摘要
近年来化石能源危机,环境危机使得可再生能源得到空前发展。风能作为环保型,无穷无尽之能源,在20世纪80年代后进入了发展的黄金时期。中国作为能源消费大国,近年来风电得到国家层面上的大力支持从而得到快速发展。但起步较晚使中国风电技术与风电发达国家差距很大,MW级以上风电设备设计技术基本依赖进口,作为风电机组关键部件之一的叶片尤其如此。本文在国家“十一五”科技支撑计划项目(2006BAA01A09)支持下,根据现有进口叶片,着重对大型水平轴风机叶片进行气动性能计算和结构设计进行了研究,取得如下成果:
(1)风轮气动性能主要包括功率、轴力、转矩以及其对应的功率系数、轴力系数和转矩系数,本文采用叶素动量理论,结合前人研究成果,建立了较完善的风轮叶片气动性能计算模型,考虑风轮实度(叶片数)、安装角、锥角、倾角以及叶片宽度、厚度,风轮偏航等因素,采用迭代法计算叶素诱导因子,编制matlab计算程序,分析了这些因素对风轮气动性能的影响。并在整个叶片翼展方向,对轴向诱导因子和周向诱导因子以及叶素功率分布进行了详细分析。分析结果表明,风轮实度、安装角对功率影响显著,锥角和倾角将会导致风轮各项气动性能下降。叶片宽度和厚度对风轮气动性能影响不大。
(2)完成了一整套利用有限元软件对大型叶片进行校核分析的方法,摸索出了具有复杂气动外形和内部铺层结构的复合材料叶片建模的有效方法。并直接利用软件对叶片各截面、各方向刚度进行近似计算,与理论值吻合良好,表明该方法可行、有效。与理论法相比,该方法简便易行,特别适合非规则截面复合材料构件刚度的计算。对叶片动力行为模态进行了理论上的探讨,推导出了叶片自振频率的估算公式,模态分析表明叶片第一阶模态发生在挥舞方向,第二阶发生在摆振方向,高阶模态逐渐复杂化,呈现出混合振型形式。应变的校核分析表明,叶片主要在叶根和最大弦长处有较大应变值。在稳定性分析中,发现叶尖区域是叶片可能发生失稳的一部分。
(3)对叶片设计的关键之一,结构铺层设计进行了研究,建立了大型叶片初步结构设计的理论方法。叶片采用分段原则,以叶片挥舞方向极限弯矩为设计载荷,综合运用前人总结的经验公式,以及经典层合板理论和Euler-Bernoulli梁理论,在外形不变的前提下,对现有750KW叶片在结构铺层上进行重新设计研究。研究表明,理论设计不是最终设计,前面的有限元校核分析,修正将起到十分重要的作用。通过对比分析,本文对750KW叶片的结构铺层设计比较合理,在叶片重量、挥舞方向刚度、叶尖挠度均占优势,仅在稳定性方面不如原有叶片。
(4)在主梁上用碳纤维材料替代玻璃纤维作为叶片主要承载构件的增强材料,研究了叶片弯扭耦合设计的可行性。首先对叶片弯扭设计进行了参数化研究,建立控制弯扭耦合的主要参数α,从理论和数值分析两个方面估算α可能的取值范围。进行弯扭耦合设计可以从几个方面进行,比如几何外形上,或者将材料主轴与主受力方向成一角度。本文采用后者,在主梁将碳纤维主轴与主受力方向成0°、10°、15°和20°角。对弯扭耦合设计后的叶片整体性能进行了分析,并与本文新设计的叶片结构进行了对比分析,研究表明,运用弯扭耦合设计理念,叶片结构性能在几乎所有方面都有了提高,这表明弯扭耦合的巨大意义,同时也显示了碳纤维运用到叶片结构设计中的潜力。
The renewable energy has greatly developed in recent years due to the crisis of fossil energy and environment. As a type of environment-friendly and inexhaustible energy, wind energy went into its golden time of development in 80s, 20th century. China, as a large consumer of energy, wind power has got quick development in recent years with the state's support. But the MW-class wind turbine technologies almost are all imported because of the deep gap between China and west countries with advanced wind power technology, especially rotor blade, which is one of the key components of wind turbine. With the support of Beijing FRP company and aid of National "11th five-year" Scientific Support Plan (2006BAA01A09), researches were focused on the aerodynamic performance calculation and structural design of rotor blade on the basis of the existing imported blade. The main achievements are as follow:
(1) The aerodynamic performance was defined by power, thrust, torque and their corresponding coefficients. In this paper, by the use of blade element and momentum theory and in combination with the research results finished by our predecessors, a relatively complete calculation model for the aerodynamic performance of rotor blade is built with the consideration of rotor solidity (blade number), pitch angle, zone angle, tilt angle and blade width, thickness, yaw angle etc. Matlab codes adopted the iterative algorithm are generated and the influences of these factors on the aerodynamic performance are analyzed. Also, detailed analyses on the distribution of axial and tangential induction factors and the blade element power along the whole blade are performed. Analyses above show that solidity and pitch angle have a great effect on the aerodynamic performance while blade width and thickness affect little and the existences of zone and tilt angle will lead reduction of aerodynamic performance of rotor blade.
(2) An entire set of method of large-scale blade analysis is completed by using finite element software, and also an effective approach of building the FE model of composite blade with complex aerodynamic shape and internal laminate structure is investigated. And then directly use software to calculate the sectional stiffness approximately, the results from which are identical with the theoretical ones. Compared with theoretical method, FE method is easy and convenient, especially applied at rigidity calculation of composite structures with irregular cross section. Theoretical investigation is made on blade dynamic behavior (modal analysis), approximate computation equation of blade natural frequency is derived. Modal analysis shows that the first mode happens in flapwise direction and the second in edgewise direction. High order mode shapes are getting complicated, which are mixed mode. It is clear that bigger strains occur In the region of blade root and station with maximum chord length. In the buckling analysis, it is found that blade tip area is one part that maybe easily be buckled.
(3) Study work is carried out on the structure design, which is one of the key design of blade, the preliminary structural design theory is achieved. Based on the section-design principle, structural is redesigned with the same external shape as the existing blade by using classical laminate theory and Euler-Bernoulli beam theory. Structure study shows that theoretical design is not the final design, it is important to combine with FE analysis to check and modify repeatedly, through which final structural schedule will be determined. Through comparison of blade weight, stiffness at flapwise and tip deformation with the existing blade, the approach in this paper is reasonable, except the stability.
(4) Feasibility of FRP replaced by GRP in spar cap to introduce bend-twist couple design is investigated. First Parametric study of bend-twist design is implemented and then finds out the main controlling parameterα, and then makes an approximation of value range of this parameter from theoretical and numerical aspects. Bend-twist coupling design can be implemented from several aspects, such as geometrically or by using unbalanced off axis fibers oriented at an angle with respect to the primary loading direction. The latter is preferred in this paper and the oriented angles are 0°, 10°, 15°and 20°.respectively. Analysis and comparison work between the blades with different design approach are done and shows that the performance of blade structure is getting higher designed by bend-twist coupling.
引文
1.朱向东.可再生能源—我国超常规跨越式发展的历史机遇(上).建材发展导向,2007,4:63-66
2.张国伟,龚光彩,吴志.风能利用的现状及展望.节能技术,2007,25(1):71-76
3.陈达,张玮.风能利用和研究综述.节能技术,2007,25(4):339-359
4.李登峰,张烈辉,郭了萍.中国21世纪可替代能源和可再生能源.天然气工业,2006,26(5):1-5
5.刘万锟,张志英,李银凤.风能与风力发电技术.北京:化学工业出版社,2006
6.郭健.风力发电机整机性能评估与载荷计算的研究:大连理工大学硕士学位论文.大连:控制工程系,2003
7.Emesto Benini,Andrea Toffolo.Optimal design of horizontal Axis wind turbines using blade.element theory and evolutionary computation[J].ASME Journal of Solar Energy Engineering,2002,124:357-363.
8.刘雄,陈严,叶枝全.水平轴风力机气动性能计算模型.太阳能学报,2005,26(6):792-800.
9.Tony Burton,David Sharpe,Nick Jenkins,Ervin Bossanyi.Wind Energy Handbook.Chichester:John Wiley & Sons,Ltd.,2001,59-65
10.贺德馨.风工程与工业空气动力学.北京:国防工业出版社,2006
11.Betz A.Sohrauben Propeller mit geringstem energieverlust.Gottinger Nachr.,Germany,1919
12.Stoddard F S.Momentum Theory and Flow States for Windmills.Wind Technology Journal,1977,1
13.Tony Burton著,武鑫译.风能技术.北京:科学技术出版社,2007
14.Stoddard F S.Dynamic Load of a 10-Meter Diameter Wind Turbine Generator System.The Annual Conference of American Wind Energy Association,San Francisco,1979
15.Stoddard F S.Dynamic Rotor Loads of a Wind Turbine Via Hand-Held Calculators.AIAA 800611R,1980.
16.Miller R H,Duaundji J,et al.Methods for Design Analysis of Horizontal Axis Wind Turbines,ASRL-TR-184-7,1978.
17.Cherrit A W,Gaidelis J A.100KW Metal Wind Turbine Blade Basic Data,Loads and Stress Analysis.NASA CR-134956,1975.
18.Jones C M.Blade Element Performance in Horizontal-Axis Wind Turbine Rotors,Wind Engineering,1983,7(3).
19.Rijs A P E Smulders P L.Blade Element Theory for Performance of Slow Running Wind Turbine,Wind Engineering,1990,14(2).
20.Wilson R E,Lissaman P B S.Applied Aerodynamics of Wind Power Machines,NSF/RA/N 74114,Oregon State University,Corvallis,1974.
21.Kotb M A,Soliman H A.Performance Analysis of a HAWT under Non-Uniform Flow with Swirl Wind Engineering and Industrial Aerodynamics,1991,37:102-111.
22.Prandtl L.Appendix to wind turbines with minimum energy losses.In:Betz A,editor.Goettenger News,Goettenger,1919,pp.193-217.
23.Goldstein,S.On the Vortex Theory of Screw.Propellers.Preceeding,Royal Society,1929,A 123:440-465..
24.Lock,C.N.H,H.Batemen,and H.C.H.Townsend.An Extension of the Vortex Theory of Airscrews with Applications to Airscrews of Small Pitch,.Including.Experimental Results.Aeronautical Research Committee Reports and Memoranda,No.1014,London,1926.
25.Glauert H.The analysis of experimental results in the windmill brake and vortex ring states of an airscrew.Reports and Memoranda,1926
26.Wilson R E,Lissaman P B S,Walker S N.Aerodynamic performance of Wind Turbine.Oregon State University,1976
27.柴国钟,牛山泉.水平轴风轮气动特性及优化设计.浙江工学院学报.1991,4:15-24
28.Anderson M B,Milborrow D J,Ross J N.In:Fourth International Symposium on wind Energy System,1982:113-135.
29.郭天威,方景龙.风力发电机组风轮叶片气动外形优化设计及风轮气动性能计算研究.中美清洁能源技术论坛.PP:103-108.
30.James L.Tangler,J.David Kocurek.Wind Turbine Post-Stall Airfoil Performance Characteristics Guidelines for Blade-Element Momentum Methods.NREL/CP-500-36900,October 2004
31.Bongani Malinga.Modeling and Control of a Wind Turbine as a Distributed Resource in an Electric Power System.Master thesis,West Virginia University,2001
32.Guanpeng Xu.Computational Studies of Horizontal Axis Wind Turbines.PHD thesis.Georgia Institue of Technology,2001
33.Koki Kishinami,Hiroshi Taniguchi,Jun Suzuki.Theoretical and experimental study on the aoredynamic characteristics of a horizontal axis wind turbine.Energy.2005,30:2089-2100.
34.Md Quamrul ISLAM,A.K.M.Sadrul ISLAM.The Aerodynamic Performance of a Horizontal Axis Wind Turbine Calculated by Strip Theory and Cascade Theory.JSME International Journal. Series B. 1994, 37(4): 871-877
35. Kotb M A, Adbel Haq M M. A Rigid Wake Model for a Horizontal Axis Wind Turbine. Wind Engineering, 1992,16(2): 95-108
36. Anderson M B. a Vortex-Wake Analysis of the Horizontal-Axis Wind Turbine and Comparison with Modified Blade Element Theory. Third International Symposium on Wind Energy Systems, the Technical University of Denmark, 1980
37. Hernandez J, Crepo A. Aerodynamic Calculation of the Performance of Horizontal Axis Wind Turbines and Comparison with Experiment Results. Wind Engineering, 1987,11(4)
38. Gohard J C. Free Wake Analysis of Wind Turbine Aerodynamics. ASRL, TR-184-14, Aeroelastic and Structures Research Laboratory Department of Aeronautics and Astronauts, MIT, 1978
39. Humes T M. The Calculation of Unsteady Air Loads Acting on a Wind Turbine Rotor Blades: [thesis]. Massachusetts Institute of Technology, 1976.
40. Afjeh A A, Kieth T G. A Vortex Lift Line method for the analysis of horizontal axis wind turbines. Journal of solar energy engineering, 1986, 108: 303—309.
41. Miller R H. Rotor hovering performance using the method of fast free wake analysis. AIAA 20th aerospace science meeting. AIAA-82-0094, Orlando, Florida, 1982.
42. Miller R H. Simplified free wake analysis for rotors. MIT Report ASRL-TR-194-3.
43. Miller R H. The aerodynamic and dynamic analysis of horizontal axis wind turbines. Journal of wind engineering and Industrial aerodynamics, 1985,15: 329-340.
44. Afjeh A A, Kejth J T G. Simplified wake flow models of horizontal axis wind turbine. Proceeding wind power'85, San Francisco, CA, 1985, 8:469-475.
45. Afjeh A A, Kejth J T G. A simplified free wake method for horizontal axis wind turbine performance predication. ASME, Journal of fluids engineering, 1986,108: 400-406.
46. Rosen A, Lavie I, Seginer A. A general free-wake efficient analysis of horizontal axis wind turbine. Wind Engineeing. 1990, 14(6): 362-373.
47. Piers W J. A non-linear lifting line method for the calculation of the flow around a rotating system, part I: The conventional wind turbine. NLR TRR 85052L, The Netherlands, 1985.
48. Piers W J. A non-linear lifting line method for the calculation of the flow around a rotating system, part II: The tipvane turbine.
49. Van Egmond J A. Evaluation of two performance prediction methods for horizontal axis wind turbine by comparison with experimental results. NLR TRR 850522L, The Netherlands, 1985.
50.Koh S G,Wood D H.Formulation of a vortex wake model for horizontal axis wind turbine wind engineering,1991,15(4):196-210
51.Koh S G,Wood D H.Implementation of a vortex wake model for horizontal axis wind turbine wind engineering,1991,15(5):262-274
52.窦秀荣.水平轴风力机气动性能及结构动力学特性研究.山东工业大学博士学位论文,1996.
53.O.L.Hansen Martin.Aerodynamics of wind turbines.James & James,London,2002
54.宋宪耕,窦秀荣,艾兴等.水平轴风轮空气动力性能的分析计算.空气动力学学报.1996,14(1):92-97.
55.Mayer RM.Design of composite structures against fatigue applications to wind blades.Chippehham:Antony Rowe Ltd.1996:195-208.
56.Gourieres DLE.Wind power plants theorY and design.New York:Pergamon Press.1982.
57.Kong C,Kim J.A study on structural and aerodynamic design of composite blade for large scale HAWT system.Final report,Hankuk Fiber Ltd.2000.
58.Roger Scherer.Blade design aspects.Renewable Energy,1999,16:1272-1277.
59.Mayer,R.M.Design of Composite Structures Against Fatigue,.Mechanical Engineering Publications Limited,ISBN 0 85298-957-1,first publication 1996.
60.Jame L.Tangler.The evolution of rotor and blade design.NREL/CP-500-28410,2000
61.Dayton A.Griffin,Thomas D.Ashwill.Alternative composite materials for megawatt-scale wind turbine blades:design considerations and recommended testing.AIAA-2003-0696
62.Dutton,A.G.,et,al.Design Concepts for Sectional Wind Turbine Blades.Proceedings of the 1999 European Wind Energy Conference,Nice France.PP:285-288.
63.Joosse,P.A.,et al.Economic Use of Carbon Fibres in Large Wind Turbine Blades.Proceedings of AIAA/ASME Wind Energy Symposium.Reno,NV
64.Joosse,P.A.,et al.Toward Cost Effective Large Turbine Components with Carbon Fibers.Presented at the 2001 European Wind Energy Conference and Exhibition,Copen.hagen.
65.Joosse,P.A.,et al.Fatigue Properties of Low-Cost Carbon Fiber Material.Presented at the 2001 European Wind Energy Conference and Exhibition,Copenhagen.
66.Cheng-Huat Ong,Stephen W.Tsai.The use of carbon fibers in wind turbine blade design.SAND 2000-0478,2000
67.Akira Kuraishi,Stephen W.Tsai,Julie Wang.Material characterization of glass,carbon and hybrid-fiber SCRIMP panels.SAND2002-3538,2002
68.Dayton A.Griffin.Blade system design studies volume Ⅱ:Preliminary blade design and recommended test matrix.SAND2004-0073,2004
69.中人民共和国机械行业标准.风力发电机组风轮叶片.JB/T 10194-2000,国家机械工业局发布,2000
70.陈宗来,陈余岳.大型风力机复合材料叶片技术及进展.玻璃钢/复合材料.2005,3:53-56
71.Kong C,Jeong J.Improvement of design by structural test for 750KW HAWT composite blade,J KSPE 2000,4(3):22-29
72.Kong C,Bang J,Jeong S,Ryu J,Kim Y.Structural design of medium scale composite wind turbine blade.Proceedings of the third Asian-Pacific conference on aerospace technology and science(APCATS2000).2000,pp:376-384
73.Kong C,Jeong S,Jang B,Bang J.Design improvement on wind turbine blade of medium scale HAWT by considering fatigue life.J KSPE 2000,4(3):29-37.
74.Kong C,Kim J.Structural design of medium scale composite wind turbine blade.KSAS Int J 2000,1(1):92-102.
75.Kong C,Bang J,Kang M,Jeong S,Yoo J.Structural design of medium scale composite wind turbine blade.Thirteen international conference on composite materials(ICCM-13),2001.
76.C.Kong,J.Bang,Y.Sugiyama.Structural investigation of composite wind turbine blade considering various load cases and fatigue life.Energy,2005,30:2101-2114
77.Bechly ME,Clausent PD.Technical note:structural design of a composite wind turbine blade using finite element analysis.Computers & Structures 1997,63(3):639-646
78.Knut O.Ronold,Carl J.,.Christensen.Optimization of a design code for wind-turbine rotor blades in fatigue.Engineering Structures.2001,23:993-1004.
79.Karam Y,Maalawi,Hani M.Negro.Optimal frequency design of wind turbine blades.Journal of Wind Engineering and Industrial Aerodynamics.2002,90:961-986.
80.S.Us,S.Tolun.Structural Design and Analysis of Wind Turbine Rotor Blades Using Laminated Sandwich Com.posites.Earth & Space,2004,pp:492-498.
81.P.Giguere,M.S.Selig.Blade design trade-offs using low-lift airfoil for stall-regulated HAWTs.NREL/CP-500-26091,1999
82.Dayton A.Griffin.WindPACT turbine design scaling studies technical area 1-composite blades for 80-120-meter rotor.NREL/SR-500-29492,2002
83.D.J.Malcolm.WindPACT turbine rotor design study.NREL/SR-500-32495,20002.
84.Dayton A,Griffin.Blade system design studies volume Ⅰ:composite technologies for large wind turbine blades.SAND2002-1879,2002.
85.Cheng-Huat Ong.Composite wind turbine blades.PhD Dissertation.Stanford university.2000.
86.C.H.Hong and I.Chopra.Aeroelastic stability analysis of a composite blade.Journal of the American Helicopter Society.1985,30(3):57-67..
87.C.H.Hong and I.Chopra.Aeroelastic stability analysis of a composite bearingless rotor blade.Journal of the American Helicopter Society.1986,31(4):29-35..
88.E.C.Smith,I.Chopra.Formulation and Evaluation of an Analytical Model for Composite Box-Beams.AIAA-90-0962-CP,1990.
89.Ramesh Chandra,Alan D.Stemple,Inderjit Chopra.Thin-walled Composite Beams Under Bending,Torsional,and Extensional Loads.Journal of Aircraft,1990,27(7):619-626.
90.D.W.Lobitz,P.S.Veers.Aeroelastic behavior of twist-coupled HAWT blades.AIAA-98-0029,1998 ASME Wind Energy Symposium held at 36~(th)AIAA aerospace sciences meeting and exhibition,Reno,NV,Jan.1998..
91.D.W.Lobitz,D.J.Laino.Load mitigation with twist-coupled HAWT blades.AIAA-99-0033,Proceedings of the 1999 ASME Wing Energy Symposium,Reno,1999..
92.李军向,薛忠民,王继辉等.大型风轮叶片设计技术的现状与发展趋势.玻璃钢/复合材料.2008,1:48-52..
93.Andrew T Lee,BE(Hons).Compliant blades for wind turbines.IPENZ Transation,1999,26(1):7-12.
94.W.C.de Goeji,M.J.L.,van Tooren,A.Beukers.Implementation of bending-torsion coupling in the design of a wind-turbine rotor blade.Applied Energy 1999,63:191-207.
95.San Diego.California,Knight & Carver Builds First STAR Blade for the DOE.http://www.renewableenergyaccess.com/.
96.李德源,叶枝全,陈严等.风力机叶片载荷谱及疲劳寿命分析.工程力学,2004,21(6):118-123.
97.郭健.风力发电机整机性能评估与载荷计算的研究.大连理工大学硕士论文,2003.
98.R I Rawlinson-Smith.Load calculations for a Generic 1.5MW wind turbine to IEC ⅡA conditions.Garrad Hassan and Partners Ltd,1040/BR/01,2004
99.陈严,王楠.水平轴风力机极限载荷预测方法的研究.汕头大学学报(自然科学版),2005,20(1):43-47
100.虞择斌.水平轴风力机气动载荷计算及桨毂有限元分析.全国第一届风能技术应用年会论文集.pp:31-37.
101.Gunner C.Larsen,Sten Frandsen,Poul Sorensen,Michael S.Courtney.Design Basis for Horizontal axis Wind Turbines Theoretical Background.Riso National Laboratory,Rlso-M-2836,1989.
102.陈余岳,张锦南,王强等.660KW风力机玻璃钢叶片研制.玻璃钢学会第十五届全国坡璃钢/复合材料学术年会论文集.2003,PP:196-205..
103.王勖成等.有限单元法基本原理与数值计算.清华大学出版社.1988,北京
104.孙菊芳等.有限元法及其应用.北京航空航天大学出版社.1989,北京
105.M.Jureczko,M.Pawlak,A.Mezyk.Optimisation of wind turbine blades.Journal of Materials Processing Technology.2005,167:463-471.
106.Dr.Jiangtao Wei,Tian Ye,Tian Weiguo.Derivation and validation of a beam type FE model of a glass fibre blade for blade and wind turbine load analysis.ZhongHang(Baoding)Huiteng windpower equipment Co.,Ltd.2003.
107.Patek M.H.and Garrad,A.D.,The development of a finite element method for the dynamic analysis of wind turbines.Wind Energy Conversion,Proceedings of the 12th British Wind Enernv Association Conference.1990,pp.315-318.-
108.El Chazly,N.M.,Static and dynamic analysis of wind turbine blades using the finite element method.Computers and Structures,1993,48(2):273-290.
109.Prandtl.L,Tietjens O G.Applied hydro and aerodynamics.Dover Publication,1957..
110.Moment R,Pastore J.Wind energy conversion.In:A short seminar presented to the royal scientifiC society by rocky flats wind energy research center,rocKWell international corporation,USAID,March.1984.P.4-10.
111.Robert,E Wilson,Peter B S Lissaman,Stel N Walker.Aerodynamic performance of wind turbines.Department of Mechanical Engineering,Oregon State University,1976.
112.Spera,D A.Wind turbine technology[M].New York:AS.ME Press,1994.
113.L.R McKittrick,D.S Cairns,J.Mandell.,D.C.Combs.,D.A Rabern and R.D Van Luchene,Analysis of a Composite Blade Design for the AOC 10/50 Wind Turbine using a Finite Element Model,Sandia National Laboratories,Report SAND 2001-1441,2001
11 4.王勖成 编著.有限单元法.清华大学出版社,2003.
115.Thomson,W.T.Theory of Vibration with Applications.George Allen & Union,London,1981.
116.小飒工作室编.最新经典ANSYS及Workbench教程.电子工业出版社.2004,北京.
117.博嘉科技 编著.有限元分析软什-ANSYS融会与贯通.中国水利水电出版社.2002,北京
118.Sullivan T.A Review of Resonance Response in Large,Horizontal-axis Wind Turbines.In Thresher,R.,editor,Proceedings,Wind Turbine Dynamics Workshop,Volume NASA Conference Publication 2185,1981,PP:237-244.
119.Gunner C.Larsen,Sten Frandsen,Poul Sorensen,Michael S.Courtney.Design Basis for Horizontal-Axis Wind Turbines Theoretical Background.Riso National Laboratory,DK-4000Roskilde,Denmark,1989.Riso-M-2836.
120.孙训方,方孝淑,关来泰.材料力学(第三版).高等教育出版社,1993.
121.William H.Press,Saul A.Teukolsky,William T.Vetteding,Brian P.Flannery.NUMERICAL RECIPES,The Art of Scientific Computing(Third Edition),Cambridge University,New Youk,2007.
122.李顺林,王兴业主编.复合材料结构设计基础.武汉:武汉工业大学出版社,1996.
123.王耀先编著.复合材料结构设计.北京:化学工业出版社,2001.
124.上海玻璃钢结构研究所.玻璃钢结构设计.北京:中国建筑工业出版社,1980.
125.赵渠森编译.复合材料.北京:国防工业出版社,1979.
126.孙训方编.材料力学(下册).北京:高等教育出版社,1995.
127.徐芝纶.弹性力学简明教程(第三版).北京:高等教育出版社,2002.
128.曹人靖,刘道兴.水平轴风力机风轮静态结构特性试验研究.太阳能学报.2001,22(4):436-439
129.NWTC Design Codes(YawDyn by Dr.David J.Laino,A.Craig Hansen).http://wind.nrel.gov.Last modified 26-May-2005;accessed 26-May-2005.
130.James Locke,Ulyses Valencia.Design Studies for Twist-Coupled Wind Turbine Blades.SAND 2004-0522,2004.
131.D.W Lobitz,P.S.Veers and P.G.Migliore.Enhanced Performanced of HAWT's Using Adaptive Blades.Proc.Wind Energy 96,ASME Wing Energy Symposium,Houston,Jan.29-Feb.2,1996,pp.41-45.
132.Ronald E Gibson.Principles of Composite Material Mechanics.New York:McGraw-Hill,Inc,1994.