A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz.
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| Title: | A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz. |
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| Authors: | Ma, Lixia1,2,3 (AUTHOR), Zhou, Qiang4 (AUTHOR), Yi, Lijun1,2 (AUTHOR) yilijun@nbu.edu.cn, Wang, Ji1 (AUTHOR) |
| Source: | Applied Mathematics & Mechanics. Jun2025, Vol. 46 Issue 6, p1089-1106. 18p. |
| Subjects: | Crystal oscillators, Crystal resonators, Quartz crystals, Finite element method, Azimuth, Quartz |
| Abstract: | This study presents a closed-form solution for central stress, a semi-analytical model, and a modified anisotropic semi-analytical model to efficiently calculate the force-frequency coefficients (FFCs) of square quartz crystal resonators (QCRs) with different side lengths and azimuth angles under eccentrically concentrated and distributed loads. The semi-analytical model is validated by comparisons between the experimental results and the nonlinear finite element method (FEM) simulation results. Based on the semi-analytical model for the FFC and nonlinear FEM simulations, the FFC variations of square QCRs under external loads and the related mechanisms are investigated. Among the initial stresses caused by external loads, the central stress parallel to the x-crystallographic axis is the primary factor influencing the FFC of quartz. Our findings can provide practical tools for calculating the FFC, and help the design and development of square quartz force sensors. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 185620358 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ma%2C+Lixia%22">Ma, Lixia</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhou%2C+Qiang%22">Zhou, Qiang</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yi%2C+Lijun%22">Yi, Lijun</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> yilijun@nbu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Ji%22">Wang, Ji</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Mechanics%22">Applied Mathematics & Mechanics</searchLink>. Jun2025, Vol. 46 Issue 6, p1089-1106. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Crystal+oscillators%22">Crystal oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Crystal+resonators%22">Crystal resonators</searchLink><br /><searchLink fieldCode="DE" term="%22Quartz+crystals%22">Quartz crystals</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Azimuth%22">Azimuth</searchLink><br /><searchLink fieldCode="DE" term="%22Quartz%22">Quartz</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study presents a closed-form solution for central stress, a semi-analytical model, and a modified anisotropic semi-analytical model to efficiently calculate the force-frequency coefficients (FFCs) of square quartz crystal resonators (QCRs) with different side lengths and azimuth angles under eccentrically concentrated and distributed loads. The semi-analytical model is validated by comparisons between the experimental results and the nonlinear finite element method (FEM) simulation results. Based on the semi-analytical model for the FFC and nonlinear FEM simulations, the FFC variations of square QCRs under external loads and the related mechanisms are investigated. Among the initial stresses caused by external loads, the central stress parallel to the x-crystallographic axis is the primary factor influencing the FFC of quartz. Our findings can provide practical tools for calculating the FFC, and help the design and development of square quartz force sensors. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10483-025-3255-6 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1089 Subjects: – SubjectFull: Crystal oscillators Type: general – SubjectFull: Crystal resonators Type: general – SubjectFull: Quartz crystals Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Azimuth Type: general – SubjectFull: Quartz Type: general Titles: – TitleFull: A semi-analytical model and mechanism analysis for force-frequency effect and coefficient of square quartz. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ma, Lixia – PersonEntity: Name: NameFull: Zhou, Qiang – PersonEntity: Name: NameFull: Yi, Lijun – PersonEntity: Name: NameFull: Wang, Ji IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02534827 Numbering: – Type: volume Value: 46 – Type: issue Value: 6 Titles: – TitleFull: Applied Mathematics & Mechanics Type: main |
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