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

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (7) : 164-168.

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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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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.

Key words

Fractional-order Ver Del Pol-Duffing system / Autonomous system / Harmonic load / Seismic load

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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