Nonlinear Vibrations of Systems of MEMS Oscillators

微尺度和纳米尺度机电系统是用于传感、导航、时钟、打印机、药物输送、个人健康护理和其他应用的极小（微观）装置。 例如，移动的电话包含多个微尺度传感器，其功能是确定哪个方向是向上的，以测量压力和温度，或者找到地球的磁北。 许多微系统包括振动或共振的微米至纳米尺度的柔性结构。结构元件可以简单到从硅片蚀刻的悬臂梁，也可以是由多层材料构建的复杂三维架构。 因此，谐振微尺度振荡器的“设计空间”是巨大的。 充分利用这一空间需要对材料、制造、包装、电子、光学和机械有深入的了解。 本项目将侧重于推进知识的非线性动力学的单个，成对和阵列的谐振器和振荡器。 该项目带来的发现将扩大设计空间，并可能导致新技术和新设备的出现。新一代的科学家将接受这项研究的培训。除了接受传统科学学科的培训外，通过国际合作，他们还将了解和欣赏跨越地理距离的合作研究的协同作用。该项目还将通过有意义的参与研究来激励本科生在学习中脱颖而出，并攻读STEM研究生学位。研究人员将被鼓励考虑将这项研究开发的技术转移到现有或初创公司，以促进经济发展。这项研究将涉及光学自激微米至纳米尺寸器件的物理实验，并与数学建模和分析紧密结合。 实验和模型将从一个光激励的单个振荡器开始，然后通过静电场或磁场耦合到成对和阵列。具体目标包括：演示振荡器对和阵列的锁定，观察新现象，提高频率稳定性，量化系统响应与关键参数的关系，并开发，分析和验证数学模型，以增强对观察到的现象的理解，并作为MEMS系统设计的基础。通过实验工作和相关的数学模型，该项目将通过解决物理实现为微米级器件的极限环振荡器阵列的夹带和锁定的可行性和条件问题，推进非线性振荡器动力学领域的知识。 该项目汇集了来自康奈尔大学、特拉维夫大学和美国国家标准与技术研究所（NIST）的经验丰富的研究团队，涵盖了实验力学、理论、设计和制造方面所需的专业知识。

Micro-scale and nano-scale electromechanical systems are extremely small (microscopic) devices which are used in sensing, navigation, clocks, printers, drug delivery, personal health care and other applications. For example, mobile phones contain multiple micro-scale sensors which function to determine which direction is up, to measure pressure and temperature, or to find magnetic North of the Earth. Many micro systems incorporate vibrating, or resonant, micron to nanometer scale flexible structures. The structural elements could be as simple as a cantilever beam etched from a silicon wafer, to complex three-dimensional architectures built from multiple layers of materials. As a result the "design space" for resonant micro-scale oscillators is tremendous. Making best use of this space requires a deep understanding of materials, fabrication, packaging, electronics, optics and mechanics. This project will focus on advancing knowledge of the nonlinear dynamics of single, pairs and arrays of resonators and oscillators. Discoveries enabled by the project will enlarge the design space and potentially lead to new technologies and devices. A new generation of scientists will be trained in this research. In addition to their training in traditional scientific disciplines, as a result of the international collaboration, they will develop an understanding and appreciation of the synergies of collaborative research that bridges geographical distances. The project will also result in undergraduates inspired through meaningful participation in research to excel in their studies and to pursue graduate degrees in STEM. The researchers will be encouraged to consider transfer technology developed from this research into existing or startup companies to promote economic development.The research will involve physical experiments on optically self-excited micron- down to nanometer-size scale devices, closely coupled to mathematical modeling and analysis. The experiments and models will start with an optically excited single oscillator, then build to pairs and arrays coupled through electrostatic or magnetic fields. Specific goals include: demonstrating locking of oscillator pairs and arrays, observing new phenomena, improving frequency stability, quantifying the relation of system response to key parameters and developing, analyzing and validating mathematical models that enhance understanding of observed phenomena and that underlie the design of MEMS systems. Through the experimental work and associated mathematical models the project will advance knowledge in the field of dynamics of nonlinear oscillators by addressing questions on the feasibility of and conditions for entrainment and locking of arrays of limit cycle oscillators physically realized as micron scale devices. Spanning the needed expertise in experimental mechanics, theory, design and fabrication, the project brings together an experienced research team from Cornell University, Tel Aviv University and the National Institute of Standards and Technology (NIST).