Dynamic behaviors of nonlinear fractional-order differential oscillator

被引:0
作者
Wei Zhang
Shao-kai Liao
Nobuyuki Shimizu
机构
[1] JiNan University,Department of Electronic Engineering
[2] Institute of Mechanical Science and Technology,Department of Mechanical and Power Engineering
[3] Iwaki Meisei University,undefined
来源
Journal of Mechanical Science and Technology | 2009年 / 23卷
关键词
Nonlinearity; Fractional calculus; Bifurcation; Chaos; Viscoelasticity;
D O I
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中图分类号
学科分类号
摘要
The nonlinear dynamic behaviors of oscillators described by fractional-order differential are presented in this paper. The background of the research is based upon two engineering practices. First is that the visco-elastic behaviors of some advanced polymeric materials can be accurately modeled by the fractional calculus constitutive law. Second is that the influence of nonlinear visco-elasticity described by the fractional operator cannot be neglected in some cases such as the vibration with large displacement or large strain and thermo-visco-elastic coupled problems. The numerical scheme for solving the nonlinear equation of motion is developed. The results show that because of the introduction of nonlinear damping modeled by the fractional-order operator, the bifurcation and chaos of the oscillator appear in forced vibration. Furthermore, the fraction value of the fractional operator evidently affects the dynamic behavior of the nonlinear fractional differential oscillator.
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页码:1058 / 1064
页数:6
相关论文
共 7 条
[1]  
Zhang W.(1998)Numerical Algorithm for Dynamic Problems Involving Fractional Operators Int. J. of JSME, Ser. C 41 364-370
[2]  
Shimizu N.(2004)Numerical analysis formulation of viscoelastic solids modeled by fractional operator ACTA MECHANICA SINICA 36 617-621
[3]  
Zhang W.(2008)Dynamics of fractional Duffing oscillator Journal of Dynamics and Control 6 122-125
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