Thickness-shear and thickness-twist vibrations of an AT-Cut quartz mesa resonator

Huijing He; Jinxi Liu; Jiashi Yang

doi:10.1109/TUFFC.2011.2055

Thickness-shear and thickness-twist vibrations of an AT-Cut quartz mesa resonator

Huijing He, Jinxi Liu, Jiashi Yang

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We study thickness-shear and thickness-twist vibrations of an AT-cut quartz plate mesa resonator with stepped thickness. The equations of anisotropic elasticity are used with the omission of the small elastic constant c ₅₆. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and energy trapping are calculated and examined. The solution shows that a mesa resonator exhibits strong energy trapping of thickness-shear and thickness-twist modes, and that the trapping is sensitive to some of the structural parameters of the resonator.

Original language	English (US)
Article number	6039995
Pages (from-to)	2050-2055
Number of pages	6
Journal	IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Volume	58
Issue number	10
DOIs	https://doi.org/10.1109/TUFFC.2011.2055
State	Published - Oct 2011
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received March 15, 2011; accepted July 17, 2011. This work was supported by the national nature science Foundation of china (no. 10972147) and the Program for changjiang scholars and Innovative research Team in University (no. IrT0971).

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title = "Thickness-shear and thickness-twist vibrations of an AT-Cut quartz mesa resonator",

abstract = "We study thickness-shear and thickness-twist vibrations of an AT-cut quartz plate mesa resonator with stepped thickness. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and energy trapping are calculated and examined. The solution shows that a mesa resonator exhibits strong energy trapping of thickness-shear and thickness-twist modes, and that the trapping is sensitive to some of the structural parameters of the resonator.",

author = "Huijing He and Jinxi Liu and Jiashi Yang",

note = "Funding Information: Manuscript received March 15, 2011; accepted July 17, 2011. This work was supported by the national nature science Foundation of china (no. 10972147) and the Program for changjiang scholars and Innovative research Team in University (no. IrT0971).",

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AU - He, Huijing

AU - Liu, Jinxi

AU - Yang, Jiashi

N1 - Funding Information: Manuscript received March 15, 2011; accepted July 17, 2011. This work was supported by the national nature science Foundation of china (no. 10972147) and the Program for changjiang scholars and Innovative research Team in University (no. IrT0971).

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N2 - We study thickness-shear and thickness-twist vibrations of an AT-cut quartz plate mesa resonator with stepped thickness. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and energy trapping are calculated and examined. The solution shows that a mesa resonator exhibits strong energy trapping of thickness-shear and thickness-twist modes, and that the trapping is sensitive to some of the structural parameters of the resonator.

AB - We study thickness-shear and thickness-twist vibrations of an AT-cut quartz plate mesa resonator with stepped thickness. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and energy trapping are calculated and examined. The solution shows that a mesa resonator exhibits strong energy trapping of thickness-shear and thickness-twist modes, and that the trapping is sensitive to some of the structural parameters of the resonator.

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ER -

Thickness-shear and thickness-twist vibrations of an AT-Cut quartz mesa resonator

Abstract

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