Nonlinear Dynamics of Coupled MEMS Oscillators

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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.