TY - JOUR
T1 - Effects of middle plane curvature on vibrations of a thickness-shear mode crystal resonator
AU - Yang, Jiashi
AU - Yang, Xiaomeng
AU - Turner, Joseph A.
AU - Kosinski, John A.
AU - Pastore, Robert A.
AU - Zhang, Weiping
PY - 2006/12
Y1 - 2006/12
N2 - 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.
AB - 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.
KW - Resonator
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U2 - 10.1016/j.ijsolstr.2006.04.004
DO - 10.1016/j.ijsolstr.2006.04.004
M3 - Article
AN - SCOPUS:33750298278
SN - 0020-7683
VL - 43
SP - 7840
EP - 7851
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 25-26
ER -