Abstract

Analytical formulas for the amplitude–frequency and phase–frequency characteristics, as well as forced oscillations, of a fractional oscillator have been derived using the harmonic balance method. It has been found that these characteristics depend on the dissipative properties of a medium—memory effects, which are described by fractional-order derivatives. It has been shown that fractional orders of derivatives influence the decay of the oscillatory process and are related to its Q factor. Analytical curves of forced oscillation characteristics for a linear fractional oscillator give the idea that fractional orders can be considered as control parameters for an oscillatory process in a dissipative medium.

中文翻译：

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线性分数振荡器的强迫振荡的品质因数

摘要

使用谐波平衡法，得出了分数振荡器的幅度-频率和相位-频率特性以及强迫振荡的解析公式。已经发现，这些特性取决于介质的耗散特性-记忆效应，这由分数阶导数描述。已经表明，导数的分数阶会影响振荡过程的衰减，并且与它的Q因子有关。线性分数振荡器的强迫振荡特性的分析曲线给出了这样的想法，即分数阶可以被视为耗散介质中振荡过程的控制参数。