Effects of middle plane curvature on vibrations of a thickness-shear mode crystal resonator

Jiashi Yang, Xiaomeng Yang, Joseph A. Turner, John A. Kosinski, Robert A. Pastore, Weiping Zhang

Research output: Contribution to journalArticlepeer-review


We study the effects of a small curvature of the middle plane of a thickness-shear mode crystal plate resonator on its vibration frequencies, modes and acceleration sensitivity. Two-dimensional equations for coupled thickness-shear, flexural and extensional vibrations of a shallow shell are used. The equations are simplified to a single equation for thickness-shear, and two equations for coupled thickness-shear and extension. Equations with different levels of coupling are used to study vibrations of rotated Y-cut quartz and langasite resonators. The influence of the middle plane curvature and coupling to extension is examined. The effect of middle plane curvature on normal acceleration sensitivity is also studied. It is shown that the middle plane curvature causes a frequency shift as large as 10-8 g-1 under a normal acceleration. These results have practical implications for the design of concave-convex and plano-convex resonators.

Original languageEnglish
Pages (from-to)7840-7851
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number25-26
StatePublished - Dec 2006

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Resonator

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