参数激励诱导MEMS和Lienard振子的极端事件
Parametric excitation induced extreme events in MEMS and Lienard oscillator
摘要：
研究了两种典型的参数激励非线性振动模型。作者为这些系统中极端事件（EE）的出现提供了理论证据。首先，作者考虑了一个著名的Lienard型振荡器，通过两个分岔路线：间歇性和周期加倍路线的激励频率的两个不同的临界值，显示了EE的出现。作者还计算了两个连续的EE的返回时间，定义为事件间的时间间隔，遵循泊松分布，证实了事件的罕见性。此外，Lienard振子的总能量的估计，以解释的机制，为发展的EE。接下来，作者证实了在参数激励的微机电系统中EE的出现。在该模型中，由于在系统的不连续边界附近出现粘滑分岔，从而导致了系统的机电耦合效应。由于参数激励是遇到在几个现实世界的工程模型，如宏观和微观力学振荡器，本文提出的结果的影响，也许是有益的，以了解在这样的振荡系统中的EE的发展。
英文摘要：
The two paradigmatic nonlinear oscillatory models with parametric excitation are studied. The authors provide theoretical evidence for the appearance of extreme events (EEs) in those systems. First, the authors consider a well known Lienard type oscillator that shows the emergence of EEs via two bifurcation routes: Intermittency and period-doubling routes for two different critical values of the excitation frequency. The authors also calculate the return time of two successive EEs, defined as inter-event intervals, that follow Poisson-like distribution, confirm the rarity of the events. Further, the total energy of the Lienard oscillator is estimated to explain the mechanism for the development of EEs. Next, the authors confirmed the emergence of EEs in a parametrically excited microelectromechanical system. In this model, EEs occur due to the appearance of stick-slip bifurcation near the discontinuous boundary of the system. Since the parametric excitation is encountered in several real-world engineering models, like macro and micromechanical oscillators, the implications of the results presented in this paper are perhaps beneficial to understand the development of EEs in such oscillatory systems.
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