Five parametric resonances in a microelectromechanical system

Kimberly L. Turner (), Scott A. Miller, Peter G. Hartwell, Noel C. MacDonald, Steven H. Strogatz and Scott G. Adams
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Kimberly L. Turner: Cornell University
Scott A. Miller: School of Applied and Engineering Physics, Cornell University
Peter G. Hartwell: School of Electrical Engineering and the Cornell Nanofabrication Facility, Cornell University
Noel C. MacDonald: School of Electrical Engineering and the Cornell Nanofabrication Facility, Cornell University
Steven H. Strogatz: Cornell University
Scott G. Adams: Cornell University

Nature, 1998, vol. 396, issue 6707, 149-152

Abstract: Abstract The Mathieu equation1 governs the forced motion of a swing2, the stability of ships3 and columns4, Faraday surface wave patterns on water5,6, the dynamics of electrons in Penning traps7, and the behaviour of parametric amplifiers based on electronic8 or superconducting devices9. Theory predicts that parametric resonances occur near drive frequencies of 2ω0/n, where ω0 is the system's natural frequency and n is an integer ⩾1. But in macroscopic systems, only the first instability region can typically be observed, because of damping and the exponential narrowing10 of the regions with increasing n. Here we report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system. Five instability regions can be measured, due to the low damping, stability and precise frequency control achievable in this system. The centre frequencies of the instability regions agree with theoretical predictions. We propose an application that uses parametric excitation to reduce the parasitic signal in capacitive sensing with microelectromechanical systems. Our results suggest that microelectromechanical systems can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.

Date: 1998
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DOI: 10.1038/24122

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