title: Parametric Excitation of Coupled Nonlinear Microelectromechanical Systems
Creators: name: Barakat Mosaad, Ahmed AbdelMonem
Publisher: name: UNSPECIFIED
Year: 2023

description: The commencement of the semi-conductor industry in the second half of the last century gave a surprising new outlook for engineered dynamical mechanical systems. It enabled, thanks to the continuously evolving microfabrication methods, the implementation of Micro Electromechanical systems (MEMS) followed by their nano-counterpart or NEMS. Nowadays M/NEMS constitute a massive portion of the small-scaled sensors industry, in addition to electrical, optical and telecommunication components. Since these tiny dynamical electromechanical systems involve sometimes couplings between degrees of freedom as well as nonlinearities, the theory of stability in dynamical systems plays a significant role in their design and implementation. From a practical point of view, the approach to stability problems often takes two different perspectives. The first one, most commonly in linear systems, aims to avoid any instability which could cause destructive consequences for mechanical structures or for electrical and electronic components. On the contrary in nonlinear systems, the second perspective aims to drive the system into regions of instability for the trivial solution, while searching for stable nontrivial steady-state solutions of the underlying differential equations. With the advent of micro and nanosystems, the second perspective could acquire increased importance. This is attributed to their capability to exhibit typical nonlinear behavior and higher amplitudes at normal operation conditions, when compared to macroscale systems. Higher amplitudes, in this sense, allows for a better amplification of an input excitation, and thereby higher sensitivity for miniature sensors and measurement devices. In addition, if the system parameters were time-periodic, the trivial solution could turn to be unstable at the so called parametric resonances. Known as parametric pumping in micro and nanosystems, the system’s response is usually amplified at these resonance frequencies for higher sensitivity and accuracy. For these reasons, this work is mainly focused on parametrically excited nonlinear systems. Nevertheless, a systematic approach is followed in this thesis, where the origins of destabilization are surveyed in time-invariant systems before proceeding to carry out a theoretical study on time-periodic systems in general, and time-periodic nonlinear systems in particular. Through this theoretical study, a novel idea for the M/NEMS industry is presented, namely the broadband parametric amplification using a bimodal excitation method. This idea is then implemented in microsystems, by investigating a particular example, that is the microgyorscope. Given the low-cost of this device in comparison with other inertial sensors, it is being currently enhanced to reach a relatively higher sensitivity and accuracy. To this end, the theoretical findings, including the mentioned idea, are implemented in this device and prove to contribute effectively to its performance. Moreover, an experimental investigation is carried out on an analogous microsystem. Through the experimental study, an electronic system is introduced to apply the proposed bimodal parametric excitation method on the microsystem. By comparing the stability charts in theory and experiment, the theoretical model could be validated. In conclusion, a theoretical study is carried out through this work on parametrically excited nonlinear systems, then implemented on microgyroscopes, and finally experimentally validated. Thereby, this work puts a first milestone for the utilization of the proposed excitation method in the M/NEMS industry.