Effects of mass layer dimension on a finite quartz crystal microbalance

Y. P. Kong; J. X. Liu; H. J. He; J. S. Yang

doi:10.1007/s00707-011-0522-y

Effects of mass layer dimension on a finite quartz crystal microbalance

Y. P. Kong, J. X. Liu, H. J. He, J. S. Yang

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Abstract

In this paper, we investigate free thickness-shear and thickness-twist vibrations of a finite crystal resonator ofAT-cut quartz carrying a thin mass layer at the central portion of its top surface operating as a quartz crystal microbalance. The equations of anisotropic elasticity are used with the omission of the small elastic constant c₅₆. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes and vibration confinement by the mass layer are calculated and examined.

Original language	English (US)
Pages (from-to)	103-113
Number of pages	11
Journal	Acta Mechanica
Volume	222
Issue number	1-2
DOIs	https://doi.org/10.1007/s00707-011-0522-y
State	Published - Nov 2011
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments This work is supported by the National Natural Science Foundation of China (Foundation No. 10972147), the Natural Science Foundation of Hebei Province, China (Foundation No. A2010001052), and the Program for Changjiang Scholars and Innovative Research Team in University.

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AU - Liu, J. X.

AU - He, H. J.

AU - Yang, J. S.

N1 - Funding Information: Acknowledgments This work is supported by the National Natural Science Foundation of China (Foundation No. 10972147), the Natural Science Foundation of Hebei Province, China (Foundation No. A2010001052), and the Program for Changjiang Scholars and Innovative Research Team in University.

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N2 - In this paper, we investigate free thickness-shear and thickness-twist vibrations of a finite crystal resonator ofAT-cut quartz carrying a thin mass layer at the central portion of its top surface operating as a quartz crystal microbalance. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes and vibration confinement by the mass layer are calculated and examined.

AB - In this paper, we investigate free thickness-shear and thickness-twist vibrations of a finite crystal resonator ofAT-cut quartz carrying a thin mass layer at the central portion of its top surface operating as a quartz crystal microbalance. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes and vibration confinement by the mass layer are calculated and examined.

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Effects of mass layer dimension on a finite quartz crystal microbalance

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