准零刚度隔振系统吸引子迁移控制研究
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摘要
以准零刚度隔振系统为对象,建立动力学模型,画出分岔图研究吸引子共存现象,并利用点映射方法分析共存吸引子的吸引域。在共存吸引子的吸引域之间建立一条目标轨道,分别采用开环、闭环和开环加闭环控制方法使系统迁移至目标轨道,实现系统吸引子迁移控制。同时,对开环加闭环控制方法的稳定性和可行性进行了分析。仿真结果表明:该系统同时存在两个稳定的不同振幅的周期1吸引子,开环和闭环控制方法难以使系统迁移至目标轨道,无法实现吸引子迁移控制;开环加闭环控制可使系统沿着目标轨道在两个周期1吸引子的吸引域之间进行迁移,当其运行在较大振幅的周期1吸引子上时,可控制系统迁移至较小振幅的周期1吸引子上,从而实现减振降噪。该方法为提高非线性隔振系统的隔振效果提供了新的思路。
The dynamic model for a vibration isolation system with quasi zero stiffness was established. The phenomenon of attractor coexistence was studied by drawing a bifurcation diagram,and the corresponding attraction domains were also analysed. A target orbit was established between the coexisting attractors,and the open loop control,closed loop control,open plus closed loop control were adopted to migrate the system to the target orbit respectively,in order to achieve the attractor migration control. The stability and feasibility of the open plus closed loop control method was investigated. The simulation results show that: the system has two stable periodic 1 attractors with different amplitudes. The open loop control method and closed loop control method are difficult to migrate the system to the target orbit,while the open plus closed loop control can make the system migrate between the attractions of two periodic 1 attractors along the target orbit,so,the system can be migrated to the periodic 1 attractor with small amplitude when it operates on the periodic 1 attractor with large amplitude,and thus achieves the vibration and noise reduction. The method provides a new way to improve the vibration isolation effect of nonlinear vibration isolation systems.
The dynamic model for a vibration isolation system with quasi zero stiffness was established. The phenomenon of attractor coexistence was studied by drawing a bifurcation diagram,and the corresponding attraction domains were also analysed. A target orbit was established between the coexisting attractors,and the open loop control,closed loop control,open plus closed loop control were adopted to migrate the system to the target orbit respectively,in order to achieve the attractor migration control. The stability and feasibility of the open plus closed loop control method was investigated. The simulation results show that: the system has two stable periodic 1 attractors with different amplitudes. The open loop control method and closed loop control method are difficult to migrate the system to the target orbit,while the open plus closed loop control can make the system migrate between the attractions of two periodic 1 attractors along the target orbit,so,the system can be migrated to the periodic 1 attractor with small amplitude when it operates on the periodic 1 attractor with large amplitude,and thus achieves the vibration and noise reduction. The method provides a new way to improve the vibration isolation effect of nonlinear vibration isolation systems.
引文
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[14]王杰,田沛,陈陈.连续多项式混沌系统的全局控制[J].控制与决策,2000,15(3):309-313.WANG Jie, TIAN Pei, CHEN Chen. Global control of continuous polynomial chaotic systems[J]. Journal of Control and Decision,2000,15(3):309-313.
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[2]朱石坚,楼京俊,何其伟,等.振动理论与隔振技术[M].北京:国防工业出版社,2006.
[3]孟令帅,孙景工,牛福,等.新型准零刚度隔振系统的设计与研究[J].振动与冲击,2014,33(11):195-199.MENG Lingshuai,SUN Jinggong,NIU Fu,et al. Design and analysis of a novel quasi-zero stiffness vibration isolation system[J]. Journal of Vibration and Shock,2014,33(11):195-199.
[4]王毅,徐道临,周加喜.滚球型准零刚度隔振器的特性分析[J].振动与冲击,2015,34(4):142-147.WANG Yi,XU Daolin,ZHOU Jiaxi. Characteristic analysis of a ball-type vibration isolator with quasi-zero-stiffness[J].Journal of Vibration and Shock,2015,34(4):142-147.
[5]刘兴天,孙靖雅,肖锋,等.准零刚度微振动隔振器的原理和性能研究[J].振动与冲击,2013,32(21):69-73.LIU Xingtian,SUN Jingya,XIAO Feng,et al. Principle and performance of a quasi-zero stiffness isolator for microvibration isolation[J]. Journal of Vibration and Shock,2013,32(21):69-73.
[6]周加喜,王心龙,徐道临,等.含凸轮-滚轮机构的准零刚度系统隔振特性实验研究[J].振动工程学报,2015,28(3):449-455.ZHOU Jiaxi, WANG Xinlong, XU Daolin, et al.Experimental study on vibration isolation characteristics of the quasi-zero stiffness isolator with cam-roller mechanism[J].Journal of Vibration Engineering,2015,28(3):449-455.
[7] JACKSON E A. The entrainment and migration control of multiple attractor systems[J]. Phys Lett A,1990,151:478-484.
[8] METTIN R,HUBLER A,SCHEELINE A,et al. Parametric entrainment control of chaotic systems[J]. Phys Rev E,1995,51:4065-4075.
[9] JACKSON E A,GROSU I. An open plus closed loop control of complex dynamic system[J]. Phys D,1995,85(1):1-9.
[10] CHEN L Q. An open plus closed loop control for discrete chaos and hyperchaos[J]. Physics Letters A,2001,281(5/6):327-333.
[11] CHEN L Q,LIU Y Z. An open plus closed loop control approach to synchronization of chaotic and hyper-chaotic maps[J]. Intenational Journal of Bifurca-tion and Chaos,2002,12(5):1219-1225.
[12] CHEN L Q. The parametric open plus closed loop control of chaotic maps and its robustness[J]. Chaos,Solutions and Fractals,2004,21:113-118.
[13]沈建和,陈树辉.混沌Mathieu-Duffing振子的开闭环控制[J].应用数学和力学,2009,30(1):21-29.SHEN Jianhe,CHEN Shuhui. The open loop plus closed loop control of chaotic mathieu-duffing oscillator[J]. Journal of Applied Mathematics and Mechanics,2009,30(1):21-29.
[14]王杰,田沛,陈陈.连续多项式混沌系统的全局控制[J].控制与决策,2000,15(3):309-313.WANG Jie, TIAN Pei, CHEN Chen. Global control of continuous polynomial chaotic systems[J]. Journal of Control and Decision,2000,15(3):309-313.
[15] CHEN L Q. An open plus nonlinear closed loop control of chaotic oscillators[J]. Chinese Physics,2002,11(9):900-904.
[16] CARRELLA A,BRENMAN M J,WATERS T P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic[J]. Journal of Sound and Vibration,2007,301(3/4/5):678-689.
[17]杨庆超,楼京俊,朱石坚,等.准零刚度系统力传递率特性及实验研究[J].海军工程大学学报,2014,26(3):19-23.YANG Qingchao, LOU Jingjun, ZHU Shijian, et al.Experimental study on force transmissibility of quasi zero stiffness system[J]. Journal of Naval University of Engineering,2014,26(3):19-23.