Control of chaotic oscillation for helicopter rotor blade
-
摘要: 在直升机旋翼桨叶动平衡试验中,桨叶挥舞模型可表述为带周期激扰的Duffing型振动方程.对控制桨叶挥舞的混沌振动问题,提出了用改变Duffing模型激扰项的方法来抑制系统的混沌振动状态.在Duffing模型中耦合3倍周期的振动激扰,用解析的Melnikov方法分别分析了Duffing模型在单倍周期激扰信号、3倍周期激扰信号或者在两种激扰信号共同作用下振动方程的混沌阈值区间,并根据不同的激扰信号对桨叶挥舞振动模型进行了仿真试验.结果证明在引入3倍周期的耦合激扰项后,系统混沌振动的区间范围大大减小了.Abstract: The flapping model of rotor blade can be expressed as the model of Duffing′ oscillator with periodic exciting force in the dynamic balance test of helicopter rotor. To control the chaotic vibration in flapping, a method of changing exciting signals in Duffing′ model was proposed to restrain the chaos state in Duffing′ system. To couple a triple-period exciting signal in Duffing′ model, with the analytic method of Melnikov′ function based on chaos analysis, the chaos threshold of Duffing′ function were analyzed in the states of periodic exciting signal only, triple-period exciting signal only or combined action of the two signals respectively. Simulation experiments were also conducted according to the three kinds of exciting signals. The results indicate that the chaos range is reduced more evidently by coupling the triple-period exciting signal than that by period exciting signal only.
-
Key words:
- rotor blade /
- dynamic balance test /
- chaos threshold /
- chaos control
-
[1] Feigenbaum M J.Quantitative universality for a class of nonlinear transformations[J].Journal of Statistical Physics,1978,19(1):25-52 [2] Li T Y, Yorke J A. Period three implies chaos[J]. American Mathematical Monthly,1975,82:985-992 [3] 闵富红,徐振源,须文波.利用x|x|控制混沌系统[J].物理学报,2003,52(6):1360-1364 Min Fuhong, Xu Zhenyuan, Xu Wenbo. Controlling chaos via x|x|[J]. Acta Physica Sinica, 2003,52(6):1360-1364(in Chinese) [4] Ott E, Grebogi C, Yorke J.A. Controlling chaos[J]. Physical Review Letter, 1990,64(11):1196-1199 [5] Hunt E R. Stabilizing high-periodic orbits in a chaotic system:the diode resonator[J].Physical Review Letter,1991,67(15):1953-1955 [6] 王兴元.复杂非线性系统中的混沌[M].北京:电子工业出版社,2003:106-108 Wang Xingyuan. Chaos in complex nonlinear system[M]. Beijing:Publishing House of Electronics Industry,2003:106-108(in Chinese) [7] 薛海峰,向锦武,张晓谷.直升机旋翼动力传动系统模型及耦合影响[J].北京航空航天大学学报,2004,30(5):438-443 Xue Haifeng, Xiang Jinwu, Zhang Xiaogu. Coupled helicopter rotor/propulsion/transmission system torsional vibration analytical model and coupled influence investigation[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(5):438-443(in Chinese) [8] Chen R T N. Effect of primary rotor of parameters on flapping dynamics . NASA-TP-1431,1979 [9] Tyler J C, Leishame J G.Analysis of pitch and plunge effects on unsteady airfoil behavior[J]. Journal of American Helicopter Society,1992,37(4):4-15 [10] 陈仁良,高正.旋翼桨叶非定常挥舞运动的分析计算方法[J].空气动力学学报,1997,15(3):407-413 Chen Renliang, Gao Zheng. A method of analysis and calculation about unsteady flapping motion of rotor blade[J]. Acta Aerodynamic Sinica, 1997,15(3):407-413(in Chinese) [11] Du Zhengdong, Zhang Weinian. Melnikov method for homoclinic bifurcation in nonlinear impact oscillators[J]. Computers and Mathematics with Applications,2005,50(3):445-458 [12] 李亚峻,李月,卢金,等.微弱信号混沌检测系统混沌阈值的确定[J].吉林大学学报(信息科学版),2004,22(2):106-110 Li Yajun, Li Yue, Lu Jin, et al.Determination of chaotic threshold for chaos-based weak signal detection system[J]. Journal of Jilin University(Information Science Edition), 2004,22(2):106-110(in Chinese)
点击查看大图
计量
- 文章访问数: 2792
- HTML全文浏览量: 202
- PDF下载量: 1037
- 被引次数: 0