A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates

Ji Wang; Yang Yang Chen; Rong Xing Wu; Li Hong Wang; Hui Min Jing; Jian Ke Du; Yuan Tai Hu; Guo Qing Li

doi:10.1109/SPAWDA.2011.6167259

A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates

Ji Wang^*, Yang Yang Chen, Rong Xing Wu, Li Hong Wang, Hui Min Jing, Jian Ke Du, Yuan Tai Hu, Guo Qing Li

^*Corresponding author for this work

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

1 Citation (Scopus)

Abstract

We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorisms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations. We considered both kinematic and material nonlinearities in vibrations analyses, and obtained the frequency-amplitude relations. We also compared distributions of the thickness-shear deformation at different amplitudes. This nonlinear finite element software can be further improved to study nonlinear phenomena arising from miniaturized quartz crystal resonators.

Original language	English
Title of host publication	Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011
Pages	339-343
Number of pages	5
DOIs	https://doi.org/10.1109/SPAWDA.2011.6167259
Publication status	Published - 2011
Externally published	Yes
Event	2011 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, SPAWDA 2011 - Shenzhen, Guangdong, China Duration: 9 Dec 2011 → 11 Dec 2011

Publication series

Name	Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011

Conference

Conference	2011 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, SPAWDA 2011
Country/Territory	China
City	Shenzhen, Guangdong
Period	9/12/11 → 11/12/11

Keywords

Finite element method
Mindlin plate theory
Nonlinear
Quartz
Resonators

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10.1109/SPAWDA.2011.6167259

Cite this

Wang, J., Chen, Y. Y., Wu, R. X., Wang, L. H., Jing, H. M., Du, J. K., Hu, Y. T., & Li, G. Q. (2011). A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates. In Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011 (pp. 339-343). Article 6167259 (Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011). https://doi.org/10.1109/SPAWDA.2011.6167259

Wang, Ji ; Chen, Yang Yang ; Wu, Rong Xing et al. / A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates. Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011. 2011. pp. 339-343 (Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011).

@inproceedings{32cf7b5052be467284370621457381e6,

title = "A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates",

abstract = "We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorisms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations. We considered both kinematic and material nonlinearities in vibrations analyses, and obtained the frequency-amplitude relations. We also compared distributions of the thickness-shear deformation at different amplitudes. This nonlinear finite element software can be further improved to study nonlinear phenomena arising from miniaturized quartz crystal resonators.",

keywords = "Finite element method, Mindlin plate theory, Nonlinear, Quartz, Resonators",

author = "Ji Wang and Chen, \{Yang Yang\} and Wu, \{Rong Xing\} and Wang, \{Li Hong\} and Jing, \{Hui Min\} and Du, \{Jian Ke\} and Hu, \{Yuan Tai\} and Li, \{Guo Qing\}",

year = "2011",

doi = "10.1109/SPAWDA.2011.6167259",

language = "English",

isbn = "9781467310789",

series = "Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011",

pages = "339--343",

booktitle = "Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011",

note = "2011 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, SPAWDA 2011 ; Conference date: 09-12-2011 Through 11-12-2011",

}

Wang, J, Chen, YY, Wu, RX, Wang, LH, Jing, HM, Du, JK, Hu, YT & Li, GQ 2011, A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates. in Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011., 6167259, Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011, pp. 339-343, 2011 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, SPAWDA 2011, Shenzhen, Guangdong, China, 9/12/11. https://doi.org/10.1109/SPAWDA.2011.6167259

A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates. / Wang, Ji; Chen, Yang Yang; Wu, Rong Xing et al.
Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011. 2011. p. 339-343 6167259 (Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

TY - GEN

T1 - A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates

AU - Wang, Ji

AU - Chen, Yang Yang

AU - Wu, Rong Xing

AU - Wang, Li Hong

AU - Jing, Hui Min

AU - Du, Jian Ke

AU - Hu, Yuan Tai

AU - Li, Guo Qing

PY - 2011

Y1 - 2011

N2 - We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorisms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations. We considered both kinematic and material nonlinearities in vibrations analyses, and obtained the frequency-amplitude relations. We also compared distributions of the thickness-shear deformation at different amplitudes. This nonlinear finite element software can be further improved to study nonlinear phenomena arising from miniaturized quartz crystal resonators.

AB - We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorisms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations. We considered both kinematic and material nonlinearities in vibrations analyses, and obtained the frequency-amplitude relations. We also compared distributions of the thickness-shear deformation at different amplitudes. This nonlinear finite element software can be further improved to study nonlinear phenomena arising from miniaturized quartz crystal resonators.

KW - Finite element method

KW - Mindlin plate theory

KW - Nonlinear

KW - Quartz

KW - Resonators

UR - https://openalex.org/W1996724953

UR - https://www.scopus.com/pages/publications/84862842267

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DO - 10.1109/SPAWDA.2011.6167259

M3 - Conference Paper published in a book

SN - 9781467310789

T3 - Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011

SP - 339

EP - 343

BT - Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011

T2 - 2011 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, SPAWDA 2011

Y2 - 9 December 2011 through 11 December 2011

ER -

Wang J, Chen YY, Wu RX, Wang LH, Jing HM, Du JK et al. A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates. In Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011. 2011. p. 339-343. 6167259. (Proceedings of the 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications, SPAWDA 2011). doi: 10.1109/SPAWDA.2011.6167259

A nonlinear finite element analysis of high frequency vibrations of quartz crystal plates

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