TY - JOUR

T1 - An estimate of the second-order in-plane acceleration sensitivity of a Y-cut Quartz thickness-shear resonator

AU - He, Huijing

AU - Yang, Jiashi

AU - Kosinski, John A.

N1 - Publisher Copyright:
© 1986-2012 IEEE.

PY - 2015/8/1

Y1 - 2015/8/1

N2 - We perform a theoretical analysis of the secondorder in-plane acceleration sensitivity of a Y-cut quartz thickness-shear mode resonator. The second-order nonlinear theory of elasticity for anisotropic crystals is used to determine the biasing fields in the resonator under in-plane acceleration. The acceleration-induced frequency shift is determined from a perturbation analysis based on the plate equations for small-amplitude vibrations superposed on a finite bias. We show that, whereas the first-order acceleration-induced frequency shift is zero for a structurally symmetric resonator under in-plane acceleration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants of quartz have never been measured, we can only estimate the magnitude of the second-order frequency shift. For a particular case of interest, we find Δω/ω0~10-18, 10-16, and 10-14 when the acceleration is 1, 10, and 100 g, respectively.

AB - We perform a theoretical analysis of the secondorder in-plane acceleration sensitivity of a Y-cut quartz thickness-shear mode resonator. The second-order nonlinear theory of elasticity for anisotropic crystals is used to determine the biasing fields in the resonator under in-plane acceleration. The acceleration-induced frequency shift is determined from a perturbation analysis based on the plate equations for small-amplitude vibrations superposed on a finite bias. We show that, whereas the first-order acceleration-induced frequency shift is zero for a structurally symmetric resonator under in-plane acceleration, the second-order frequency shift is nonzero and is quadratic in the acceleration. As the fourth-order nonlinear elastic constants of quartz have never been measured, we can only estimate the magnitude of the second-order frequency shift. For a particular case of interest, we find Δω/ω0~10-18, 10-16, and 10-14 when the acceleration is 1, 10, and 100 g, respectively.

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U2 - 10.1109/TUFFC.2015.007033

DO - 10.1109/TUFFC.2015.007033

M3 - Article

AN - SCOPUS:84939229093

SN - 0885-3010

VL - 62

SP - 1421

EP - 1428

JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

IS - 8

M1 - 7185009

ER -