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Investigation of the Mechanical Behavior of Microbeam-Based MEMS Devices
Younis, Mohammad Ibrahim
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An investigation into the responses of microbeams to electric actuations is presented. Attention is focused mainly on the use of microbeams in two important MEMS-based devices: capacitive microswitches and resonant microsensors. Nonlinear models are developed to simulate the behavior of the microbeams in each device. The models account for mid-plane stretching, an applied axial load, a DC electrostatic force, and, for the case of resonant sensors, an AC harmonic force. Further, a novel method that uses a reduced-order model is introduced for simulating the behavior of microbeams under a DC electrostatic force. The presented method shows attractive features, like for example, a high stability near the pull-in and a low computational cost. Thus, it can be of significant benefit to the development of MEMS design software. The static behavior of microbeams under electrostatic forces is studied using two methods. One method employs a shooting technique for solving the boundary-value problem that governs the static behavior. The second method is based on solving an algebraic system of equations obtained from the reduced-order model. Further, the eigenvalue problem describing the vibrations of a microbeam around its statically deflected position is solved using a shooting method to obtain the microbeam mode shapes and natural frequencies. The dynamic behavior of resonant microbeams is also investigated. A perturbation method, the method of multiple scales, is used to obtain two first-order nonlinear ordinary-differential equations that describe the amplitude and phase of the response and its stability. The results show that an inaccurate representation of the system nonlinearities may lead to an erroneous prediction of the nonlinear resonance frequency of a microbeam. The case of three-to-one internal resonance between the lowest two modes is treated. Finally, the reduced-order model is used to study the dynamic behavior of the electrostatically actuated microbeams. The proposed models are validated by comparing their results with experimental results available in the literature.
- Masters Theses