Modeling and dynamics of micromechanical oscillators

Micromechanical oscillators, due to their small mass and low damping, display a rich range of behavior rarely seen in macroscopic structures. Examples include multiple parametric resonances, optically driven limit cycles, entrainment, tunability, super- and sub- harmonic resonances. These devices have potential applications in signal processing, pattern recognition and mass sensing to name a few. This thesis is an attempt to build accurate models for micromechanical oscillators. A first principle (continuum) approach is adopted to model these oscillators (primarily using ideas from continuum mechanics). We use the resulting models to analyze and study the dynamics of these oscillators.; In the first part of this thesis, we report a thermally induced transition in the resonant response of the first translation mode in a prestressed doubly-clamped beam. To understand this transition, the mode of the beam is modeled using an ODE model that captures mechanical and thermal aspects of the problem. Finite element and nonlinear mechanics approaches are used to extract parameters of the model. Perturbative and numerical approaches are then used to analyze the model developed. It is found in this work that the detection mechanism can play a very crucial role in the dynamics of micromechanical oscillators. Since micron-scaled devices have very low mass and damping, the detection mechanism alters the dynamics in profound and sometimes counter-intuitive ways.; In the second part of the thesis we propose a feasible approach to building coupled micromechanical oscillators. We pick dome oscillators as an example. A model for these oscillators is built by performing a Galerkin projection on the governing von Karman equations. We then perform a bifurcation analysis of the model and study the ability of coupled oscillators to synchronize. This work forms the first steps to analyze the feasibility of making resonant clock networks, data storage devices and neurocomputers.; Even though we have picked particular examples of oscillators to model and study, the overall approach, numerical and perturbative methods used are more encompassing in their applications. Further, similar micromechanical oscillators are expected to have similar dynamics. The main message we want the reader to take away is that without accurate models of micromechanical oscillators important dynamics may be missed; which can be detrimental for design and usability purposes.