| Today, Micro-Electro-Mechanical Systems (MEMS) applications exist in all areas of a person's home-electronics, communication, entertainment, automobile, office supplies, medical care etc. Its market is growing dramatically with more and more successfully developed commercial MEMS devices. Typically, MEMS consist of integrated microstructures (usually beams or plates) that are suspended and anchored, or captured and set into motion by mechanical, electrical, thermal, magnetic acoustical or photonic energy sources. Accurate and efficient design and simulation of those microstructures will be one of the key driving forces for this astonishing technology. This dissertation addresses electrostatic actuation, but the methods and techniques developed should be applicable to similar forms of actuation like acoustic or magnetic actuation in an analogous manner.; Numerical simulation of electrically actuated MEMS devices with microstructures has been carried out for around a decade or so. The electrical and mechanical domains are coupled through electrostatic actuation and require a hybrid multi-physics approach. This dissertation addresses a fully Lagrangian approach to the coupled problem by employing the Finite Element Method (FEM) to analyze mechanical deformation in the elastic conducting structures and the Boundary Element Method (BEM) to obtain the electric field in the region exterior to the conductors, Self-consistent solutions are obtained with the use of both the relaxation approach and Newton's method. Severe problems arise with the charge density computation of MEMS made of plates with high aspect ratio geometries using the BEM. An approach suitable for BEM analysis of the electric field in a region exterior to thin beam shaped or thin plate shaped conductors is formulated and used for the coupled analysis in this work.; Most MEMS devices used today are limited in operation by inherent instability present in these systems. This instability named "Pull-In" instability by Nathanson, occurs when the voltage applied to the system exceeds a critical value. Beyond this critical value there is no longer a stable steady state configuration of the device where mechanical members remain separate. The above coupled FEMBEM approach is used to predict the pull-in behavior of MEMS made of flexible conducting plates. Since MEMS often are encapsulated in a fluid medium, any realistic simulation of dynamic behavior must take into account the forces generated by the surrounding fluid medium. This is a challenging task as the fluid medium of interest is exterior to these thin conducting plates and usually extends to infinity. A new formulation for fluid force computation for such structures is developed and shown to be accurate and stable even for very high geometric aspect ratios. Finally, several possible extensions of current work like the use of Fast Multipole Method (FMM) have been pointed out in the conclusions chapter. |
