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From Analysis of Piezoelectric Devices
7.3. A Beam BimorphAn electric field in a piezoelectric material causes strain but not curvature. Therefore, in the previous two sections, different electric fields on opposite sides of a beam are needed to produce flexure. Another way of producing flexure in a beam is to use a bimorph. Consider the gyroscope shown in Fig. 7.3.1 [80]. Fig. 7.3.1: A ceramic bimorph piezoelectric gyroscope. The part in 0< x 1< a 1 is the driving portion and a 1< x 1< l is the receiving or sensing portion. The polarizations in the two layers are opposite. When a driving voltage V 1 is applied across the electrodes at x 3= c, one layer extends while the other contracts due to switched polarizations. This allows the beam to be driven into the lowest flexural mode in the x 3 direction with a proper driving frequency. If the beam is rotating about the x 1-axis with a constant angular rate ?, the Coriolis force causes a flexural motion in the x 2 direction. This Coriolis force generated flexure produces a voltage V 2 in the receiving portion which can be picked up by the sensing electrodes. Flexure in the x 3 direction alone does not cause any output voltage. 7.3.1. Governing equationsTo obtain one-dimensional equations for the elementary (classical) flexural motion of the gyroscope, we begin with the following approximations of the three-dimensional mechanical displacement and electric potential:
Copyright World Scientific Publishing Co. Pte. Ltd. 2006 under license agreement with Books24x7
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Topics of Interest
7.4. An Inhomogeneous Shell
Consider the two modes of a circular cylindrical shell of radius R, length l, and thickness h shown in Fig. 7.4.1. The bottom of the shell is fixed and the top is free.
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7.8. A Ceramic Plate by Zero-Dimensional Equations
In this section we analyzed the ceramic plate gyroscope in the previous section using zero-dimensional equations of a piezoelectric parallelepiped...
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7.7. A Ceramic Plate by Two-Dimensional Equations
Consider a rectangular ceramic plate poled in the thickness direction as shown in Fig. 7.7.1 [84].
Fig. 7.7.1: A ceramic plate piezoelectric...
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7.6. A Concentrated Mass and Ceramic Rods
In this section we study probably the simplest gyroscope [83, 10]. Consider a concentrated mass M connected to two thin rods of polarized ceramics as shown...
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