We study frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. Important types of such resonators are nano- and microelectromechanical systems. Various noise sources are considered, with the emphasis on the fundamentally unavoidable noise that comes along with dissipation from the coupling to a thermal reservoir. The formulation in terms of the action-angle variables of the resonator allows us to analyze a deeply nonlinear regime. In this regime the vibration frequency as a function of the action can have an extremum. We show that frequency fluctuations can be strongly reduced by choosing the operation point at this extremum. We suggest a practical implementation of a nanoresonator that has the appropriate property and show explicit results for the corresponding model.

中文翻译：

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抑制欠阻尼非线性谐振器中自持振动的频率波动

我们研究基于非线性欠阻尼谐振器的自持式振荡器的频率波动。这种谐振器的重要类型是纳米和微机电系统。考虑了各种噪声源，重点是从联轴器到蓄热器的耗散带来的基本不可避免的噪声。根据谐振器的作用角变量的表述使我们能够分析深层非线性状态。在这种情况下，振动频率作为作用的函数可以具有极值。我们表明，通过选择此极值处的工作点可以大大降低频率波动。我们建议具有适当特性的纳米谐振器的实际实现，并为相应的模型显示出明确的结果。