The modulation of response caused by the fractional derivative in the Duffing system under super-harmonic resonance

The dynamic characteristics of the 3:1 super-harmonic resonance response Duffing oscillator with fractional derivative are studied. Firstly, approximate solution amplitude-frequency system is obtained by using periodic characteristic response. Secondly, a set critical parameters for qualitative change derived according to singularity theory and two types responses obtained. Finally, components 1X 3X frequencies system?s time history extracted spectrum analysis, then correctness theoretical analysis verified comparing them solution. It found that can be changed essentially changing order coefficient derivative. method used in this paper design controller adjusting dynamical system.