of fish locomotion[J]．Proceedings ofthe Royal Society B: Biological Sciences，1971，179（1055）：125-138．
[103] F. Candelier， F. Boyer， A. Leroyer． Three-dimensional extension of Lighthill'slarger-amplitude elongated-body theory of fish locomotion[J]．J. Fluid Mech.，2011，674：196-226.
[104] C. Eloy，N. Kofman，L. Schouveiler．The origin of hysteresis in the flag instability[J]．Journalof Fluid Mechanics，2011，691：583-593.
[105] T. S. Balint，A. D. Lucey．Instability of a cantilevered flexible plate in viscous channelflow[J]．Journal of Fluids and Structures，2005，20（7）：893-912．
[106] H. Ma，W. Sun．A Legendre-Petrov-Galerkin and Chebyshev Collocation Method forThird-Order Differential Equations[J]．SIAM Journal on Numerical Analysis，2000，38（5）：1425-1438．
[107] U. Ehrenstein，R. Peyret．A Chebyshev collocation method for the Navier–Stokes equationswith application to double‐diffusive convection[J]．International Journal for NumericalMethods in Fluids，1989，9（4）：427-452．
[108] P. Boomkamp，B. J. Boersma，R. Miesen，G. V. Beijnon．A Chebyshev collocation methodfor solving two-phase flow stability problems[J]．Journal of Computational Physics，1997，132（2）：191-200．
[109] C. Souilliez，C. Eloy，L. Schouveiler．An experimental study of flag flutter[C]．SME PressureVessels and Piping Division Conference，Vancouver, Canada，2006：
[110]朱伟强．福建省沿海风力资源特性分析[J]．电力勘测设计，2006，1：33-36．
[111]李艳，耿丹，董新宁，朱焱．1961-2007年重庆风速的气候变化特征[J]．大气科学学报，2010，33（3）：336-340．
[112]彭小云，袁剑．高层建筑室外风速简化计算方法研究[J]．四川建筑科学研究，2011，37（3）：37-39．
[113]叶征伟．山区高墩大跨连续刚构桥风环境及风荷载研究[D]．浙江：浙江大学，2012：3-19．
[114]胡俊．大跨度悬索桥现场实测数据、风雨激励响应及风振疲劳研究[D]．大连：大连理工大学，2012：3-21．
[115]申建红，李春祥．强风作用下超高层建筑风场特性的实测研究[J]．振动与冲击，2010，29（05）：62-68．
[116]王福军，周佩剑．铁路风力发电灯具[P]．中国，201010227422.4，2010-07-07．
[117]董文华，张维智．扰动风速风力发电系统及其垂直轴微型风力机[P]．中国，200410040054.7，2004-06-24．
[118]张红涛，寇晓霞．一种隧道风力发电装置[P]．中国，200920195174.2，2009-09-22．
[119]刘惟信．机械可靠性设计[M]．北京：清华大学出版社，1996：57-102．
[120] T. Fett，D. Munz，G. Thun．Bending strength of a PZT ceramic under electric fields[J]．Journalof the European Ceramic Society，2003，23（2）：195-202．
[121] M. Okayasu，G. Ozeki，M. Mizuno．Fatigue failure characteristics of lead zirconate titanatepiezoelectric ceramics[J]．Journal of the European Ceramic Society，2010，30（3）：713-725．
[2]刘路，解晶莹．微能源[J]．电源技术，2002，26（6）：470-474．
[3]秦冲，苑伟政，孙磊，乔大勇．微能源发展概述[J]．光电子技术，2005，25（4）：218-221．
[4] P. B. Koeneman，I. J. Busch-Vishniac，K. L. Wood．Feasibility of micro power supplies forMEMS[J]．Journal of Microelectromechanical Systems，1997，6（4）：355-362．
[5] A. P. Chandrakasan，D. C. Daly，J. Kwong，Y. K. Ramadass．Next generation micro-powersystems[C]．VLSI Circuits,2008IEEE Symposium on，Honolulu，USA，2008：2-5．
[6] S. R. Anton，H. A. Sodano．A review of power harvesting using piezoelectric materials (2003–2006)[J]．Smart Materials and Structures，2007，16（3）：R1-R21．
[7] K. A. Cook-Chennault，N. Thambi，A. M. Sastry．Powering MEMS portable devices—a reviewof non-regenerative and regenerative power supply systems with special emphasis onpiezoelectric energy harvesting systems[J]．Smart Materials and Structures，2008，17（4）：43001．
[8] S. P. Beeby，M. J. Tudor，N. M. White．Energy harvesting vibration sources for microsystemsapplications[J]．Measurement science and technology，2006，17（12）：R175-R195．
[9] N. E. DuToit， B. L. Wardle． Experimental verification of models for microfabricatedpiezoelectric vibration energy harvesters[J]．AIAA journal，2007，45（5）：1126-1137．
[10] N. E. DuToit，L. W. BRIAN，K. Sang-Gook．Design considerations for MEMS-scalepiezoelectric mechanical vibration energy harvesters[J]．Integrated Ferroelectrics，2005，71（1）：121-160．
[11] E. E. Aktakka，R. L. Peterson，K. Najafi．Multi-layer PZT stacking process for piezoelectricbimorph energy harvesters[C]．11th International Conference on Micro and Nanotechnologyfor Power Generation and Energy Conversion Applications (PowerMEMS'11)，Seoul，Republic of Korea，2011：139-142．
[12] A. Erturk，D. J. Inman．On mechanical modeling of cantilevered piezoelectric vibration energyharvesters[J]．Journal of Intelligent Material Systems and Structures，2008，19（11）：1311-1325．
[13] H. Liu，C. J. Tay，C. Quan，T. Kobayashi，C. Lee．Piezoelectric MEMS energy harvester forlow-frequency vibrations with wideband operation range and steadily increased outputpower[J]．Journal Microelectromechanical Systems，2011，20（5）：1131-1142．
[14] R. Vullers，M. Renaud，R. Elfrink，R. van Schaijk．MEMS based vibration harvesting: Facingthe ugly facts[C]．The17th International Conference on Solid-State Sensors, Actuators andMicrosystems，Barcelona，Spain，2013：685-688．
[15] J. C. Park，J. Y. Park．Asymmetric PZT bimorph cantilever for multi-dimensional ambientvibration harvesting[J]．Ceramics International，2013，39（1）：S653-S657．
[16] W. Yang，J. Chen，G. Zhu，X. Wen，P. Bai，Y. Su，Y. Lin，Z. Wang．Harvesting vibrationenergy by a triple-cantilever based triboelectric nanogenerator[J]．Nano Research，2013，1-7．
[17] Y. Y. Tao， Z. R. Li， G. Q. Shang， C. H. Sun． On Piezoelectric HarvestingTechnology[J]．Advanced Materials Research，2012，516：1496-1499.
[18] A. Harb．Energy harvesting: State-of-the-art[J]．Renewable Energy，2011，36（10）：2641-2654．
[19] T. Kim． Fully-integrated micro PEM fuel cell system with NaBH4hydrogengenerator[J]．International Journal of Hydrogen Energy，2012，37（3）：2440-2446．
[20] T. Kim．Hydrogen generation from sodium borohydride using microreactor for micro fuelcells[J]．International Journal of Hydrogen Energy，2011，36（2）：1404-1410．
[21] P. Su， F. B. Prinz． Nanoscale membrane electrolyte array for solid oxide fuelcells[J]．Electrochemistry Communications，2012，16（1）：77-79．
[22] B. C. Yen，F. Herrault，K. J. Hillman，M. G. Allen，F. F. Ehrich，S. Jacobson，C. Ji，J. H.Lang，H. Li，Z. S. Spakovszky．Characterization of a fully-integrated permanent-magnetturbine generator[C]．the8th International Workshop on Micro and Nanotechnology forPower Generation and Energy Conversion Applications (PowerMEMS2008)，Sendai，Japan，2008：121-124．
[23] A. Iizuka，M. Takato，M. Kaneko，T. Nishi，K. Saito，F. Uchikoba．Millimeter Scale MEMSAir Turbine Generator by Winding Wire and Multilayer Magnetic CeramicCircuit[J]．Modern Mechanical Engineering，2012，2（2）：41-46．
[24] C. Pan，T. Wu．Development of a Rotary Electro-magnetic Microgenerator[J]．Journal ofMicromechanics and Microengineering，2007，17（1）：120-128．
[25] A. S. Holmes，G. Hong，K. R. Pullen．Axial-flux permanent magnet machines for micropowergeneration[J]．Journal of microelectromechanical systems，2005，14（1）：54-62．
[26] A. S. Holmes，G. Hong，K. R. Pullen，K. R. Buffard．Axial-flow microturbine withelectromagnetic generator: design, CFD simulation, and prototype demonstration[C]．MicroElectro Mechanical Systems,2004.17th IEEE International Conference on.(MEMS)，Maastricht，The Netherlands，2004：568-571．
[27] S. Roundy， P. K. Wright． A piezoelectric vibration based generator for wirelesselectronics[J]．Smart Materials and Structures，2004，13（5）：1131．
[28] S. Roundy，P. K. Wright，J. Rabaey．A study of low level vibrations as a power source forwireless sensor nodes[J]．Computer Communications，2003，26（11）：1131-1144．
[29] S. Priya．Modeling of electric energy harvesting using piezoelectric windmill[J]．AppliedPhysics Letters，2005，87（18）：184101．
[30] S. Priya，C. Chen，D. Fye，J. Zahnd．Piezoelectric windmill: a novel solution to remotesensing[J]．Japanese Journal of Applied Physics，2005，44（3）：104-107．
[31] H. Chang，D. Kim，J. Park．Design and analysis of portable loadless wind power source forubiquitous sensor network[C]．Computer and Automation Engineering (ICCAE),2010The2nd International Conference on，Singapore，2010：93-96．
[32]孙加存，陈荷娟．风动压电发电机的结构设计及实验研究[J]．压电与声光，2012，34（6）：860-863．
[33]宋久振，赵劲草，庄静，冯玮，尤云祥．均匀粘性流体中截断直立圆柱体受迫振荡的三维数值模拟[J]．舰船科学技术，2012，34（8）：12-17．
[34] W. P. Robbins，I. Marusic，D. Morris，T. O. Novak．Wind-generated electrical energy usingflexible piezoelectric materials[C]．International Mechanical Engineering Congress andExposition，Chicago，United States，2006：1-9．
[35] H. D. Akayd n，N. Elvin，Y. Andreopoulos．Wake of a cylinder: a paradigm for energyharvesting with piezoelectric materials[J]．Experiments in Fluids，2010，49（1）：291-304．
[36] S. Pobering，S. Ebermeyer，N. Schwesinger．Generation of electrical energy using shortpiezoelectric cantilevers in flowing media[C]．Proc. SPIE7288, Active and Passive SmartStructures and Integrated Systems2009，San Diego, California，USA，2009：728801-728807．
[37] W. B. Hobbs．Piezoelectric energy harvesting: vortex induced vibrations in plants, soap films,and arrays of cylinders[D]．Atlanta, USA：Georgia Institute of Technology，2010：7-58.
[38] J. Hwang，K. Yang，S. Sun．Reduction of flow-induced forces on a circular cylinder using adetached splitter plate[J]．Physics of Fluids，2003，15（8）：2433-2436．
[39] S. Ozono．Flow control of vortex shedding by a short splitter plate asymmetrically arrangeddownstream of a cylinder[J]．Physics of Fluids，1999，11（10）：2928-2934．
[40] B. G. Dehkordi，H. H. Jafari．On the suppression of vortex shedding from circular cylindersusing detached short splitter-plates[J]．Journal of fluids engineering，2010，132（4）：44501．
[41] J. J. Allen，A. J. Smits．Energy harvesting eel[J]．Journal of Fluids and Structures，2001，15（3）：629-640．
[42] S. Kwon．A T-shaped piezoelectric cantilever for fluid energy harvesting[J]．Applied PhysicsLetters，2010，97（16）：164102．
[43] L. Tang，M. P. Pa doussis．On the instability and the post-critical behaviour of two-dimensionalcantilevered flexible plates in axial flow[J]．Journal of Sound and Vibration，2007，305（1）：97-115．
[44] S. Michelin， O. Doaré． Energy harvesting efficiency of piezoelectric flags in axialflows[J]．Journal of Fluid Mechanics，2013，714：489-504.
[45] L. Tang，M. P. Pa doussis，J. Jiang．Cantilevered flexible plates in axial flow: Energy transferand the concept of flutter-mill[J]．Journal of Sound and Vibration，2009，326（1）：263-276．
[46] S. M. Frayne．Fluid-induced energy converter with curved parts[P]．US，7772712，2010-08-10．
[47] S. M. Frayne． Generator utilizing fluid-induced oscillations[P]． US，20090309362，2009-12-17．
[48] S. Li， H. Lipson． Vertical-stalk flapping-leaf generator for wind energyharvesting[C]．Conference on Smart Materials, Adaptive Structures and Intelligent Systems(SMASIS2009)，Oxnard，California，USA，2009：1-9．
[49] S. Li， J. Yuan， H. Lipson． Ambient wind energy harvesting using cross-flowfluttering[J]．Journal of Applied Physics，2011，109（2）：26104．
[50] M. Bryant，E. Wolff，E. Garcia．Aeroelastic flutter energy harvester design: the sensitivity of thedriving instability to system parameters[J]．Smart Materials and Structures，2011，20（12）：125017．
[51] M. Bryant， E. Garcia． Modeling and testing of a novel aeroelastic flutter energyharvester[J]．Journal of vibration and acoustics，2011，133（1）：11010．
[52]雷军命．引信气流谐振压电发电机[J]．探测与控制学报，2009，23（1）：23-26．
[53]杨芳，隋丽，石庚辰．气动柔性带压电发电机[J]．探测与控制学报，2013，35（1）：1-5．
[54] D. St Clair，A. Bibo，V. R. Sennakesavababu，M. F. Daqaq，G. Li．A scalable concept formicropower generation using flow-induced self-excited oscillations[J]．Applied PhysicsLetters，2010，96（14）：144103．
[55]季军．基于谐振腔和簧片阀结构的风能回收装置[D]．合肥：中国科学技术大学，2010：1-47．
[56]杜志刚，贺学锋．带谐振腔的微型压电风能采集器[J]．传感技术学报，2012，25（6）：748-750．
[57] J. Sirohi，R. Mahadik．Harvesting wind energy using a galloping piezoelectric beam[J]．Journalof vibration and acoustics，2012，134（1）：11009．
[58] H. Jung，I. Kim，S. Jang．An energy harvesting system using the wind-induced vibration of astay cable for powering a wireless sensor node[J]．Smart Materials and Structures，2011，20（7）：75001．
[59] H. Liu，S. Zhang，R. Kathiresan，T. Kobayashi，C. Lee．Development of piezoelectricmicrocantilever flow sensor with wind-driven energy harvesting capability[J]．AppliedPhysics Letters，2012，100（22）：223905．
[60] D. Zhu，S. Beeby，J. Tudor，N. White，N. Harris．A novel miniature wind generator for wirelesssensing applications[C]．Sensors,2010IEEE，Waikoloa, Hawaii，USA，2010：1415-1418．
[61] Y. B. Jeon，R. Sood，J. H. Jeong，S. G. Kim．MEMS power generator with transverse mode thinfilm PZT[J]．Sensors and Actuators A: Physical，2005，122（1）：16-22．
[62] L. Zhou，J. Sun，X. J. Zheng，S. F. Deng，J. H. Zhao，S. T. Peng，Y. Zhang，X. Y. Wang，H. B. Cheng．A model for the energy harvesting performance of shear mode piezoelectriccantilever[J]．Sensors and Actuators A: Physical，2012，179：185-192.
[63] C. B. Williams， R. B. Yates． Analysis of a micro-electric generator formicrosystems[J]．Sensors and Actuators A: Physical，1996，52（1）：8-11．
[64] Y. B. Jeon，R. Sood，J. Jeong，S. Kim．MEMS power generator with transverse mode thin filmPZT[J]．Sensors and Actuators A: Physical，2005，122（1）：16-22．
[65] H. Fang，J. Liu，Z. Xu，L. Dong，D. Chen，B. Cai，Y. Liu．A MEMS-based piezoelectric powergenerator for low frequency vibration energy harvesting[J]．Chinese Physics Letters，2006，23（3）：732-734．
[66] D. Shen，J. Park，J. Ajitsaria，S. Choe，C. W. Howard III，D. Kim．The design, fabricationand evaluation of a MEMS PZT cantilever with an integrated Si proof mass for vibrationenergy harvesting[J]．Journal of Micromechanics and Microengineering，2008，18（5）：55017．
[67] N. E. du Toit，L. W. Brian，K. Sang-Gook．Design considerations for MEMS-scale piezoelectricmechanical vibration energy harvesters[J]．Integrated Ferroelectrics，2005，71（1）：121-160．
[68] S. Chen，G. Wang，M. Chien．Analytical modeling of piezoelectric vibration-induced micropower generator[J]．Mechatronics，2006，16（7）：379-387．
[69] F. Lu，H. P. Lee，S. P. Lim．Modeling and analysis of micro piezoelectric power generators formicro-electromechanical-systems applications[J]．Smart Materials and Structures，2004，13（1）：57-63．
[70] A. Erturk，D. J. Inman．An experimentally validated bimorph cantilever model for piezoelectricenergy harvesting from base excitations[J]．Smart Materials and Structures，2009，18（2）：25009．
[71] A. Erturk，D. J. Inman．A distributed parameter electromechanical model for cantileveredpiezoelectric energy harvesters[J]．Journal of Vibration and Acoustics，2008，130（4）：41002．
[72] S. Priya，D. J. Inman．Energy harvesting technologies[M]．New York, USA：Springer，2008：41-128.
[73]克拉夫，彭津，王光远．结构动力学[M]．北京：高等教育出版社，2006：195-227．
[74]倪振华．振动力学[M]．西安：西安交通大学出版社，1989：338-429．
[75] K. D. Hjelmstad．Fundamentals of Structural Mechanics[M]．New York, USA：Springer-VerlagNew York Inc.，2005：34-75.
[76]王喆垚．微系统设计与制造[M]．北京：清华大学出版社，2008：32-78．
[77] R. Andosca，T. G. McDonald，V. Genova，S. Rosenberg，J. Keating，C. Benedixen，J.Wu． Experimental and theoretical studies on MEMS piezoelectric vibrational energyharvesters with mass loading[J]．Sensors and Actuators A: Physical，2012，178：76-87.
[78]贺学锋，温志渝，温中泉，尚正国，刘海涛，廖海洋．振动式压电发电机的理论模型与实验[J]．纳米技术与精密工程，2007，5（4）：307-310．
[79] Y. C. Shu，I. C. Lien．Analysis of power output for piezoelectric energy harvestingsystems[J]．Smart materials and structures，2006，15（6）：1499．
[80]张福学，王丽坤．现代压电学[M]．北京：科学出版社，2002：84-100．
[81]栾桂冬，张金铎，王仁乾．压电换能器和换能器阵[M]．北京：北京大学出版社，1990：99-183．
[82]党沙沙，许洋，张红松．ANSYS12.0多物理耦合场有限元分析从入门到精通[M]．北京：机械工业出版社，2010：1-91．
[83]白莱文斯R. D.，吴恕三，王觉．流体诱发振动[M]．北京：机械工业出版社，1981：9-49．
[84]道尔E. H.，小柯蒂斯H. C.，斯坎伦R. H.，西斯托F.，陈文俊，尹传家．气动弹性力学现代教程[M]．北京：中国宇航出版社，1991：78-101．
[85]黄本才．结构抗风分析原理及应用[M]．上海：同济大学出版社，2001：64-134．
[86]项海帆．现代桥梁抗风理论与实践[M]．北京：人民交通出版社，2005：50-109．
[87]克莱斯·迪尔比耶，斯文·奥勒·汉森．结构风荷载作用[M]．北京：中国建筑工业出版社，2006：135-166．
[88] K. Y. Billah，R. H. Scanlan．Resonance, Tacoma Narrows bridge failure, and undergraduatephysics textbooks[J]．American Journal of Physics，1991，59（2）：118-124．
[89] H. Petroski，H. Petroski，H. Petroski．To engineer is human: The role of failure in successfuldesign[M]．New York, USA：Vintage books New York，1992：1-27.
[90] A. Erturk，W. Vieira，C. De Marqui，D. J. Inman．On the energy harvesting potential ofpiezoaeroelastic systems[J]．Applied Physics Letters，2010，96（18）：184103．
[91] L. Huang．Flutter of cantilevered plates in axial flow[J]．Journal of Fluids and Structures，1995，9（2）：127-147．
[92] C. Q. Guo，M. P. Paidoussis．Stability of rectangular plates with free side-edges intwo-dimensional inviscid channel flow[J]．Journal of Applied Mechanics，2000，67（1）：171-176．
[93] C. Eloy，C. Souilliez，L. Schouveiler．Flutter of a rectangular plate[J]．Journal of fluids andstructures，2007，23（6）：904-919．
[94] C. Eloy，R. Lagrange，C. Souilliez，L. Schouveiler．Aeroelastic instability of cantileveredflexible plates in uniform flow[J]．Journal of Fluid Mechanics，2008，611（1）：97-106．
[95] T. S. Balint，A. D. Lucey．Instability of a cantilevered flexible plate in viscous channelflow[J]．Journal of Fluids and Structures，2005，20（7）：893-912．
[96] M. Argentina，L. Mahadevan．Fluid-flow-induced flutter of a flag[J]．Proceedings of theNational academy of Sciences of the United States of America，2005，102（6）：1829-1834．
[97] D. M. Tang， H. Yamamoto， E. H Dowell． Flutter and limit cycle oscillations oftwo-dimensional panels in three-dimensional axial flow[J]．Journal of Fluids and Structures，2003，17（2）：225-242．
[98]赵文胜．轴向流中板结构流固耦合动力学研究[D]．武汉：武汉大学，2011：1-97．
[99] K. Singh，S. Michelin，E. De Langre．The effect of non-uniform damping on flutter in axial flowand energy-harvesting strategies[J]．Proceedings of the Royal Society A: Mathematical,Physical and Engineering Science，2012，468（2147）：3620-3635．
[100] A. Kornecki，E. H. Dowell，J. O'Brien．On the aeroelastic instability of two-dimensional panesin uniform incompressible flow[J]．Journal of Sound and Vibration，1976，47（2）：163-178．
[101] S. Michelin，S. G. L. Smith．Linear stability analysis of coupled parallel flexible plates in anaxial flow[J]．Journal of Fluids and Structures，2009，25（7）：1136-1157．
[102] M. J. Lighthill．Large-amplitude elongated-body theory of fish locomotion[J]．Proceedings ofthe Royal Society B: Biological Sciences，1971，179（1055）：125-138．
[103] F. Candelier， F. Boyer， A. Leroyer． Three-dimensional extension of Lighthill'slarger-amplitude elongated-body theory of fish locomotion[J]．J. Fluid Mech.，2011，674：196-226.
[104] C. Eloy，N. Kofman，L. Schouveiler．The origin of hysteresis in the flag instability[J]．Journalof Fluid Mechanics，2011，691：583-593.
[105] T. S. Balint，A. D. Lucey．Instability of a cantilevered flexible plate in viscous channelflow[J]．Journal of Fluids and Structures，2005，20（7）：893-912．
[106] H. Ma，W. Sun．A Legendre-Petrov-Galerkin and Chebyshev Collocation Method forThird-Order Differential Equations[J]．SIAM Journal on Numerical Analysis，2000，38（5）：1425-1438．
[107] U. Ehrenstein，R. Peyret．A Chebyshev collocation method for the Navier–Stokes equationswith application to double‐diffusive convection[J]．International Journal for NumericalMethods in Fluids，1989，9（4）：427-452．
[108] P. Boomkamp，B. J. Boersma，R. Miesen，G. V. Beijnon．A Chebyshev collocation methodfor solving two-phase flow stability problems[J]．Journal of Computational Physics，1997，132（2）：191-200．
[109] C. Souilliez，C. Eloy，L. Schouveiler．An experimental study of flag flutter[C]．SME PressureVessels and Piping Division Conference，Vancouver, Canada，2006：
[110]朱伟强．福建省沿海风力资源特性分析[J]．电力勘测设计，2006，1：33-36．
[111]李艳，耿丹，董新宁，朱焱．1961-2007年重庆风速的气候变化特征[J]．大气科学学报，2010，33（3）：336-340．
[112]彭小云，袁剑．高层建筑室外风速简化计算方法研究[J]．四川建筑科学研究，2011，37（3）：37-39．
[113]叶征伟．山区高墩大跨连续刚构桥风环境及风荷载研究[D]．浙江：浙江大学，2012：3-19．
[114]胡俊．大跨度悬索桥现场实测数据、风雨激励响应及风振疲劳研究[D]．大连：大连理工大学，2012：3-21．
[115]申建红，李春祥．强风作用下超高层建筑风场特性的实测研究[J]．振动与冲击，2010，29（05）：62-68．
[116]王福军，周佩剑．铁路风力发电灯具[P]．中国，201010227422.4，2010-07-07．
[117]董文华，张维智．扰动风速风力发电系统及其垂直轴微型风力机[P]．中国，200410040054.7，2004-06-24．
[118]张红涛，寇晓霞．一种隧道风力发电装置[P]．中国，200920195174.2，2009-09-22．
[119]刘惟信．机械可靠性设计[M]．北京：清华大学出版社，1996：57-102．
[120] T. Fett，D. Munz，G. Thun．Bending strength of a PZT ceramic under electric fields[J]．Journalof the European Ceramic Society，2003，23（2）：195-202．
[121] M. Okayasu，G. Ozeki，M. Mizuno．Fatigue failure characteristics of lead zirconate titanatepiezoelectric ceramics[J]．Journal of the European Ceramic Society，2010，30（3）：713-725．