Dynamics of a beam-based micro-electromechanical resonator is investigated theoretically and experimentally. The resonant structure comprises a micro-beam and two electrostatic comb-drives, one for exciting the vibration, and the other for detecting the response. Two identical resonators of this type can form a double-ended tuning fork.
An analytical linear model of these resonators is developed by assuming the beam to obey the thin beam theory subjected to an axial force. The comb-drives are initially treated as a point mass. The point mass is free to be placed anywhere along the beam span. The exact natural frequencies and mode shapes of vibration are obtained. Further, the mass is considered to have rotary inertia. The influence of the rotary inertia on the natural frequencies and mode shapes of vibration are investigated. Subsequently, the model of a beam with a guided mass is studied to determine the upper limit of the natural frequencies of the resonator. The advantage of this model over the previous ones is in providing detailed insight into the dynamics of the resonator, particularly when the comb-drives are placed at locations other than the mid-point of the beam. It has been shown that the mode shapes of vibration of these resonators are not orthogonal to each other under its classic definition. The orthogonality condition of the mode shapes of the beam-lumped mass system is introduced, and used for studying the forced vibration response.
The nonlinear vibration of the system due to stretching is considered for the case of free vibration and the primary resonance. The nonlinear model is used to investigate the effect of damping on the resonator response.
The interaction of the electrostatic governing equations and the mechanical model is studied. This model is employed for designing the experiment circuits for testing fabricated resonators. The fabrication processes used are explained, and the design parameters of each resonator are provided. The experimental results are reported, and used to find the axial force and stress of the resonant beams.
The model and results of this dissertation can be used in the design of beam-based micromachined resonators for different applications.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/16793 |
| Date | 20 January 2009 |
| Creators | Hassanpour Asl, Pezhman |
| Contributors | Cleghorn, William L., Esmailzadeh, Ebrahim, Mills, James |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 11365530 bytes, application/pdf |
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