title: Thickness-shear mode shapes and mass-frequency influence surface of a circular and electroded AT-cut quartz resonator.
abstract: 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.
authors.affiliation: Rutgers Univ., Piscataway, NJ.
authors.forename: Y K
authors.initials: YK
authors.lastname: Yong
authors.forename: J T
authors.initials: JT
authors.lastname: Stewart
authors.forename: J
authors.initials: J
authors.lastname: Detaint
authors.forename: A
authors.initials: A
authors.lastname: Zarka
authors.forename: B
authors.initials: B
authors.lastname: Capelle
authors.forename: Y
authors.initials: Y
authors.lastname: Zheng