论文标题
分数阻尼对行驶振荡器的瞬态动力学的影响
Fractional damping effects on the transient dynamics of the Duffing oscillator
论文作者
论文摘要
我们认为在存在分数阻尼的情况下，在不同的物理情况下具有特征性的非线性螺旋振荡器。对系统进行了越来越较大的阻尼参数值，我们称之为失业和抑制过度的态度。在这两个中，我们都研究了分数参数，振荡的幅度和达到渐近行为的时代，称为渐近时代。在过度阻尼的政权中，研究表明，也在这里，分数阶导数及其振幅和渐近时代也可能突然变化，因为分数参数的较小变化可能会发生变化。此外，在后一种制度中，对于系统参数的合适值，可以发生类似谐振的行为。通过计算相应的Q因子来证实这些结果。我们预计，这些结果对于更好地理解分数动态及其可能的应用可能很有用，就像建模通常需要复杂阻尼项的不同种类的材料一样。
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of the oscillations and the times to reach the asymptotic behavior, called asymptotic times. In the overdamped regime, the study shows that, also here, there are oscillations for fractional order derivatives and their amplitudes and asymptotic times can suddenly change for small variations of the fractional parameter. In addition, in this latter regime, a resonant-like behavior can take place for suitable values of the parameters of the system. These results are corroborated by calculating the corresponding Q-factor. We expect that these results can be useful for a better understanding of fractional dynamics and its possible applications as in modeling different kind of materials that normally need complicated damping terms.
