Thickness-Shear Mode Shapes and Mass-Frequency Influence Surface of a Circular and Electroded AT-Cut Quartz Resonator

Yong Kong Yong, Jacques Détaint, Albert Zarka, Bernard Capelle, Yunlin Zheng, James T. Stewart

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 plates 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.

Original languageEnglish (US)
Pages (from-to)609-617
Number of pages9
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number5
StatePublished - Sep 1992

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Thickness-Shear Mode Shapes and Mass-Frequency Influence Surface of a Circular and Electroded AT-Cut Quartz Resonator'. Together they form a unique fingerprint.

Cite this