Dynamic Characterization and Uncertainty Quantification of a Class of Angular Rate Sensing and Switching Systems

采用解析/数值和实验相结合的方法，研究了一类振动式角速率传感器和微动开关的非线性响应和不稳定性。提出的研究的动机来自于一类基于MEMS的陀螺仪以及基于MEMS和NEMS的开关的应用。拟议的研究设想集中在随机和非线性不稳定行为的环型振动结构。 基于最大李雅普诺夫指数的分析方法将被追求来预测随机不稳定性，考虑白噪声以及窄带随机信号形式的激励。 基于微悬臂梁结构的弹跳瞬态动力学在开关系统的情况下将是感兴趣的。 此外，静态以及动态性能的Casimir驱动的纳米开关，结合表面效应也将通过拟议的研究预测。这类新兴的卡西米尔力装置被认为是通过纯粹改变卡西米尔力的大小来操作的。此外，不确定性量化研究提出了全面的系统模型的基础上，通过一个有效的随机建模框架，使这类设备的性能上的各种设计参数的随机变化的影响可以量化。 所获得的结果将能够预测临界输入/激励频率和幅度以及角速率传感器情况下的其他临界系统/操作参数，同时洞察开关参数，例如第一次开关闭合、动态吸合/拉出电压以及开关系统情况下第一次显著反弹的细节。

An investigation into nonlinear response and instabilities of a class of vibratory angular rate sensors as well as micro-switches is proposed via analytical/numerical and experimental methods. Motivation for the proposed study comes from application to a class of MEMS-based gyroscopes as well as MEMS and NEMS-based switches. The proposed study envisages to focus on stochastic and non-linear instability behavior of ring-type vibratory structures. An analytical approach based on the maximal Lyapunov exponent will be pursued to predict stochastic instabilities considering excitations in the form of white-noise as well as narrow-band random signals. Bouncing transient dynamics of micro-cantilever based structures will be of interest in the case of switching systems. Further, static as well as dynamic performances of Casimir actuated nano-switches incorporating surface effects will also be predicted via the proposed research. This emerging class of Casimir-force devices is considered to be operated by pure alteration of Casimir force magnitudes. In addition, an uncertainty quantification study is proposed based on comprehensive system models via an efficient stochastic modeling framework so that the effects of stochastic variations in various design parameters on the performance of this class of devices may be quantified. The results to be obtained will be able to predict critical input/excitation frequencies and magnitudes as well other critical system/operating parameters in the case of angular rate sensors while giving insight into the switching parameters such as first time switch closure, dynamic pull-in/pull-out voltages and details on first significant bounce in the case of switching systems.