098 - Vibration of rotating silicon rings excited by electric field - an application to micro-rate sensors
Chang C., Chou C.
Abstract
In order to merge the mechanical sensors and the detecting electrical circuit into a single silicon wafer, we are forced to use the Silicon (100), for the mechanical sensors, rather than the Silicon (111), the latter is closed to isotropic, while the former is highly anisotropic but has the advantage of ease in etching and lower cost. The vibrational equations of the Si (100) ring are a set of partial differential equations in polar coordinates with variable coefficients. We find the exact solutions for the natural frequencies and mode shapes of the exciting and sensing bending modes, these two frequencies are the same for isotropic material, but quite different for anisotropic one. Trough optimization techniques we can reconcile these two natural frequencies by varying the thickness, along the circumference, of a circular ring but still remaining the middle line of the ring being a circle. The purpose of doing so is that we want the amplitude of vibrating sensing mode is not too small to be measured and is close to that of the exciting mode. We excite the ring at the anti-node by capacity-type electric field with frequency equating the natural frequency of the first bending mode. When the ring is set into rotation, the Coriolis force induces the second bending mode, and both the exciting and sensing modes change from originally standing waves to traveling waves. We use the perturbation technique, that is, the method of multiple scales, to find the analytical expression which relates the displacement of the ring at the nodal point to the angular--velocity input. We also employ the phase-lock technique to enhance the amplitude of vibration and find that there exists a critical value of the applied voltage, over that value the vibration amplitude decreases.
Citation
Chang C.; Chou C.: Vibration of rotating silicon rings excited by electric field - an application to micro-rate sensors, CD-ROM Proceedings of the Thirtheenth International Congress on Sound and Vibration (ICSV13), July 2-6, 2006, Vienna, Austria, Eds.: Eberhardsteiner, J.; Mang, H.A.; Waubke, H., Publisher: Vienna University of Technology, Austria, ISBN: 3-9501554-5-7
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