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

采用解析、数值和实验方法对一类振动角速率传感器和微动开关的非线性响应和不稳定性进行了研究。提出的研究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。提出的研究设想集中在环型振动结构的随机和非线性失稳行为。基于最大李雅普诺夫指数的分析方法将用于预测考虑白噪声和窄带随机信号形式激励的随机不稳定性。基于微悬臂梁结构的弹跳瞬态动力学将在开关系统中引起人们的兴趣。此外，结合表面效应的卡西米尔驱动纳米开关的静态和动态性能也将通过提出的研究进行预测。这种新兴的卡西米尔力装置被认为是通过卡西米尔力大小的纯粹改变来操作的。此外，通过高效的随机建模框架，提出了基于综合系统模型的不确定性量化研究，以便量化各种设计参数的随机变化对该类器件性能的影响。在角速率传感器的情况下，获得的结果将能够预测临界输入/激励频率和幅度以及其他关键系统/操作参数，同时深入了解开关参数，例如开关首次闭合，动态拉入/拉出电压以及开关系统中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.