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Analytical Free Vibration Solutions of Rectangular Thin Plates Subjected to Three Edges Rotationally-Restrained and One Edge Free.

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Title: Analytical Free Vibration Solutions of Rectangular Thin Plates Subjected to Three Edges Rotationally-Restrained and One Edge Free.
Authors: Zhang, Jinghui1,2 (AUTHOR), Gao, Pin2 (AUTHOR), Diao, Xingjian3 (AUTHOR), Ullah, Salamat4 (AUTHOR), Li, JiaPeng5 (AUTHOR), Zhang, Yuwei6 (AUTHOR), Qi, Wenyue1,2 (AUTHOR) wenyueqi@ysu.edu.cn
Source: International Journal of Structural Stability & Dynamics. 2/15/2026, Vol. 26 Issue 5, p1-27. 27p.
Subjects: Free vibration, Rectangular plates (Engineering), Integral transforms, Analytical solutions, Boundary value problems, Computer simulation, Isotropic properties
Abstract: Due to the challenges in mathematical solving, accurate analytical solutions for rectangular thin plates are mainly limited to these plates subject to simple Lévy-type boundary conditions (BCs). Conversely, plates with more complicated BCs are more frequently encountered in practical engineering applications. This study employs the finite integral transform method to analyze the free vibration behavior of isotropic rectangular thin plates with three edges rotationally-restrained and one edge free, which is difficult for other methods. Primarily, the method adopted eliminates the necessity for predetermining trial function for plate deflection, offering simplicity and generality for plate mechanical problems. Furthermore, the approach establishes one way to allow one solving linear algebraic equations instead of handling complex boundary value problems of higher-order vibration partial differential equation (PDE), resulting precise and rapidly converging analytical solutions. Finally, new accurate free vibration studies for plates with four non-Lévy-type BCs and three non-classical BCs are presented via altering the introduced rotating fixed coefficients. The results obtained are contrasted with the numerical simulations from ABAQUS software and existing literature works, confirming the accuracy of this method and providing benchmark results for further exploration of free vibration problems of rectangular plates. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Structural Stability & Dynamics is the property of World Scientific Publishing Company 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: 191103696
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Label: Title
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  Data: Analytical Free Vibration Solutions of Rectangular Thin Plates Subjected to Three Edges Rotationally-Restrained and One Edge Free.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Jinghui%22">Zhang, Jinghui</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Gao%2C+Pin%22">Gao, Pin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Diao%2C+Xingjian%22">Diao, Xingjian</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ullah%2C+Salamat%22">Ullah, Salamat</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+JiaPeng%22">Li, JiaPeng</searchLink><relatesTo>5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yuwei%22">Zhang, Yuwei</searchLink><relatesTo>6</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Qi%2C+Wenyue%22">Qi, Wenyue</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> wenyueqi@ysu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Structural+Stability+%26+Dynamics%22">International Journal of Structural Stability & Dynamics</searchLink>. 2/15/2026, Vol. 26 Issue 5, p1-27. 27p.
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  Data: <searchLink fieldCode="DE" term="%22Free+vibration%22">Free vibration</searchLink><br /><searchLink fieldCode="DE" term="%22Rectangular+plates+%28Engineering%29%22">Rectangular plates (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+transforms%22">Integral transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Isotropic+properties%22">Isotropic properties</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Due to the challenges in mathematical solving, accurate analytical solutions for rectangular thin plates are mainly limited to these plates subject to simple Lévy-type boundary conditions (BCs). Conversely, plates with more complicated BCs are more frequently encountered in practical engineering applications. This study employs the finite integral transform method to analyze the free vibration behavior of isotropic rectangular thin plates with three edges rotationally-restrained and one edge free, which is difficult for other methods. Primarily, the method adopted eliminates the necessity for predetermining trial function for plate deflection, offering simplicity and generality for plate mechanical problems. Furthermore, the approach establishes one way to allow one solving linear algebraic equations instead of handling complex boundary value problems of higher-order vibration partial differential equation (PDE), resulting precise and rapidly converging analytical solutions. Finally, new accurate free vibration studies for plates with four non-Lévy-type BCs and three non-classical BCs are presented via altering the introduced rotating fixed coefficients. The results obtained are contrasted with the numerical simulations from ABAQUS software and existing literature works, confirming the accuracy of this method and providing benchmark results for further exploration of free vibration problems of rectangular plates. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Structural Stability & Dynamics is the property of World Scientific Publishing Company 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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        Value: 10.1142/S0219455425502669
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        Text: English
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        PageCount: 27
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      – SubjectFull: Free vibration
        Type: general
      – SubjectFull: Rectangular plates (Engineering)
        Type: general
      – SubjectFull: Integral transforms
        Type: general
      – SubjectFull: Analytical solutions
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      – SubjectFull: Boundary value problems
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      – SubjectFull: Computer simulation
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      – SubjectFull: Isotropic properties
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      – TitleFull: Analytical Free Vibration Solutions of Rectangular Thin Plates Subjected to Three Edges Rotationally-Restrained and One Edge Free.
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            NameFull: Zhang, Jinghui
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              M: 02
              Text: 2/15/2026
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              Y: 2026
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