分数阶Ver Del Pol-Duffing系统的非线性动力学行为分析

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (7) : 164-168.

论文

分数阶Ver Del Pol-Duffing系统的非线性动力学行为分析

李媛萍1,2; 张卫3

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Nonlinear dynamics behavior of Fractional-order Ver Del Pol-Duffing system

LI Yuan-ping1,2 ; ZHANG Wei3

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摘要

利用分数导数本构模型模拟系统的阻尼特性，构造了分数阶Ver Del Pol-Duffing系统，探讨了系统的动力特性随特征参数的变化规律。分析发现：该非线性振子具有与经典Ver Del Pol系统相似的自激振动特性，但其非线性强弱受分数导数阶值以及阻尼系数和非线性大位移系数的影响；在简谐荷载作用下，随着外荷载幅值的增大或阻尼系数的减小，系统由拟周期振动变为周期三振动最后发展为单周期振动；在地震荷载作用下，分数导数阶值的变化能改变系统的输出能量。

Abstract

A fractional differential Ver Del Pol-Duffing system，in which fractional derivative model introduced to simulate system’s damping characteristics，is proposed. The numerical computation scheme of fractional derivative is deducted. The dynamic characteristics influenced by the characteristic parameters under different external load are investigated. The results show that: this nonlinear system has the same self-excited vibration characteristics as the classic Ver Del Pol system, the q-order derivative has a large impact upon the system dynamics,namely in the period of the output oscillation. On the other hand, and as expected, the higher the value of damping coefficient and the nonlinear displacement coefficient the more nonlinear the system becomes. Under harmonic load, as the increase of amplitude or decrease of damping coefficient, the system should undergo quasi periodic motions to period-three vibration until to single period vibration. Under seismic load, the q-order derivative has a large impact upon the output energy.

导出引用

李媛萍; 张卫. 分数阶Ver Del Pol-Duffing系统的非线性动力学行为分析[J]. 振动与冲击, 2011, 30(7): 164-168

LI Yuan-ping;;ZHANG Wei. Nonlinear dynamics behavior of Fractional-order Ver Del Pol-Duffing system[J]. Journal of Vibration and Shock, 2011, 30(7): 164-168