直升机标准桨叶特性参数测量技术研究
|
摘要
直升机标准桨叶是直升机批生产桨叶特性参数检测和调试的参照标准,是保存该型号直升机桨叶特性参数的原始标准,是实现直升机桨叶单片互换的基础。桨叶是直升机旋翼升力系统的重要部件,其特性参数直接影响到直升机的飞行品质,每一片批生产桨叶在装机前都要进行动平衡检测和调整,使其特性参数与标准桨叶一致。我国某型号直升机3片标准桨叶由法国引进,复合材料制造,其中1片标准桨叶的特性已发生变化,与原始校准数据和其他2片标准桨叶参数无法对应,已经停止其作为标准桨叶的特性参数传递过程,严重影响了某型直升机批生产桨叶的检测任务,若再有1片标准桨叶特性参数发生变化则会造成很严重的后果,必须对3片标准桨叶的特性参数进行系统调整,使其恢复到出厂时的技术参数水平,保持标准桨叶特性参数长期稳定性和一致性,为标准桨叶的系统校准奠定基础。
本文把标准桨叶动平衡过程中桨叶挥舞角按Taylor基数展开,建立了标准桨叶带复杂空气动力激扰的Duffing非线性挥舞运动方程,通过Melnikov方法分析了桨叶所受气动力、气动阻尼、2倍和3倍周期不平衡空气动力激扰作用对挥舞方程稳定性和标准桨叶挥舞参数的影响,得出标准桨叶挥舞参数是稳定的,但对旋翼桨毂特性和试验环境参数比较敏感。
桨叶挥舞高度参数受到标准桨叶本身特性参数和其他试验参数的影响,通过在动平衡试验台上交换标准桨叶安装位置的方法,获得标准桨叶的动平衡试验参数,实现标准桨叶特性参数与旋翼桨毂参数的解耦。根据标准桨叶动平衡和标准传递过程,确定标准桨叶需要测量和调整的静态特性参数和动态特性参数;针对标准桨叶挥舞运动对环境阵风引起的不平衡空气动力的挥舞响应,文中提出了桨叶动平衡试验环境中风速影响的分析方法,通过仿真试验和实际测量数据,得出了在桨叶挥舞参数误差要求范围内的风速极值,结果与法国相关的试验标准相吻合,进而确定了标准桨叶特性参数测量与调整过程的环境风速条件,奠定了准确恢复标准桨叶特性参数的基础。
本文采用激光测量技术来测量桨叶的挥舞参数。进一步研究了激光器安装定位参数的测量方法,利用激光器本身的结构和标定算法,实现了激光器定位参数的标定;利用一定厚度的模拟桨叶切割激光光路的方法标定标准桨叶挥舞参数测量系统,实现了标准桨叶挥舞参数测量系统的标定和溯源。最后,对标准桨叶挥舞参数测量系统和测量结果进行了不确定度分析。
对于标准桨叶铰链力矩的测量,文中设计了基于RBF神经网络的铰链力矩载荷识别和动态特性补偿方法,神经网络的结构避免了建立系统的结构模型,把扭矩载荷识别和标定的反问题都做为正问题处理。用同步采样的实际静态载荷和正弦扭矩载荷数据训练神经网络,并对训练结果进行了试验数据验证,实现了铰链力矩测量系统的动态标定,提高了标准桨叶铰链力矩的测量准确度。
本文针对某型号标准桨叶静态特性参数和动态特性参数进行了具体的试验测量,通过实测数据与法国出厂校准数据的比较,找出了标准桨叶特性参数变化的趋势,提出了标准桨叶特性参数整体调整恢复的方法,使标准桨叶特性参数恢复到出厂时的参数水平,保证了标准桨叶特性参数的延续性和长期稳定性。
The primary standard blade is the reference standard of natural parameters for work rotor blades on measurement and adjustment process, the transmission standard for batch productions, as well as the base of interchangeability for single rotor blade. The rotor blades are the important parts that determinate the flight quality of helicopters. Each piece of rotor blades must be measured and adjusted on a dynamic balance tester in order to make the parameters uniform as the primary standard blade before the final assembly. The three pieces of primary standard rotor blades in our country are made in France with the composite material, the natural parameters of one piece of standard blades have been changed, parameters in which disagree with the original data and other two standard blades. Once a standard rotor blade stops work, it will have a strong impact on the other types of helicopter rotor blades. The result is extremely serious if the other standard blade parameters are changed. The primary mission is to calibrate and adjust the standard rotor blade parameters, and recover its original parameters in order to keep the long-time stability and uniformity.
With the dynamic balance testing process, a method is proposed by deriving the flapping equation, expanding the flapping angle by the method of Taylor radix and building the nonlinear Duffing’s flapping equation with complex aerodynamics perturbation for the primary standard rotor blade. The stability of flapping equation with the action of aerodynamics, aerodynamic damping, double-period and triple-period aerodynamics perturbation are analyzed with Melnikov method. The result is that the rotor flapping is stable on flapping equation and sensitive on testing environment.
The flapping parameters are impacted by the natural parameters of standard rotor blade and other testing parameters. Using the method of changing the installation position on rotor hub, the testing parameters of standard rotor blades are obtained and the standard rotor blade parameters from hub parameters are uncoupled. The gust can influence the results of dynamic parameters for the primary standard rotor blade, an analysis method with wind speed in a dynamic balance testing environment is proposed for the flapping response by non-balance aerodynamics perturbation caused by gust, the extreme value of wind speed in the dynamic balance testing is determined by the emulator program and actual data, the result is the same as the French testing standard. The wind speed in the process of calibration is determined for primary standard rotor blade, and the base of parameters recovery process is settled.
With the measurement technique of laser, a method is proposed to measure the flapping parameters of primary standard rotor blades,and a further design of measurement method is applied in calibrating the spatial location parameters of laser. At the same time, a method is proposed to calibrate the flapping measurement system with a definite thickness simulator as blade and the measurement system is calibrated. Finally, the uncertainty of measurement system and flapping parameter are analyzed.
For the measurement of flapping hinge moment, a recognition method for load and compensation on a dynamic characteristic is proposed based on RBF neural network, this method avoids to build the mathematical model for the measurement system, and inverts the indirect problem of recognition process and calibration process into a direct problem. To train and check the networks with the synchronous sampling data of sine torque moment, the hinge moment measurement system is calibrated dynamically, and the measurement uncertainty is improved in flapping hinge moment for primary standard rotor blade.
For the actual data of static parameters and dynamic parameters of some primary standard rotor blade, a calibration and adjustment method is proposed by comparing the actual data with data from France. With the calibration and adjustment process, the parameters of primary standard rotor blades resume the initial state. This proposed method guarantees the long-time stability of natural parameters for the primary standard rotor blades.
本文把标准桨叶动平衡过程中桨叶挥舞角按Taylor基数展开,建立了标准桨叶带复杂空气动力激扰的Duffing非线性挥舞运动方程,通过Melnikov方法分析了桨叶所受气动力、气动阻尼、2倍和3倍周期不平衡空气动力激扰作用对挥舞方程稳定性和标准桨叶挥舞参数的影响,得出标准桨叶挥舞参数是稳定的,但对旋翼桨毂特性和试验环境参数比较敏感。
桨叶挥舞高度参数受到标准桨叶本身特性参数和其他试验参数的影响,通过在动平衡试验台上交换标准桨叶安装位置的方法,获得标准桨叶的动平衡试验参数,实现标准桨叶特性参数与旋翼桨毂参数的解耦。根据标准桨叶动平衡和标准传递过程,确定标准桨叶需要测量和调整的静态特性参数和动态特性参数;针对标准桨叶挥舞运动对环境阵风引起的不平衡空气动力的挥舞响应,文中提出了桨叶动平衡试验环境中风速影响的分析方法,通过仿真试验和实际测量数据,得出了在桨叶挥舞参数误差要求范围内的风速极值,结果与法国相关的试验标准相吻合,进而确定了标准桨叶特性参数测量与调整过程的环境风速条件,奠定了准确恢复标准桨叶特性参数的基础。
本文采用激光测量技术来测量桨叶的挥舞参数。进一步研究了激光器安装定位参数的测量方法,利用激光器本身的结构和标定算法,实现了激光器定位参数的标定;利用一定厚度的模拟桨叶切割激光光路的方法标定标准桨叶挥舞参数测量系统,实现了标准桨叶挥舞参数测量系统的标定和溯源。最后,对标准桨叶挥舞参数测量系统和测量结果进行了不确定度分析。
对于标准桨叶铰链力矩的测量,文中设计了基于RBF神经网络的铰链力矩载荷识别和动态特性补偿方法,神经网络的结构避免了建立系统的结构模型,把扭矩载荷识别和标定的反问题都做为正问题处理。用同步采样的实际静态载荷和正弦扭矩载荷数据训练神经网络,并对训练结果进行了试验数据验证,实现了铰链力矩测量系统的动态标定,提高了标准桨叶铰链力矩的测量准确度。
本文针对某型号标准桨叶静态特性参数和动态特性参数进行了具体的试验测量,通过实测数据与法国出厂校准数据的比较,找出了标准桨叶特性参数变化的趋势,提出了标准桨叶特性参数整体调整恢复的方法,使标准桨叶特性参数恢复到出厂时的参数水平,保证了标准桨叶特性参数的延续性和长期稳定性。
The primary standard blade is the reference standard of natural parameters for work rotor blades on measurement and adjustment process, the transmission standard for batch productions, as well as the base of interchangeability for single rotor blade. The rotor blades are the important parts that determinate the flight quality of helicopters. Each piece of rotor blades must be measured and adjusted on a dynamic balance tester in order to make the parameters uniform as the primary standard blade before the final assembly. The three pieces of primary standard rotor blades in our country are made in France with the composite material, the natural parameters of one piece of standard blades have been changed, parameters in which disagree with the original data and other two standard blades. Once a standard rotor blade stops work, it will have a strong impact on the other types of helicopter rotor blades. The result is extremely serious if the other standard blade parameters are changed. The primary mission is to calibrate and adjust the standard rotor blade parameters, and recover its original parameters in order to keep the long-time stability and uniformity.
With the dynamic balance testing process, a method is proposed by deriving the flapping equation, expanding the flapping angle by the method of Taylor radix and building the nonlinear Duffing’s flapping equation with complex aerodynamics perturbation for the primary standard rotor blade. The stability of flapping equation with the action of aerodynamics, aerodynamic damping, double-period and triple-period aerodynamics perturbation are analyzed with Melnikov method. The result is that the rotor flapping is stable on flapping equation and sensitive on testing environment.
The flapping parameters are impacted by the natural parameters of standard rotor blade and other testing parameters. Using the method of changing the installation position on rotor hub, the testing parameters of standard rotor blades are obtained and the standard rotor blade parameters from hub parameters are uncoupled. The gust can influence the results of dynamic parameters for the primary standard rotor blade, an analysis method with wind speed in a dynamic balance testing environment is proposed for the flapping response by non-balance aerodynamics perturbation caused by gust, the extreme value of wind speed in the dynamic balance testing is determined by the emulator program and actual data, the result is the same as the French testing standard. The wind speed in the process of calibration is determined for primary standard rotor blade, and the base of parameters recovery process is settled.
With the measurement technique of laser, a method is proposed to measure the flapping parameters of primary standard rotor blades,and a further design of measurement method is applied in calibrating the spatial location parameters of laser. At the same time, a method is proposed to calibrate the flapping measurement system with a definite thickness simulator as blade and the measurement system is calibrated. Finally, the uncertainty of measurement system and flapping parameter are analyzed.
For the measurement of flapping hinge moment, a recognition method for load and compensation on a dynamic characteristic is proposed based on RBF neural network, this method avoids to build the mathematical model for the measurement system, and inverts the indirect problem of recognition process and calibration process into a direct problem. To train and check the networks with the synchronous sampling data of sine torque moment, the hinge moment measurement system is calibrated dynamically, and the measurement uncertainty is improved in flapping hinge moment for primary standard rotor blade.
For the actual data of static parameters and dynamic parameters of some primary standard rotor blade, a calibration and adjustment method is proposed by comparing the actual data with data from France. With the calibration and adjustment process, the parameters of primary standard rotor blades resume the initial state. This proposed method guarantees the long-time stability of natural parameters for the primary standard rotor blades.
引文
1 Sane S P, Dickinson M H. The Control of Flight Force by a Wing: Lift and Drag Production. Journal of Experimental Biology. 2001,204(19):2607-2626
2林为才,乔延风,孙宁.利用激光技术测量直升机旋翼共锥度系统.光学精密工程. 2005,13(11):52-55
3 Lind R. Flight-test Evaluation of Flutter Prediction Methods. Journal of Aircraft. 2003,40(5):964-970
4邵鹏飞.海豚系列直升机的发展特点.直升机技术. 1999,120(4):45-50
5李萍,庄开莲,李静.国外直升机翼型研究综述.直升机技术. 2007, 151(3):103-109
6 Lehmann F O. The Mechanisms of Lift Enhancementin Insect Flight. Naturwissenschaften. 2004,91:101–122
7 Ansari S A, Zbikowski R, Knowels K. Aerodynamics Modeling of Insect Like Flapping Flight for Micro Air Vehicles. Progress in Aerospace Science. 2006,42:129–172
8 Wilby P G. The Development of Rotor Airfoil Testing in the UK. Journal of the American Helicopter Society. 2001,46(3):210-220
9陈平剑.直升机旋翼气动设计中的几个问题.直升机技术. 2006, 147(3):60-64
10 Borglund D, Ringertz U. Efficient Computation of Robust Flutter Boundaries Using theμ-k Method. Journal of Aircraft. 2006,43(6):1763-1769
11 Baldelli D H, Lind R, Brenner M J. Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification. Journal of Guidance, Control and Dynamics. 2005,28(5):1056-1064
12秦超敏,程卫真,李万新.直升机运动参数试飞技术.飞行力学. 2004 ,22(2):65-68
13李岩,孟祥旺,许志广等.直升机旋翼挥舞、摆振的激光动态测试系统.光学技术.2001,27(3):214-216
14薛伟松,邢士喜,郑牧等.直升机旋翼锥体及动平衡设备校验系统的研究.测控技术. 2006,25(3):4-7
15 Sun. M, Xiong Y. Dynamic Flight Stability of a Hovering Bumblebee. Journal of Experimental Biology. 2005,208(3):447-459
16 Kyung Suna, Kirn Jihwan. Dynamic Analysis for the Deployment of a Multi- Link Flexible Structure Undergoing Locking. AIAA, A01-25215, 2001
17 Cao Yihua. Modeling the Unsteady Aerodynamic Forces of a Maneuvering Rotor.Aircraft. Engineering and Aerospace Technology. 2004,71(5):444-450
18 Anderson D. Modification of a Generalized Inverse Simulation Technique for Rotorcraft Flight. Journal of Aerospace Engineering. 2003,1:61-73
19 Hodges D H, Pierce G A. Introduction to Structural Dynamics and Aero- elasticity. Cambridge:Cambridge University Press. 2002
20 Houbolt J C, Brooks G W. Differential Equations of Motion for Combined Flapwise Bending, Chordwise Bending and Torsion of Twisted Nonuniform Rotor Blades. NACA Report,1346, 1958
21 Hodges D H, Dowell E H. Nonlinear Equation of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades. NASA, TND-7818, 1974
22 Fridmann P, Tong P. Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight. NASA, CR-114485, 1972
23 Fridmann P, Allende M R. Aeroelastic Stability of Coupled Flap lag Torsional Motion of Helicopter Rotor Blades in Forward Flight. AIAA, Paper77-455, San Diego, California,1977
24 Fridmann P. Influence of Modeling and Blade Parameters on the Aeroelastic Stability of a Cantilevered Rotor. AIAA,vol.15,No.2,Feb.1977
25程永明,任革学,郑兆昌.直升机旋翼/机身耦合系统的气弹响应分析(一)旋翼系统的建模.应用力学学报. 1999,3(1):33-38
26王浩文.复合材料板壳动力特性研究及直升机旋翼/机体耦合气弹稳定性分析.清华大学博士学位论文. 1998
27 Wang Haowen, Gao Zhen. Rotor Vibratory Load Prediction Based on Generalized Forces. Chinese Journal of Aeronautics. 2004,17(1):28-33
28 Wang Haowen, Gao Zheng, Zheng Zhaochang. Aero-Elastic Response and Stability of Helicopter Rotor Blades in Forward Flight. Journal of Vibration Engineering. 1999,12(4):521~528
29王浩文,高正,郑兆昌.直升机旋翼/机身耦合系统气动/机械稳定性分析.航空动力学报. 2001,16(1):59-62
30 Brown R E, Houston S S. Comparison of Induced Velocity Models for Helicopter Flight Mechanics. Journal of Aircraft. 2000,37(4):623-633
31 Rosen Aviv. Approximate Actuator Disk Model of a Rotor in Hover or Axial Flow Based on Vortex Modeling. Journal of AHS. 2004,49(1):66-79
32 Rosen Aviv.Approximate Actuator Disk Model of a Rotor in Hover or Axial Flow Based on Potential Flow Equations. Journal of AHS. 2004,49(1):80-92
33王适存.升力螺旋桨在桨盘上的诱导速度分布.力学学报.1964, 7(3):211-221
34 Bartlett F D, Flannelly W D. Modal Verification of Force Determination for Measuring Vibration Loads. Journal of the American Helicopter Society. 1979, 10-18
35 Chuiton, Frederic L. Actuator Disc Modeling for Helicopter Rotors. Aerospace Science and Technology. 2004,8:285-297
36张方,朱德懋.基于神经网络模型的动载荷识别.振动工程学报. 1997,10(2):156-161
37余忠烜,刘丙坤.直11型直升机旋翼系统动部件飞行载荷测试技术.直升机技术. 2006,4:47-50
38原正庭,王远明,马乐瑜等.直升机旋翼挥舞力矩飞行试验技术研究.飞行试验. 2002,18(4):19-21
39黄俊钦.几种传感器动态校准方法特点分析研究.测控技术. 2004, 23(12):5-7
40 de Almeida L A L L, Deep G S, Lima A M N. A Hysteretic Model for a anadium Dioxide transitionedge microbolometer. IEEE Trans Instrum Meas, 2001,50(4):1030- 1035
41 Huang Junqin. Dynamic Calibration Method for Ultra High Rressure Transducers. Proceedings of the IMEKO TC-16, International Symposium on Pressure and Vacuum. Beijing, 2003-05,22-24
42 Simani S, Fantuzzi C, Spina P R. Application of a Neural Network in Gas Turbine Control Sensor Fault Detection. IEEE International Conference on Control Application, Univerita di Ferrara, Ferrara Italy, September, 1998, 182-186
43田社平,赵阳,韦红雨等.基于BP神经网络的传感器非线性补偿测.试验技术学报. 2007,21(1):85-89
44侯立群,仝卫国,何同祥.基于RRF神经网络的传感器静态误差综合校正方力法.传感技术学报. 2004,12(4):643-645
45 Tian S P, Ding C Q, Yan D T. Nonlinear Dynamic Modeling of Sensors Based on Recurrent Neural Network. Chinese Journal of Test and Measurement Technology. 2004,18(2):99-103
46陈仁良,高正.基于ADS 33的直升机纵向操纵响应研究.南京航空航天大学学报. 2003,35(3):231-236
47程永明,任革学,郑兆昌.直升机旋翼/机身耦合系统的气弹响应分析(二)方程的求解.应用力学学报. 1999,6(12):33-36
48 Wang Haowen, Gao Zhen. A New Aeromechanical Stability Analysis Methodology for Coupled Rotor/Fuselage System of Helicopters. Transactions of Nanjing University of Aeronautics & Astronautics, 2001, 18(1):47-52
49 Yu W B, Hodges D H. Generalized Timoshenko Theory of the Variational Asymptotic Beam Sectional Analysis. Journal of the American Helicopter Society. 2005,50(1):46-55
50 Taylor G K, Thomas A L R. Dynamic Flight Stability in the Desert Locust Schistocerca Gregaria. Journal of Experimental Biology. 2003,206(16): 2803-2829
51王适存.直升机空气动力学.航空专业教材编审组. 1985, 37-49
52高正,陈仁良.直升机飞行动力学.北京:科学出版社. 2003, 24-43
53 Jones K D, Castro B M, Mahamoud O, et al. A Collobirative Numerical and Experimental Investigation of Flapping-Wing Propulsion. AIAA, 2002-0706, 2002
54陈仁良,高正.旋翼桨叶非定常挥舞运动的分析计算方法.空气动力学学报. 1997,15(3):406-413
55韩东,高正,王浩文等.直升机桨叶刚柔耦合特性及计算方法分析.航空动力学报. 2006,21(1):36-40
56王适存.直升机空气动力学中的几个疑点.南京航空航天大学学报. 2003,35(3):225-230
57 Neishtadt A I. Capturing into Resonance and Scattering on Resonances in Two-Frequency Systems. Proceedings of the Steklov Institute ofMathematics. 2005,250:183–203
58 Ju H, Park. Adaptive Synchronization of Rossler System with Uncertain Parameters, Chaos, Solitons and Fractals. 2005,25:333–338
59 Ju H, Park. Adaptive Synchronization of Hyperchaotic Chen System with Uncertain Parameters. Chaos, Solitons and Fractals. 2005,26:959–964
60郝柏林.从抛物线谈起-混沌动力学引论.上海:上海科技教育出版社,1993,1-10
61楼京俊,何其伟,朱石坚.多频激励软弹簧型Duffing系统中的混沌.应用数学和力学. 2004,25(12):1299-1304
62李芳,徐振源.具有异宿轨道Duffing方程的混沌控制.江南大学学报(自然科学版). 2005,4(5):460-464
63 Ge Z M, Chen C C. Phase Synchronization of Coupled Chaotic Multiple Time Scales systems, Chaos, Solitons and Fractals. 2004,20:639–647
64 Ott Edward. Chaos in Dynamical Systems(second edition). Cambridge University Press. 2002,6-20
65李士林,尹成群,尚秋峰等.基于图像识别理论的混沌特性判别方法.中国电机工程学报. 2003,23(10):47-50
66吕金虎,张锁春. Lyapunov指数的数值计算方法.非线性动力学学报. 2001, 1:81-92
67 Lim C W, Wu B S, A New Analytical Approach to the Duffing-Harmonic Oscillator. Physics Letters A. 2003,311:365–373
68刘曾荣.混沌研究中的解析方法.上海:上海大学出版社. 2002,20-70
69李继彬.混沌与Melnikov方法.重庆:重庆大学出版社. 1988,35-50
70李月,杨宝俊,李亚峻.微弱正弦信号检测模型混沌解的判定.地球物理学进展. 2002,17(4):711-714
71李亚峻,李月,卢金,吕宝林.微弱信号混沌检测系统混沌阈值的确定.吉林大学学报(信息科学版). 2004, 22(2):106-110
72 Xu Pengcheng, Jing Zhujun. Silnikov's Orbit in Coupled Duffing's Systems. Chaos, Solitons and Fractals. 2000,11:853-858
73 Ge Z M, Chen Y S. Synchronization of Unidirectional Coupled Chaotic Systems via Partial Stability. Chaos, Solitons and Fractals. 2004,21:101-111
74 Moukam Kakmeni F M, Bowong S, Tchawoua C, etal. Strange Attractors and Chaos Control in a Duffing–Van der Pol Oscillator with Two ExternalPeriodic Forces. Journal of Sound and Vibration. 2004,277:783–799
75 Budyansky M V, Uleysky M Y, Prants S V. Chaotic Scattering, Transport, and Fractals in a Simple Hydrodynamic Flow. Journal of Experimental and Theoretical Physics. 2004;99:1018–1027
76 Argonov V Y, Prants S V. Fractals and Chaotic Scattering of Atoms in the Field of a Standing Light Wave. Journal of Experimental and Theoretical Physics. 2003,96:832-845
77贾宝柱,任光.一类模糊切换多模型系统的分段Lyapunov稳定.大连海事大学学报. 2006,32(1):54-61
78张宾,李月,卢金. Lyapunov特性指数用于混沌判据.吉林大学学报(信息科学版). 2004,22(2):111-114
79李艳辉,马东海,秦洋.基于参数依赖型Lyapunov稳定条件的控制器设计.大庆石油学报. 2007,31(4):76-79
80苏卫卫,陈一鸣,张拥萍等.时变时滞神经网络系统时滞依赖的鲁棒稳定性准则.计算技术与自动化. 2007,26(2):1-6
81王岩,张庆灵,孙增折等.离散模糊系统分析与设计的模糊Lyapunov方法.自动化学报. 2004,30(2):255-260
82苏媛,曹义华.直升机动稳定性分析和增稳系统控制律设计.北京航空航天大学学报. 2002,28(6):636-639
83 Sun M, Tang J. Unsteady Aerodynamic Force Generation by a Model Fruit Fly Wing in Flapping Motion. Journal of Experimental Biology. 2002, 205(1):55-70
84朱世晋.直升机旋翼桨叶挥舞运动的稳定性.南京航室学院学报. 1985,19-30
85徐明,徐桂棋.海豚型旋翼桨叶气动弹性稳定性分析.南京航空学院学报. 1987,19(1):26-36
86 Wang Haowen, Gao Zheng. Rotor Vibratory Load Prediction Based on Generalized Forces. Chinese Journal of Aeronautics. 2004,17(1):28-33
87李月,杨宝俊.混沌振子检测引论.北京:电子工业出版社. 2004,49-75
88吴存利,马少娟,孙中奎等.随机参数Duffing系统中的随机混沌及其延迟反馈控制.物理学报. 2006,55(12):6253-6259
89沈亨业,樊光华.浅析我国直升机旋翼技术发展问题.直升机技术. 1998, 113(1):46-51
90孙如林.美国直升机先进旋翼技术发展和现状.直升机技术. 1995, 102(2):43-48
91艾剑波,邓景辉,樊光华等.旋翼改进研制中的动力学匹配分析.直升机技术. 2006,148(4):5-9
92 Friedrich K, Donald S, Merkley J. Design of a Smart Material Actuator for Rotor Control. Smart Materials and Structures. 1997,6(3):223-234
93胡国才.失衡旋翼的直升机自激振动分析模型.航空学报. 2006, 27(4):630-634
94苏媛,康丽霞,衰坤刚等.风切变场中直升机的稳定性和操纵性研究.航空计算技术. 2006,36(2):86-89
95 Cao Yihua, Chen Yong, Yuan Kungang. Nonlinear Inverse Dynamics Control of the Aircraft in the Presence of Windshear. Aircraft Engineering and Aerospace Technology. 2004, 76(6):592-599
96赵维义,傅百先,丁文勇等.低空风切变中直升机纵向运动特性分析.飞行力学. 2003,20(1):25-28
97孙磊.机场附近低空风切变的数值模拟预测.中山大学学报(自然科学版). 2003,42(2):150-153
98金长江,张洪,朱仁标等.低空风切变危险尺度研究.航空学报. 1992, 13(10):481-486
99刘美素,孟祥莉.近地面层风切变特征分析.内蒙古气象. 2006,4:23-25
100 Houbold J C. Atmospheric Turbulence. AIAA, April,1973
101张翼,许心钰.直升机对风切变的响应.南京航空学院学报. 1991, 23(4):37-44
102黄俊钦.静动态数学模型的实用建模方法.北京:机械工业出版社. 1988,55-90
103唐秀近.动态力识别的时域方法.大连工学院学报. 1987,26(4):21-27
104 Cook A B, Fuller C R, Brien W F. Artificial Networks in Detection for Predicting Nonlinear Dynamic Helicopter Loads. AIAA Journal. 1994, 32(5):2337-2344
105熊盛武,李元香.演化参数反演方法.武汉大学学报. 2001,47(1):38-41
106张方,朱德懋,张福祥.动载荷识别的时间有限元模型理论及其应用.振动与冲击. 1998,17(2):1-4
107徐志英,廖旭晖.动态载荷识别及其进展.常州工学院学报. 2006,19(4):13-17
108 Nagal K. Fourier Domain Reconstruction of Ultrasonic 2-D and 3-D Images Using Exact Inverse Scattering Solution .IEEE Ultrasonics Symposium. 1985, 21:804-807
109 Tao L, Ma X R, Huang W H. Time-Space Domain Incident Angle Compensation for Ray Inversion in an Inhomo-Geneous Medium .J Acoust Soc Am. 1995, 97 :410-413
110 Kishor N, Saini R P, Singh S P. Small Hydro Power Plant Identification Using NNARX Structure. Neural Computing and Applications. 2005,14: 212-222
111尚钢,吴代华.基于神经网络对扁壳结构载荷位置识别问题的研究.固体力学学报. 2001,22(1):61-63
112高保成,刘红霞,杨叔子.神经网络用于结构动荷载识别的研究.郑州工学院学报. 1996,17(2):91-94
113 Kum Patis, Kannan Parthasarathy. Identification and Control of Dynamieal Systems Using Neural Networks. IEEE Transaction on Neural Networks. 1990,1(1):4-27
114 Musielak D E, Musielak Z E, Benner J W. Chaos and Routes to Chaos in Coupled Duffing Oscillators with Multiple Degrees of Freedom. Chaos, Solitons Fract. 2005,4:907-922
115 Kohonen, Teuvo, Kaski. Self-Organization of a Massive Document Collection. IEEE Transactions on Neural Network. 2000,11(3):574-585
116王雪萍,林康红.一种利用RBF神经网络的传感器建模新方法.新疆大学学报. 2002,19(3):368-371
117 Moody J, Darken C. Learning with Localized Receptive Fields In Proceedings Connectionist Models. Carnegie Mellon University, Morgan Kaufmann Publishers. 1988:133-143
118高亚东,张曾倡,余建航.旋翼变距拉杆关节轴承磨损故障特征及磨损程度识别.南京航空航天大学学报. 2006,38(1):7-10
2林为才,乔延风,孙宁.利用激光技术测量直升机旋翼共锥度系统.光学精密工程. 2005,13(11):52-55
3 Lind R. Flight-test Evaluation of Flutter Prediction Methods. Journal of Aircraft. 2003,40(5):964-970
4邵鹏飞.海豚系列直升机的发展特点.直升机技术. 1999,120(4):45-50
5李萍,庄开莲,李静.国外直升机翼型研究综述.直升机技术. 2007, 151(3):103-109
6 Lehmann F O. The Mechanisms of Lift Enhancementin Insect Flight. Naturwissenschaften. 2004,91:101–122
7 Ansari S A, Zbikowski R, Knowels K. Aerodynamics Modeling of Insect Like Flapping Flight for Micro Air Vehicles. Progress in Aerospace Science. 2006,42:129–172
8 Wilby P G. The Development of Rotor Airfoil Testing in the UK. Journal of the American Helicopter Society. 2001,46(3):210-220
9陈平剑.直升机旋翼气动设计中的几个问题.直升机技术. 2006, 147(3):60-64
10 Borglund D, Ringertz U. Efficient Computation of Robust Flutter Boundaries Using theμ-k Method. Journal of Aircraft. 2006,43(6):1763-1769
11 Baldelli D H, Lind R, Brenner M J. Nonlinear Aeroelastic/Aeroservoelastic Modeling by Block-Oriented Identification. Journal of Guidance, Control and Dynamics. 2005,28(5):1056-1064
12秦超敏,程卫真,李万新.直升机运动参数试飞技术.飞行力学. 2004 ,22(2):65-68
13李岩,孟祥旺,许志广等.直升机旋翼挥舞、摆振的激光动态测试系统.光学技术.2001,27(3):214-216
14薛伟松,邢士喜,郑牧等.直升机旋翼锥体及动平衡设备校验系统的研究.测控技术. 2006,25(3):4-7
15 Sun. M, Xiong Y. Dynamic Flight Stability of a Hovering Bumblebee. Journal of Experimental Biology. 2005,208(3):447-459
16 Kyung Suna, Kirn Jihwan. Dynamic Analysis for the Deployment of a Multi- Link Flexible Structure Undergoing Locking. AIAA, A01-25215, 2001
17 Cao Yihua. Modeling the Unsteady Aerodynamic Forces of a Maneuvering Rotor.Aircraft. Engineering and Aerospace Technology. 2004,71(5):444-450
18 Anderson D. Modification of a Generalized Inverse Simulation Technique for Rotorcraft Flight. Journal of Aerospace Engineering. 2003,1:61-73
19 Hodges D H, Pierce G A. Introduction to Structural Dynamics and Aero- elasticity. Cambridge:Cambridge University Press. 2002
20 Houbolt J C, Brooks G W. Differential Equations of Motion for Combined Flapwise Bending, Chordwise Bending and Torsion of Twisted Nonuniform Rotor Blades. NACA Report,1346, 1958
21 Hodges D H, Dowell E H. Nonlinear Equation of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades. NASA, TND-7818, 1974
22 Fridmann P, Tong P. Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight. NASA, CR-114485, 1972
23 Fridmann P, Allende M R. Aeroelastic Stability of Coupled Flap lag Torsional Motion of Helicopter Rotor Blades in Forward Flight. AIAA, Paper77-455, San Diego, California,1977
24 Fridmann P. Influence of Modeling and Blade Parameters on the Aeroelastic Stability of a Cantilevered Rotor. AIAA,vol.15,No.2,Feb.1977
25程永明,任革学,郑兆昌.直升机旋翼/机身耦合系统的气弹响应分析(一)旋翼系统的建模.应用力学学报. 1999,3(1):33-38
26王浩文.复合材料板壳动力特性研究及直升机旋翼/机体耦合气弹稳定性分析.清华大学博士学位论文. 1998
27 Wang Haowen, Gao Zhen. Rotor Vibratory Load Prediction Based on Generalized Forces. Chinese Journal of Aeronautics. 2004,17(1):28-33
28 Wang Haowen, Gao Zheng, Zheng Zhaochang. Aero-Elastic Response and Stability of Helicopter Rotor Blades in Forward Flight. Journal of Vibration Engineering. 1999,12(4):521~528
29王浩文,高正,郑兆昌.直升机旋翼/机身耦合系统气动/机械稳定性分析.航空动力学报. 2001,16(1):59-62
30 Brown R E, Houston S S. Comparison of Induced Velocity Models for Helicopter Flight Mechanics. Journal of Aircraft. 2000,37(4):623-633
31 Rosen Aviv. Approximate Actuator Disk Model of a Rotor in Hover or Axial Flow Based on Vortex Modeling. Journal of AHS. 2004,49(1):66-79
32 Rosen Aviv.Approximate Actuator Disk Model of a Rotor in Hover or Axial Flow Based on Potential Flow Equations. Journal of AHS. 2004,49(1):80-92
33王适存.升力螺旋桨在桨盘上的诱导速度分布.力学学报.1964, 7(3):211-221
34 Bartlett F D, Flannelly W D. Modal Verification of Force Determination for Measuring Vibration Loads. Journal of the American Helicopter Society. 1979, 10-18
35 Chuiton, Frederic L. Actuator Disc Modeling for Helicopter Rotors. Aerospace Science and Technology. 2004,8:285-297
36张方,朱德懋.基于神经网络模型的动载荷识别.振动工程学报. 1997,10(2):156-161
37余忠烜,刘丙坤.直11型直升机旋翼系统动部件飞行载荷测试技术.直升机技术. 2006,4:47-50
38原正庭,王远明,马乐瑜等.直升机旋翼挥舞力矩飞行试验技术研究.飞行试验. 2002,18(4):19-21
39黄俊钦.几种传感器动态校准方法特点分析研究.测控技术. 2004, 23(12):5-7
40 de Almeida L A L L, Deep G S, Lima A M N. A Hysteretic Model for a anadium Dioxide transitionedge microbolometer. IEEE Trans Instrum Meas, 2001,50(4):1030- 1035
41 Huang Junqin. Dynamic Calibration Method for Ultra High Rressure Transducers. Proceedings of the IMEKO TC-16, International Symposium on Pressure and Vacuum. Beijing, 2003-05,22-24
42 Simani S, Fantuzzi C, Spina P R. Application of a Neural Network in Gas Turbine Control Sensor Fault Detection. IEEE International Conference on Control Application, Univerita di Ferrara, Ferrara Italy, September, 1998, 182-186
43田社平,赵阳,韦红雨等.基于BP神经网络的传感器非线性补偿测.试验技术学报. 2007,21(1):85-89
44侯立群,仝卫国,何同祥.基于RRF神经网络的传感器静态误差综合校正方力法.传感技术学报. 2004,12(4):643-645
45 Tian S P, Ding C Q, Yan D T. Nonlinear Dynamic Modeling of Sensors Based on Recurrent Neural Network. Chinese Journal of Test and Measurement Technology. 2004,18(2):99-103
46陈仁良,高正.基于ADS 33的直升机纵向操纵响应研究.南京航空航天大学学报. 2003,35(3):231-236
47程永明,任革学,郑兆昌.直升机旋翼/机身耦合系统的气弹响应分析(二)方程的求解.应用力学学报. 1999,6(12):33-36
48 Wang Haowen, Gao Zhen. A New Aeromechanical Stability Analysis Methodology for Coupled Rotor/Fuselage System of Helicopters. Transactions of Nanjing University of Aeronautics & Astronautics, 2001, 18(1):47-52
49 Yu W B, Hodges D H. Generalized Timoshenko Theory of the Variational Asymptotic Beam Sectional Analysis. Journal of the American Helicopter Society. 2005,50(1):46-55
50 Taylor G K, Thomas A L R. Dynamic Flight Stability in the Desert Locust Schistocerca Gregaria. Journal of Experimental Biology. 2003,206(16): 2803-2829
51王适存.直升机空气动力学.航空专业教材编审组. 1985, 37-49
52高正,陈仁良.直升机飞行动力学.北京:科学出版社. 2003, 24-43
53 Jones K D, Castro B M, Mahamoud O, et al. A Collobirative Numerical and Experimental Investigation of Flapping-Wing Propulsion. AIAA, 2002-0706, 2002
54陈仁良,高正.旋翼桨叶非定常挥舞运动的分析计算方法.空气动力学学报. 1997,15(3):406-413
55韩东,高正,王浩文等.直升机桨叶刚柔耦合特性及计算方法分析.航空动力学报. 2006,21(1):36-40
56王适存.直升机空气动力学中的几个疑点.南京航空航天大学学报. 2003,35(3):225-230
57 Neishtadt A I. Capturing into Resonance and Scattering on Resonances in Two-Frequency Systems. Proceedings of the Steklov Institute ofMathematics. 2005,250:183–203
58 Ju H, Park. Adaptive Synchronization of Rossler System with Uncertain Parameters, Chaos, Solitons and Fractals. 2005,25:333–338
59 Ju H, Park. Adaptive Synchronization of Hyperchaotic Chen System with Uncertain Parameters. Chaos, Solitons and Fractals. 2005,26:959–964
60郝柏林.从抛物线谈起-混沌动力学引论.上海:上海科技教育出版社,1993,1-10
61楼京俊,何其伟,朱石坚.多频激励软弹簧型Duffing系统中的混沌.应用数学和力学. 2004,25(12):1299-1304
62李芳,徐振源.具有异宿轨道Duffing方程的混沌控制.江南大学学报(自然科学版). 2005,4(5):460-464
63 Ge Z M, Chen C C. Phase Synchronization of Coupled Chaotic Multiple Time Scales systems, Chaos, Solitons and Fractals. 2004,20:639–647
64 Ott Edward. Chaos in Dynamical Systems(second edition). Cambridge University Press. 2002,6-20
65李士林,尹成群,尚秋峰等.基于图像识别理论的混沌特性判别方法.中国电机工程学报. 2003,23(10):47-50
66吕金虎,张锁春. Lyapunov指数的数值计算方法.非线性动力学学报. 2001, 1:81-92
67 Lim C W, Wu B S, A New Analytical Approach to the Duffing-Harmonic Oscillator. Physics Letters A. 2003,311:365–373
68刘曾荣.混沌研究中的解析方法.上海:上海大学出版社. 2002,20-70
69李继彬.混沌与Melnikov方法.重庆:重庆大学出版社. 1988,35-50
70李月,杨宝俊,李亚峻.微弱正弦信号检测模型混沌解的判定.地球物理学进展. 2002,17(4):711-714
71李亚峻,李月,卢金,吕宝林.微弱信号混沌检测系统混沌阈值的确定.吉林大学学报(信息科学版). 2004, 22(2):106-110
72 Xu Pengcheng, Jing Zhujun. Silnikov's Orbit in Coupled Duffing's Systems. Chaos, Solitons and Fractals. 2000,11:853-858
73 Ge Z M, Chen Y S. Synchronization of Unidirectional Coupled Chaotic Systems via Partial Stability. Chaos, Solitons and Fractals. 2004,21:101-111
74 Moukam Kakmeni F M, Bowong S, Tchawoua C, etal. Strange Attractors and Chaos Control in a Duffing–Van der Pol Oscillator with Two ExternalPeriodic Forces. Journal of Sound and Vibration. 2004,277:783–799
75 Budyansky M V, Uleysky M Y, Prants S V. Chaotic Scattering, Transport, and Fractals in a Simple Hydrodynamic Flow. Journal of Experimental and Theoretical Physics. 2004;99:1018–1027
76 Argonov V Y, Prants S V. Fractals and Chaotic Scattering of Atoms in the Field of a Standing Light Wave. Journal of Experimental and Theoretical Physics. 2003,96:832-845
77贾宝柱,任光.一类模糊切换多模型系统的分段Lyapunov稳定.大连海事大学学报. 2006,32(1):54-61
78张宾,李月,卢金. Lyapunov特性指数用于混沌判据.吉林大学学报(信息科学版). 2004,22(2):111-114
79李艳辉,马东海,秦洋.基于参数依赖型Lyapunov稳定条件的控制器设计.大庆石油学报. 2007,31(4):76-79
80苏卫卫,陈一鸣,张拥萍等.时变时滞神经网络系统时滞依赖的鲁棒稳定性准则.计算技术与自动化. 2007,26(2):1-6
81王岩,张庆灵,孙增折等.离散模糊系统分析与设计的模糊Lyapunov方法.自动化学报. 2004,30(2):255-260
82苏媛,曹义华.直升机动稳定性分析和增稳系统控制律设计.北京航空航天大学学报. 2002,28(6):636-639
83 Sun M, Tang J. Unsteady Aerodynamic Force Generation by a Model Fruit Fly Wing in Flapping Motion. Journal of Experimental Biology. 2002, 205(1):55-70
84朱世晋.直升机旋翼桨叶挥舞运动的稳定性.南京航室学院学报. 1985,19-30
85徐明,徐桂棋.海豚型旋翼桨叶气动弹性稳定性分析.南京航空学院学报. 1987,19(1):26-36
86 Wang Haowen, Gao Zheng. Rotor Vibratory Load Prediction Based on Generalized Forces. Chinese Journal of Aeronautics. 2004,17(1):28-33
87李月,杨宝俊.混沌振子检测引论.北京:电子工业出版社. 2004,49-75
88吴存利,马少娟,孙中奎等.随机参数Duffing系统中的随机混沌及其延迟反馈控制.物理学报. 2006,55(12):6253-6259
89沈亨业,樊光华.浅析我国直升机旋翼技术发展问题.直升机技术. 1998, 113(1):46-51
90孙如林.美国直升机先进旋翼技术发展和现状.直升机技术. 1995, 102(2):43-48
91艾剑波,邓景辉,樊光华等.旋翼改进研制中的动力学匹配分析.直升机技术. 2006,148(4):5-9
92 Friedrich K, Donald S, Merkley J. Design of a Smart Material Actuator for Rotor Control. Smart Materials and Structures. 1997,6(3):223-234
93胡国才.失衡旋翼的直升机自激振动分析模型.航空学报. 2006, 27(4):630-634
94苏媛,康丽霞,衰坤刚等.风切变场中直升机的稳定性和操纵性研究.航空计算技术. 2006,36(2):86-89
95 Cao Yihua, Chen Yong, Yuan Kungang. Nonlinear Inverse Dynamics Control of the Aircraft in the Presence of Windshear. Aircraft Engineering and Aerospace Technology. 2004, 76(6):592-599
96赵维义,傅百先,丁文勇等.低空风切变中直升机纵向运动特性分析.飞行力学. 2003,20(1):25-28
97孙磊.机场附近低空风切变的数值模拟预测.中山大学学报(自然科学版). 2003,42(2):150-153
98金长江,张洪,朱仁标等.低空风切变危险尺度研究.航空学报. 1992, 13(10):481-486
99刘美素,孟祥莉.近地面层风切变特征分析.内蒙古气象. 2006,4:23-25
100 Houbold J C. Atmospheric Turbulence. AIAA, April,1973
101张翼,许心钰.直升机对风切变的响应.南京航空学院学报. 1991, 23(4):37-44
102黄俊钦.静动态数学模型的实用建模方法.北京:机械工业出版社. 1988,55-90
103唐秀近.动态力识别的时域方法.大连工学院学报. 1987,26(4):21-27
104 Cook A B, Fuller C R, Brien W F. Artificial Networks in Detection for Predicting Nonlinear Dynamic Helicopter Loads. AIAA Journal. 1994, 32(5):2337-2344
105熊盛武,李元香.演化参数反演方法.武汉大学学报. 2001,47(1):38-41
106张方,朱德懋,张福祥.动载荷识别的时间有限元模型理论及其应用.振动与冲击. 1998,17(2):1-4
107徐志英,廖旭晖.动态载荷识别及其进展.常州工学院学报. 2006,19(4):13-17
108 Nagal K. Fourier Domain Reconstruction of Ultrasonic 2-D and 3-D Images Using Exact Inverse Scattering Solution .IEEE Ultrasonics Symposium. 1985, 21:804-807
109 Tao L, Ma X R, Huang W H. Time-Space Domain Incident Angle Compensation for Ray Inversion in an Inhomo-Geneous Medium .J Acoust Soc Am. 1995, 97 :410-413
110 Kishor N, Saini R P, Singh S P. Small Hydro Power Plant Identification Using NNARX Structure. Neural Computing and Applications. 2005,14: 212-222
111尚钢,吴代华.基于神经网络对扁壳结构载荷位置识别问题的研究.固体力学学报. 2001,22(1):61-63
112高保成,刘红霞,杨叔子.神经网络用于结构动荷载识别的研究.郑州工学院学报. 1996,17(2):91-94
113 Kum Patis, Kannan Parthasarathy. Identification and Control of Dynamieal Systems Using Neural Networks. IEEE Transaction on Neural Networks. 1990,1(1):4-27
114 Musielak D E, Musielak Z E, Benner J W. Chaos and Routes to Chaos in Coupled Duffing Oscillators with Multiple Degrees of Freedom. Chaos, Solitons Fract. 2005,4:907-922
115 Kohonen, Teuvo, Kaski. Self-Organization of a Massive Document Collection. IEEE Transactions on Neural Network. 2000,11(3):574-585
116王雪萍,林康红.一种利用RBF神经网络的传感器建模新方法.新疆大学学报. 2002,19(3):368-371
117 Moody J, Darken C. Learning with Localized Receptive Fields In Proceedings Connectionist Models. Carnegie Mellon University, Morgan Kaufmann Publishers. 1988:133-143
118高亚东,张曾倡,余建航.旋翼变距拉杆关节轴承磨损故障特征及磨损程度识别.南京航空航天大学学报. 2006,38(1):7-10