Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation
Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation
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DOI：
10.1109/jmems.2007.906757
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发表时间：
2007-12-01
影响因子：
2.7
通讯作者：
Turner, Kimberly L.
中科院分区：
文献类型：
--
作者：
DeMartini, Barry E.;Butterfield, Holly E.;Turner, Kimberly L.
各种微机电（MEM）振荡器是由一个版本的马蒂厄方程，窝藏线性和立方非线性时变刚度项。在本文中，混沌行为的预测和发生在这一类的MEM设备。具体地说，利用Melnikov的方法，一个不等式，描述的区域的参数空间的混沌生活。数值模拟表明，混沌确实发生在这个区域的参数空间，并研究系统的行为的各种参数。设计并制作了一个满足不等式的MEMS振荡器，该振荡器利用非指叉梳齿驱动器进行驱动和刚度调谐。该装置的实验结果与数值模拟的结果是一致的，令人信服地显示混沌行为。
A variety of microelectromechanical (MEM) oscillators is governed by a version of the Mathieu equation that harbors both linear and cubic nonlinear time-varying stiffness terms. In this paper, chaotic behavior is predicted and shown to occur in this class of MEM device. Specifically, by using Melnikov's method, an inequality that describes the region of parameter space where chaos lives is derived. Numerical simulations are performed to show that chaos indeed occurs in this region of parameter space and to study the system's behavior for a variety of parameters. A MEM oscillator utilizing noninterdigitated comb drives for actuation and stiffness tuning was designed and fabricated, which satisfies the inequality. Experimental results for this device that are consistent with results from numerical simulations are presented and convincingly show chaotic behavior.