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Vibration analysis of bolted cantilever plates using an artificial spring model with contact pressure distribution.

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Title: Vibration analysis of bolted cantilever plates using an artificial spring model with contact pressure distribution.
Authors: Zhang, Xiang1 (AUTHOR), Liu, Wenguang1 (AUTHOR) liuwg14@nchu.edu.cn, Cheng, Long1 (AUTHOR), Lin, Zhigen1 (AUTHOR), Wang, Hong1 (AUTHOR)
Source: Journal of Mechanical Science & Technology. Jan2026, Vol. 40 Issue 1, p133-145. 13p.
Subjects: Mechanical vibration research, Rayleigh-Ritz method, Stiffness (Engineering), Equations of motion, Mode shapes, Stress concentration, Parametric modeling
Abstract: The objective of this study is to analyze the vibration characteristics of bolted cantilever plates using the artificial spring model that accounts for pressure distribution. The dynamic governing equations for a bolted cantilever plate are derived based on the first-order shear deformation theory, with displacement fields represented by Chebyshev polynomials and numerically solved using the Rayleigh–Ritz method. The proposed artificial spring model incorporates non-uniform pressure distribution resulting from bolt preload. The bolted joint contact region is represented by constant stiffness springs, while the bolted joint affected region is characterized by a sinusoidal stiffness variation. The vibration characteristics of the bolted joint plate are systematically investigated through comprehensive case studies and experimental modal analysis. Numerical results demonstrate good agreement between the predicted vibration characteristics and the experimental measurements, with maximum frequency errors below 5 %. Parametric analysis demonstrates that the system's modal frequencies exhibit sensitivity to four bolt parameters: installation configuration, bolt span, bolt number, and bolt head diameter. The proposed model advances conventional linear spring modeling approaches by integrating contact pressure distribution, thereby improving the predictive accuracy of the vibration characteristics of bolted cantilever plates. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mechanical Science & Technology 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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DbLabel: Engineering Source
An: 190982715
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PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: Vibration analysis of bolted cantilever plates using an artificial spring model with contact pressure distribution.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Xiang%22">Zhang, Xiang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Wenguang%22">Liu, Wenguang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liuwg14@nchu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Cheng%2C+Long%22">Cheng, Long</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lin%2C+Zhigen%22">Lin, Zhigen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Hong%22">Wang, Hong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mechanical+Science+%26+Technology%22">Journal of Mechanical Science & Technology</searchLink>. Jan2026, Vol. 40 Issue 1, p133-145. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Mechanical+vibration+research%22">Mechanical vibration research</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh-Ritz+method%22">Rayleigh-Ritz method</searchLink><br /><searchLink fieldCode="DE" term="%22Stiffness+%28Engineering%29%22">Stiffness (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Mode+shapes%22">Mode shapes</searchLink><br /><searchLink fieldCode="DE" term="%22Stress+concentration%22">Stress concentration</searchLink><br /><searchLink fieldCode="DE" term="%22Parametric+modeling%22">Parametric modeling</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The objective of this study is to analyze the vibration characteristics of bolted cantilever plates using the artificial spring model that accounts for pressure distribution. The dynamic governing equations for a bolted cantilever plate are derived based on the first-order shear deformation theory, with displacement fields represented by Chebyshev polynomials and numerically solved using the Rayleigh–Ritz method. The proposed artificial spring model incorporates non-uniform pressure distribution resulting from bolt preload. The bolted joint contact region is represented by constant stiffness springs, while the bolted joint affected region is characterized by a sinusoidal stiffness variation. The vibration characteristics of the bolted joint plate are systematically investigated through comprehensive case studies and experimental modal analysis. Numerical results demonstrate good agreement between the predicted vibration characteristics and the experimental measurements, with maximum frequency errors below 5 %. Parametric analysis demonstrates that the system's modal frequencies exhibit sensitivity to four bolt parameters: installation configuration, bolt span, bolt number, and bolt head diameter. The proposed model advances conventional linear spring modeling approaches by integrating contact pressure distribution, thereby improving the predictive accuracy of the vibration characteristics of bolted cantilever plates. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mechanical Science & Technology 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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      – Type: doi
        Value: 10.1007/s12206-025-1210-5
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 133
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      – SubjectFull: Mechanical vibration research
        Type: general
      – SubjectFull: Rayleigh-Ritz method
        Type: general
      – SubjectFull: Stiffness (Engineering)
        Type: general
      – SubjectFull: Equations of motion
        Type: general
      – SubjectFull: Mode shapes
        Type: general
      – SubjectFull: Stress concentration
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      – SubjectFull: Parametric modeling
        Type: general
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      – TitleFull: Vibration analysis of bolted cantilever plates using an artificial spring model with contact pressure distribution.
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            NameFull: Zhang, Xiang
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            NameFull: Liu, Wenguang
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            NameFull: Cheng, Long
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            NameFull: Lin, Zhigen
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            – D: 01
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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