Complex Nonlinear Dynamics in Electrostatic Microelectromechanical Systems (MEMS)

这个集成系统提案的重点是探索微机电系统（MEMS）和包含MEMS的片上系统应用中的复杂非线性动力学。在过去的十年中，许多基于复杂数值技术和算法的计算设计工具被开发出来，以加速MEMS领域的进步。许多这些计算设计工具已被优化用于MEMS的静态分析。由于各种能量域之间复杂的相互作用，MEMS的动力学行为可能是高度非线性的，迄今为止很少有研究能够充分揭示所有有趣的和新颖的动力学。智力优势：提出(1)利用分层物理理论和拉格朗日描述各种混合能量域，并通过高效准确的算法将混合能量域结合起来，开发高效的计算设计工具，用于快速准确的MEMS动力学分析；(2)阐明MEMS中存在的所有非线性力的意义。特别是，本研究旨在从物理上理解复杂振荡和非线性动力学的起源，以探索复杂振荡和非线性动力学在MEMS中遇到的各种应用。一些设想的应用包括混沌微流控混合器，具有可移动谐振频率的MEMS滤波器，MEMS阵列和集成电路的MEMS器件，用于片上系统应用。更广泛的影响：拟议的研究可以产生更广泛的影响，因为它可以帮助加速各种微尺度传感器和执行器、微系统片上、安全通信、电子应用以及基于MEMS的化学和生物传感器的设计和开发。在MEMS，计算方法和动力学领域培训研究生，并将该项目的成果纳入UIUC提供的研究生课程是计划中的一些教育活动。

This integrative systems proposal focuses on exploring complex nonlinear dynamics in microelectromechanical systems (MEMS) and system-on-a-chip applications containing MEMS. A number of computational design tools based on sophisticated numerical techniques and algorithms have been developed over the last decade to accelerate the progress in the area of MEMS. A number of these computational design tools have been optimized for static analysis of MEMS. The dynamical behavior of MEMS can be highly nonlinear because of complex interactions between various energy domains and very few studies have been performed so far to fully uncover all the interesting and novel dynamics. Intellectual Merit: It is proposed to (1) develop efficient computational design tools for fast and accurate dynamical analysis of MEMS by employing hierarchical physical theories and Lagrangian descriptions for the various mixed-energy domains and by combining the mixed-energy domains by efficient and accurate algorithms; (2) elucidate the significance of all the nonlinear forces present in MEMS. In particular, the proposed research aims to understand, physically, the origin of complex oscillations and nonlinear dynamics to explore various applications of complex oscillations and nonlinear dynamics encountered in MEMS. Some of the envisioned applications include chaotic microfluidic mixers, MEMS filters with shiftable resonant frequencies, arrays of MEMS and MEMS devices integrated with circuits for system-on-a-chip applications. Broader Impacts: The proposed research can have a broader impact as it can help accelerate the design and development of a variety of microscale sensors and actuators, microsystems-on-a-chip, secure communications, electronic applications, and MEMS based chemical and biological sensors. Training of graduate students in the areas of MEMS, computational methods and dynamics, incorporation of results from this project into graduate courses offered at UIUC is some of the planned educational activities.