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一类三次微分系统的Hopf分支及其闭轨分支
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作者 杨德全 《松辽学刊(自然科学版)》 1998年第4期23-26,共4页
本文首先运用Hopf分支理论 ,论证了三次 微分系统 (1 ) ;对充分小的 μ >0 ,在奇点0 (0 ,0 )附近至少存在一个稳定的极限环 然后运用闭轨分支出极限环理论 ,论证了三次微分系统 (2 ) ;对充分小的|μ| ,在闭曲线x2 +x42 +y2 =740 -... 本文首先运用Hopf分支理论 ,论证了三次 微分系统 (1 ) ;对充分小的 μ >0 ,在奇点0 (0 ,0 )附近至少存在一个稳定的极限环 然后运用闭轨分支出极限环理论 ,论证了三次微分系统 (2 ) ;对充分小的|μ| ,在闭曲线x2 +x42 +y2 =740 - 1 01 0 附近存在唯一极限环 μ>0是稳定环 ;μ<0是不稳定环 同理论证了三次微分系统 (3) 对充分小的|μ| ,分别在闭曲线x2+x42 +y2 =1 31 - 2 76130 0 和x2 +x42 +y2 =1 31 +2 76130 0 附近存在复合极限环г0 和г1 μ >0 ,г0 是稳定环 ;μ<0 ,г0 是不稳定环 而 μ>0 ,г1 是不稳定环 ;μ<0 ,г1 展开更多
关键词 三次微分系统 HOPF分支 极限 闭轨分支 复合极限环
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Theoretical and Experimental Studies of Active Vibration Control for Beams Using Pole Placement Method 被引量:1
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作者 YANG Shaoxuan HU Yu SONG Zhiguang 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2022年第1期36-46,共11页
The vibration control in the frequency domain is significant.Therefore,an active vibration control in frequency domain is studied in this paper.It is generally known that piezo-intelligent structures possess satisfact... The vibration control in the frequency domain is significant.Therefore,an active vibration control in frequency domain is studied in this paper.It is generally known that piezo-intelligent structures possess satisfactory performances in the area of vibration control,and macro-fiber composites(MFCs)with high sensitivity and deformability are widely applied in engineering.So,this paper uses the MFC patches and designs a control method based on the pole placement method,and the natural frequency of the beam can be artificially designed.MFC patches are bonded on the top and bottom surfaces of the beam structure to act as the actuators and sensors.Then,the finite element method(FEM)is used to formulate the equation of motion,and the pole placement based on the out-put feedback method is used to design the active controller.Finally,the effectiveness of the active control method is verified. 展开更多
关键词 piezo-intelligent macro-fiber composite(MFC) pole placement closed-loop control finite element method(FEM)
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