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中文摘要：
本文利用解析和数值的方法研究了由双频周期信号驱动含分数阶内、外阻尼的Dufng振子的振动共振现象,并讨论了分数阶阶数对上述现象的影响.研究发现：双频周期信号同时驱动的分数阶Dufng振子响应幅值增益Q可随着高频周期激励幅值的改变达到最大值,即出现了和整数阶非线性动力系统相似的振动共振现象,而相应的分数阶导数项则分别为系统提供了内、外两种阻尼力从而导致了系统有效势函数的改变,进而引发了比整数阶动力系统更为丰富的振动共振现象.
英文摘要：
The phenomenon of vibrational resonance（VR） in a Dufng system with both fractional-order external damping and fractional-order intrinsic damping driven by the two-frequency periodic signals is investigated.It is observed that the resonance amplitude Q can be optimized by an appropriate choice of the amplitude of the high-frequency signal.The obtained relationship between VR and the fractional-orders shows that both fractional-order external damping and fractional-order intrinsic damping can induce changes of the shapes of the efective potential function and then lead to more abundant resonance behaviors than in the traditional dynamic systems.
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