Characterization of electrostatically actuated micromechanical devices based on Von Karman type geometric nonlinearity

Abstract

This thesis presents a study on the nonlinear characteristics of the typical Micro-Electro-Mechanical Systems (MEMS) devices, accounting for coupling of geometric nonlinearity, electro-mechanical nonlinear effects, intermolecular force, axial residual stress, ground electrode shape and material composition. From an extensive literature review, it is one of the first few studies that the global analyses of the influence of physical parameters and geometric factors are conducted on the MEMS devices. Numerous studies on MEMS devices have been reviewed to present a comprehensive view of the origin and development of this study. Several typical MEMS models and investigations are introduced to demonstrate their contributions and deficiencies. To give an extensive and intensive research on the static and dynamic attributes of the MEMS devices, a relatively complete, simplified and yet practical model, micro-beam model based on the parallel-plate capacitor theory, is built to take geometric nonlinearity, electric field force, intermolecular force, axial residual stress, ground electrode shape and material composition into consideration. The principle of virtual work is used to derive the nonlinear static and dynamic governing differential equation and the corresponding boundary conditions for micro-beams with three different boundaries, i.e. clamped-clamped (C-C), clamped-simply supported (C-S) and simply supported (S-S), on the basis of Euler-Bernoulli beam theory with von Karman type nonlinear kinematics. Then the differential quadrature (DQ) method is employed to study the pull-in instability of MEMS devices. The solutions are validated through direct comparisons with experimental and other existing results. A parametric study is conducted, focusing on the combined effects of geometric nonlinearity, gap ratio, slenderness ratio, Casimir force, axial residual stress and ground electrode shape on the pull-in voltage and pull-in deflection. The free vibration of the MEMS devices under combined electrostatic, intermolecular forces and axial residual stress, with an emphasis on the effect of geometrically nonlinear deformation and the influence of Casimir force is investigated. The natural frequencies and mode shapes of micro-beams for different boundary conditions are obtained using the DQ method, which are verified with published experimental results. The significant effects of geometric nonlinearity, Casimir force, axial residual stress, ground electrode shape and material composition for the natural frequencies are summarized and discussed in the parametric study. Based on the above research, the thesis presents an analytical study on the principal resonance of electrically actuated micro-beams near fundamental frequency response region, accounting for the geometric nonlinearity, intermolecular force, axial residual stress, and fringing field effect. The applied voltage is time-varying with a DC component and a small AC component. The perturbation-based method of averaging is employed to solve the nonlinear partial differential governing equations and to obtain the resonance frequency responses of the amplitude and phase of MEMS devices for different boundary conditions. The present analysis is validated through direct comparisons with published experimental results and excellent agreement has been achieved. A parametric study is conducted to show the effects of geometric nonlinearity, the electrostatic force due to DC voltage, the AC voltage induced harmonic force, the quality factor, axial residual stress and ground electrode shape on the frequency response characteristics. For an MEMS device made of a single layer material, it is almost impossible to simultaneously meet all material and operational requirements. To this end, this thesis established a micro-electro-mechanical beam model made of non-homogeneous functionally graded materials (FGM) with two material phases-germanium (Ge) and silicon (Si). The pull-in instability, free vibration and resonance response characteristics are investigated. A parametric study is presented to highlight the effect of distribution of component materials. In this comprehensive study, the static and dynamic characteristics of the MEMS devices on the basis of the beam model are systematically investigated. Remarks and directions for future works are given in conclusion.

Date of Award	15 Jul 2011
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Sritawat KITIPORNCHAI (Supervisor)