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|Title: ||Characterization of electrostatically actuated micromechanical devices based on Von Karman type geometric nonlinearity|
|Other Titles: ||Ji yu Feng Kaman ji he fei xian xing de jing dian qu dong wei ji dian zhuang zhi te xing yan jiu|
|Authors: ||Jia, Xiaoli ( 賈曉麗)|
|Department: ||Department of Building and Construction|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2011|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Microelectromechanical systems.|
Von Kármán equations.
|Notes: ||CityU Call Number: TK7875 .J53 2011|
xxiii, 164 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2011.
Includes bibliographical references (leaves 138-158)
|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
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
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.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b4086353|
|Appears in Collections:||BC - Doctor of Philosophy |
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