Abstract Nonlinearities exist in all microresonators to some extent. In most cases, designers deem nonlinearities undesirable and to be actively avoided. However there are cases where deliberately engineering nonlinearities into microresonators is advantageous. With this motivation, my group is exploring two applications gyroscopes and gravimetric sensors where nonlinearities play very different roles.
Mode-symmetric resonant gyroscopes are of interest in part due to their ability to run in "forward" or "reverse" coupling directions with the potential to cancel some sources of bias drift. This class of designs also has relatively high rotational-rate sensitivity for low drive voltages. Operating gyroscopes with quality factors over 10,000 is a challenge as even small cubic "Duffing" nonlinearities in stiffness cause relatively large distortion of the resonance characteristic along with hysteretic bifurcations as a function of drive frequency. Unlike parallel-plate capacitors, nonlinear capacitive comb-drives can tune the modal frequencies while allowing for large deflection. More sophisticated comb shaping can tune the Duffing nonlinearity and may lead to its cancellation.
Parametric resonance in microresonators can occur when an electrostatic spring is driven sinusoidally at electrical frequencies near twice the mechanical resonance. The parametric behavior is fed initially by noise and is ultimately limited in amplitude by stiffness nonlinearities in the system. Nonlinear parametric resonance gives rise to multi-valued ac steady-state solutions ("branches") as functions of drive frequency. The bifurcation from the zero to a non-zero branch occurs at a precise frequency that is a function of the mass and spring constants of the system and is exploitable for sensing. Our group has implemented a bi-state amplitude control scheme that provides stable servo operation on the bifurcation transition with large displacement amplitude. This method enables automated detection of the bifurcation frequency for future parametric resonant sensors. The nature of the nonlinear dynamics makes the alternatives of classical continuous control and frequency control techniques ineffective.
Biography Gary K. Fedder is the Associate Dean for Research in the college of engineering, the Director of the Institute for Complex Engineered Systems, and the Howard M. Wilkoff Professor of Electrical and Computer Engineering and of The Robotics Institute at Carnegie Mellon University. He earned his B.S. and M.S. from MIT and his Ph.D. from U.C. Berkeley. His personal research lies in microelectromechanical systems where he has contributed to over 240 research publications and holds several patents. He is an IEEE Fellow and serves on the editorial boards of IEEE J. MEMS, IoP J. Micromechanics and Microengineering, and IET Micro & Nano Letters and as co-editor of the Wiley-VCH Advanced Micro- and Nanosystems book series. From 2011 to 2012, Professor Fedder served as a technical co-lead in the U.S. Advanced Manufacturing Partnership where he worked with industry, academia and government to generate recommendations that motivated the launch of the National Network for Manufacturing Innovation.
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