Nonlinear Dynamics of Coupled MEMS Oscillators

摘要在过去的20年里，科学家和工程师利用集成电路制造的技术，开发出了制造微型机电设备的方法，称为MEMS(微型机电系统)和NEMS(纳米机电系统)。这些设备虽然太小，肉眼无法看到，但大小从100微米(约十分之一毫米)到100纳米(约万分之一毫米)不等，可能包含许多形状复杂的机械部件、传感器和电路。一种特别有前景的NEMS包含纳米级的光束和平板(我们称之为纳米棒)。随着木琴杆对敲击的反应而振动，纳米管可以对本质上可能是电气或机械的“输入信号”做出反应而振动。由于其小尺寸和低阻尼，纳米棒的行为可以不同于他们的大规模同行。例如，众所周知，这种光束在用直流(稳定)激光照射时会自发振动(自振荡)。这些自振荡可以与调制(AC)激光器或其他外部调制同步。如果将许多自振纳米梁放置在一个阵列中并机械连接，它们可以按照不同的模式振动，这取决于输入信号和每个纳米梁连接阵列中其他纳米梁的方式。这种耦合振荡器的阵列可用于传感、信号处理和定时应用。这项拟议的研究将实验和理论相结合，以了解振动纳米棒及其阵列的功能，发现新的现象，并找到将驱动振荡器所需的功率降至最低的方法。我们建议为设计目的开发实用的简化数学模型。简化模型的预测将与完整模型和实验进行比较。这些模型将被用于研究大型振荡器系统的动力学，目的是深入了解振荡器阵列应用的设计挑战。这项研究的结果将为阵列在信号处理和其他应用中的实际应用提供一条途径。将开发一个动手振荡器模块，并与中学生和初中或高中教师一起使用。

AbstractUsing technologies adapted from the manufacture of integrated electronic circuits, scientists and engineers have in the last 20 years developed methods for fabricating microscopic electro-mechanical machines, known as MEMS (microelectromechanical systems) and NEMS (nano electromechanical systems). These devices, although too small to be seen by eye, ranging in size from 100 microns (about 1 tenth of a mm) to 100 nanometers (about 1 ten-thousandth of a mm), may contain many intricately shaped mechanical components, sensors and circuits. One particularly promising type of NEMS contains nanometer scale beams and plates (let's call them nanobeams). As Xylophone bars vibrate in response to percussion, nanobeams can vibrate in response to "input signals" which could be electrical or mechanical in nature. Due to their small size and low damping, nanobeams can behave differently than their large scale counterparts. For example, such beams are known to vibrate spontaneously (self-oscillate) when illuminated with DC (steady) laser light. These self-oscillations can be synchronized to a modulated (AC) laser or other external modulation. If many self-oscillating nanobeams were placed in an array and connected mechanically they could vibrate in different patterns depending on the input signal and the manner in which each nanobeam is connected to the others in the array. An array of such coupled oscillators could be used for sensing, signal processing and timing applications. The proposed research integrates experiments and theory to understand the function of the vibrating nanobeams and their arrays, to discover new phenomena and to find ways to minimize the power needed to drive the oscillators. We propose to develop simplified mathematical models practical for design purposes. Predictions of the simplified models will be compared to full models and to experiments. These models will be applied to study the dynamics of large systems of oscillators with the goal of obtaining insights into the design challenges for applications of oscillator arrays. Findings of the study will provide a pathway to the real-world application of arrays for signal processing and other applications. A hands-on oscillator module will be developed and used with middle school students and with middle or high school teachers.