Angular rate sensing using nonlinear microresonators actuated by 2:1 internal resonance

The goal of this research is to introduce nonlinear microresonator designs that utilize nonlinear modal interaction for application in angular rate sensing. This dissertation specifically looks at the application of nonlinear 2:1 internal resonance, as an actuation mechanism, in micro-electro-mechanical (MEMS) gyroscopes to measure angular input rate. Many MEMS Coriolis vibratory gyroscopes work based on matching the drive- and sense-mode frequencies. The mode-tuning condition cannot be preserved without sophisticated control electronics, due to inevitable fabrication defects and fluctuations in drive parameters. The proposed principle of operation can eliminate the mode-matching requirement in conventional MEMS gyroscopes, and widen the operational frequency region with, ultimately, high flat-top signals. Moreover, it reduces the common problem in MEMS gyroscopes known as cross-coupling by moving the drive mode away from the sense mode of operation. In this thesis, we suggest and develop two microresonator designs in form of frame-shaped and H-shaped microdevices. The proposed microresonators resembled the nonlinear dynamics of spring-pendulum mechanism with forced and 2:1 internal resonances. The reduced-order modeling software was employed to design and characterize the nonlinear microresonators through comprehensive transient simulations. The simulation results revealed the sensitivity of the microresonators to the angular input rate while probing the 2:1 internal resonance. The designed microresonators were fabricated in a foundary process and tested to investigate the nonlinear modal interaction between the vibrational modes. The lumped mass-spring-damper models of the microdevice with electrostatic actuation and detection mechanism were derived and studied via two-variable expansion perturbation technique. Qualitative agreement between experiments and simulations was confirmed for both microresonators with distinct frequency ratios. Finally, the H-shaped microresonator, with closer frequency ratio to 2:1 and better nonlinear features, was mounted on the rate table for the performance evaluation. The experimental findings implied a full-scale range of sensitivity between 0 to 220 deg sec-1. This work as a proof of concept showed that the output voltage of the microresonator linearly changed with an increase in the applied angular rates. This research proposed an alternative actuation mechanism that can provide new avenues to develop the next generation of nonlinear MEMS gyroscopes.