Nonlinear Vibrations of Systems of MEMS Oscillators

微尺度和纳米尺度机电系统是非常小的（微观）设备，用于传感，导航，时钟，打印机，药物输送，个人医疗保健和其他应用。例如，移动电话包含多个微型传感器，其功能是确定向上的方向，测量压力和温度，或找到地球的磁北。许多微系统包含振动或共振，微米到纳米尺度的柔性结构。结构元素可以是简单的从硅片上蚀刻的悬臂梁，也可以是由多层材料构建的复杂的三维结构。因此，谐振微尺度振荡器的“设计空间”是巨大的。要充分利用这个空间，需要对材料、制造、包装、电子、光学和机械有深刻的理解。该项目将着重于提高单、对和阵列谐振器和振荡器的非线性动力学知识。项目带来的发现将扩大设计空间，并有可能带来新的技术和设备。新一代的科学家将接受这项研究的训练。除了他们在传统科学学科方面的训练之外，作为国际合作的结果，他们将发展对跨越地理距离的合作研究的协同作用的理解和赞赏。该项目还将使本科生通过有意义的参与研究而受到启发，从而在学习中脱颖而出，并攻读STEM研究生学位。鼓励研究人员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。该研究将涉及光学自激微米至纳米级器件的物理实验，并与数学建模和分析紧密结合。实验和模型将从一个光激发的单振荡器开始，然后建立通过静电或磁场耦合的成对和阵列。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，开发，分析和验证数学模型，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上实现为微米级器件的极限环振荡器阵列的束缚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。该项目涵盖了实验力学、理论、设计和制造方面所需的专业知识，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）经验丰富的研究团队。

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).