Techniques Of Model Order Reduction For The Electrostatically Actuated Microdevices

Using the finite element methods or boundary element methods for Micro-Electro-Mechanical Systems (MEMS) devices simulation require of intensive computational resource for solving the time integration of a very high dimensional of coupled ordinary-differential equations. Even so, those methods are inadequate for MEMS devices optimization, real-time feedback control, and predicting the MEMS dynamical behaviors under system-level simulation. As a result, abstracting lower dimensional systems from these higher dimensional ones while retaining the essence of the physical phenomena as a way to make system-level simulation and optimization is gaining attention and becomes one of the key technologies for MEMS CAD realization. It is also extremely necessary for other engineering applicationsThe objective of this dissertation is to develop an accurate model order reduction (MOR) methods and associated numerical technology which suit for the electrostatic- mechanical coupling microdevices and the electrostatic-mechanical-fluidic coupling microdevices.A systematic review of the state of the MOR for MEMS applications is presented in the first part of the dessertation. Following that, a MOR procedures for the electrostatic-mechanical coupling microdevices is introduced, which uses the undamped modal shape functions of the structural element as a basis function sets for Galerkin projection. The nonlinear characteristics of the electrostatically actuated micorbeam device were probed by using the reduced order model (ROM), and the Pull-in and release dynamic process of the devices were simulated in Simulink(?) environment. After that, The derivation of strain energy and kinetic energy expression based on nonlinear plate theory have been developed, and the formulation of the ROM of an electrostatically actuated micro-plate device has been obtained by using Rayleigh-Ritz method, and a MOR method based on system energy identification has been presented. The simulation results by using the ROM are compared well with those from high-fidelity finite element model under various electric loads, and thus this MOR approach has been validated.Considered that the dynamical behavior of MEMS devices is strongly affected by viscous fluid damping effects from the surrounding, these damping effects have to be carefully accounted for the design and optimization. The ROM of microdevices should have the ability of capturing the fluidic-structural interactions of the microdevice. And the MOR method based on Galerkin projection and subspace angles interpolation technique has been developed. The commercial software ESI-CFD(?) has been used to achieve the full coupling transient results. Subsequently, the global optimal basis functions are extracted from the full-order solution by the application of proper orthogonal decomposition (POD) methods. The nonlinear Euler-Bernoulli beam equation and the nonlinear compressible Reynolds equation are projected on the subspaces spanned by those optimal basis functions, and thus the ROMs have been obtained. Since the constructed ROMs by POD/Galerkin are valid only within a limited state-space, a subspace angles interpolation strategy is introduced to widen the range of electric loads under which the ROMs are applicable. The numerical results of ROMs show good agreement with the ESI-CFD(?) data and the experimental data available in the literature. All those have demonstrated that the ROMs can be used in the place of the full meshed coupling models for various electric loads inputs and device paramenters changing with reduced computational complexity immensely.In the final part of this dissertation, the main conclusions are summarized and the prospects for future research are suggested.