耦合非线性谐振腔阵列中的集体动力学
Collective Dynamics in Arrays of Coupled Nonlinear Resonators
摘要：
近年来，由于微机电和纳机电系统（MEMS和NEMS）领域的快速发展，耦合机械谐振器的集体非线性动力学的研究重新受到关注。我们回顾了广泛的集体动力学现象，同时强调了共同的概念和理论工具，我们已经开发了治疗它们。我们提供了详细的推导振幅方程，这使我们能够获得减少我们的复杂系统的相关动态的描述。我们应用这些振幅方程来研究（a）共振响应参数激励;（b）模式选择，或扩展模式之间的非线性竞争的情况下的多稳定性;（c）形成和动力学的固有局域模式（ILM）;和（d）自发同步的振荡器具有不同的频率。从分析不同的振幅方程得到的所有预测与基本运动方程的数值解非常一致，这表明预测的效果可以在真实的微机械或纳米机械谐振器阵列中观察到，从而激发了这些系统中的新实验。
英文摘要：
The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We review a wide range of collective dynamical phenomena, while highlighting the common concepts and theoretical tools that we have developed for treating them. We provide detailed derivations of amplitude equations, which allow us to obtain reduced descriptions for the relevant dynamics of our complex systems. We apply these amplitude equations to study (a) resonant response to parametric excitation; (b) pattern selection, or the nonlinear competition between extended modes in situations of multistability; (c) formation and dynamics of intrinsically localized modes (ILM); and (d) spontaneous synchronization of oscillators with differing frequencies. All the predictions obtained from analyzing the different amplitude equations are in excellent agreement with numerical solutions of the underlying equations of motion, suggesting that the predicted effects can be observed in arrays of real micromechanical or nanomechanical resonators, thus motivating new experiments in these systems.
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