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Thickness-shear mode shapes and mass-frequency influence surface of a circular and electroded AT-cut quartz resonator

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6 Author(s)
Yong, Y.-K. ; Rutgers Univ., Piscataway, NJ, USA ; Stewart, J.T. ; Detaint, J. ; Zarka, A.
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Finite-element solutions for the fundamental thickness shear mode and the second-anharmonic overtone of a circular, 1.87-MHz AT-cut quartz plate with no electrodes are presented and compared with previously obtained results for a rectangular plate of similar properties. The edge flexural mode in circular plates, a vibration mode not seen in the rectangular plate is also presented. A 5-MHz circular and electroded AT-cut quartz plate is studied. A portion of the frequency spectrum is constructed in the neighborhood of the fundamental thickness-shear mode. A convergence study is also presented for the electroded 5-MHz plate. A new two-dimensional (2-D) technique for visualizing the vibration mode solutions is presented. This method departs substantially from the three-dimensional (3-D) 'wire-frame' plots presented in the previous analysis. The 2-D images can be manipulated to produce nodal line diagrams and can be color coded to illustrate mode shapes and energy trapping phenomenon. A contour plot of the mass-frequency influence surface for the plated 5-MHz resonator is presented. The mass-frequency influence surface is defined as a surface giving the frequency change due to a small localized mass applied to the resonator surface.<>

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Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on  (Volume:39 ,  Issue: 5 )