On the mechanics and stability of micro-plates in electrically loaded MEMS devices

In the last decades, Micro-Electro-Mechanical Systems (MEMS) have drawn immense attention due to their potential use in a wide variety of modern applications, including micro-mechanical sensors and actuators. MEMS are devices combining mechanical and electrical components between 1 and 100 micrometers, all integrated into a single chip. The performance of these devices hinges on the deflection and movement of these micro-mechanical components and clearly, improvement and innovation of MEMS require a comprehensive knowledge and in-depth understanding of the nonlinear mechanics of these components.In spite of the simple geometry of common micro-mechanical components, modeling the mechanics of micro-mechanical sensors and actuators is rather complex. In particular, the mechanics of micro-plates in electrostatic MEMS is entangled with two influential sources of nonlinearity namely, geometrical nonlinearity and the nonlinearity due to the presence of the electric field. These sources of nonlinearity are often the origin of instability and failure in MEMS devices, but might also be exploited to achieve, for example, higher sensitivity in the device. In either way, such nonlinearities shall be incorporated in the modeling and design of these micro-mechanical components. This thesis provides an investigation on nonlinear mechanics of micro-plates in electrostatic MEMS devices. Based on the proposed models, we are able to predict some phenomena in micro-plates that have not been noticed before and to study these aspects in a detailed level which was not possible previously. In particular, based on total potential energy and a Lagrangian approach, the nonlinear mechanics and stability of a clamped circular micro-plate in interaction with an electrostatic field is studied. The effects of different loading conditions (i.e. static and dynamic electric potential, and with or without the presence of a differential pressure) on the stability of such a system are addressed. The results of this study suggest that in presence of a differential pressure the steady-state motion of an electrically actuated micro-plate can be bi-stable or even multi-stable. In fact, a differential pressure can cause additional limit points and an unstable solution branch in the -static or dynamic- steady state solutions of the system. Saddle-node and period doubling bifurcations are repeatedly observed in the results and are recognized as main mechanisms of pull-in. Furthermore, one newly observed critical point in static loading is shown to be highly sensitive to the applied differential pressure suggesting the possibility of employing this limit point for sensing applications.In addition, this thesis provides a study on analyzing nano-plates within the framework of continuum mechanics. In this regard, the nonlinear vibrations of an electrically actuated graphene resonator is modeled and a methodology is proposed for characterization of its mechanical properties. In addition, the possibility of capturing the scaling effects in the mechanical behavior of nano-plates by employing a nonlocal continuum theory is addressed. As a result, two modification factors for the extensional and bending stiffness of nano-plates are presented to account for the effect of thickness in the nonlocal elasticity formulations. Finally, the mechanical performance and instability of a micro-plate as a transducer in surface stress sensing is investigated and an optimized design for such a sensor is proposed. It is shown that using the proposed optimized design, the sensitivity and overall reliability of such capacitive surface stress sensors can be significantly improved. The proposed techniques for modeling the mechanics of micro-plates in MEMS devices are simple and computationally efficient. They can provide in-depth insight into MEMS behavior and can be useful for designing MEMS with plate-like micromechanical components.Structural Optimization and Mechanic