SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR

The super-harmonic resonance of Duffing oscillator with fractional-order derivative is studied, and the first-order approximate solution is obtained by averaging method. The definitions of equivalent linear damping coefficient and equivalent linear stiffness for super-harmonic resonance are established, and the effects of the fractional-order parameters on the equivalent linear damping coefficient and equivalent linear stiffness are also analyzed. The amplitude-frequency equation for steady-state solution associated with the stability condition is also presented, and the comparisons of the fractional-order and the traditional integer-order Duffing oscillator are fulfilled. At last the numerical simulation is used to analyze the effects of the parameters in fractional-order derivative on the amplitude-frequency curves.