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

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 39; no. 5; pp. 609 - 617
• Main Authors: Yong, Y.-K., Stewart, J.T., Detaint, J., Zarka, A., Capelle, B., Zheng, Y.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.1992; Institute of Electrical and Electronics Engineers
• Subjects: Anisotropic magnetoresistance; Boundary conditions; Data visualization; Electrodes; Equations; Exact sciences and technology; Fluctuations; Frequency; General equipment and techniques; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Physics; Shape; Surface contamination; Transducers; Two dimensional displays; Finite element method; Visualization; Quartz; Free vibration; Ultrasound; Plate
• DOI: 10.1109/58.156179
• ISSN: 0885-3010

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.< >