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《Journal of Vibration and Shock》 2011-07
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Nonlinear dynamic behavior of a fractional-order ver del pol-duffing system

LI Yuan-ping1,2,ZHANG Wei3(1.Key Lab of Disaster Forecast and Control in Engineering,Ministry of Education,Jinan University,Guangzhou 510632,China;2.Department of Mechanics and Civil Engineering,Jinan University,Guangzhou 510632,China;3.Department of Electronic Engineering,Jinan University,Guangzhou 510632,China)  
A fractional-order Ver Del Pol-Duffing system,a fractional derivative model was introduced to simulate the system's damping characteristics,was proposed.The numerical computation scheme of fractional derivative was deduced.The dynamic characteristics influenced by the feature parameters under different external loads were investigated.The results showed that this nonlinear system has the same self-excited vibration characteristics as those of the classic Ver Del Pol system,the q-order derivative has a large impact upon the system dynamic behavior;on the other hand,as expected,the higher the values of damping coefficient and the nonlinear displacement coefficient,the more nonlinear the system becomes;under harmonic load,with increase in amplitude or decrease in damping coefficient,the system motion changes from quasi periodic motion to period-three vibration until to single period vibration;under seismic load,the q-order derivative has a large impact upon the output energy.
【Fund】: 国家自然科学基金10872079
【CateGory Index】: TH113
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Chinese Journal Full-text Database 2 Hits
1 Zhang Wei Xu Hua Nubuyuki Shimizu Institute of Applied Mechanics, Jinan University, Guangzhou 510632, China The Laboratory of Modern Design and Rotor-Bearing System, Key Lab. of the Ministry of Education, Xi'an Jiao-tong University, Xi'an 710049, China Dept. of Mechanical Engineering, Iwaki Meisei University, Iwaki, Japan;THE NUMERICAL ANALYSIS FORMULATION OF THE VISCOELASTIC SOLID MODELED BY FRACTIONAL OPERATOR~1[J];Acta Mechanica Sinica;2004-05
2 LI Gen-guo, ZHU Zheng-you, CHENG Chang-jun ( Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; Department of Mathematics, Shanghai University, Shanghai 200072, China; Department of Mechanics, Shanghai University, Shanghai 200072, China);Analysis of Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beam[J];Chinese Quarterly of Mechanics;2001-03
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6 Cheng Chang-jun①, Zhu Zheng-you② ① Professor, Supervisor of Ph.D.Candidates, Department of Mechanics, ② Professor, Supervisor of Ph.D.Candidates, Department of Mechanics, College of Sciences, Shanghai Institute of Applied Mathematics and Mecanics, Shanghai University, Shanghai University, Shanghai 200436;Advance on Theory of Viscoelasticity[J];Nature Magazine;2003-03
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