Abstract

In this work, we study the conditions and scenarios for synchronizing the oscillations of weakly coupled microbeam elements of a differential resonant microelectromechanical systems (MEMS) accelerometer that operates in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained by the Galerkin method, is studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of the system parameters is determined. Along with local bifurcation analysis of the considered steady-state modes, global analysis of the evolution and branching of limit cycles in the space of slow variables is also carried out, which makes it possible to detect zones of coexistence of stable synchronization and beat modes with their basins of attraction. The effect of the factor of the designed or technologically determined nonidentity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.

中文翻译：

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微分谐振 MEMS 加速度计：弱耦合微束传感元件的同步特性

摘要

在这项工作中，我们研究了在双回路自振荡器模式下运行的差分谐振微机电系统 (MEMS) 加速度计的弱耦合微梁元件的同步振荡的条件和场景。使用多尺度方法研究了通过 Galerkin 方法获得的运动元件之间具有非线性弹性耦合的两个 Van der Pol 自激振荡器系统的模型。两个谐振器的节拍模式和振荡同步通过分析和数值方法找到，并确定了系统参数空间中这些模式之间的边界。除了对所考虑的稳态模式进行局部分岔分析外，还对慢变量空间中的极限环的演化和分支进行了全局分析，这使得检测稳定同步和节拍模式与其吸引盆共存的区域成为可能。研究了两个谐振器设计的设计或技术确定的非同一性因素对同步和节拍参数区域位置的影响。