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A novel single-variable third-order shear deformation theory for free vibration of rectangular plates.

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Title: A novel single-variable third-order shear deformation theory for free vibration of rectangular plates.
Authors: Wang, Ya-Wei1 (AUTHOR), Long, Fei1 (AUTHOR), Li, Xian-Fang1 (AUTHOR) xfli@csu.edu.cn
Source: Acta Mechanica. Dec2025, Vol. 236 Issue 12, p7057-7082. 26p.
Subjects: Free vibration, Rectangular plates (Engineering), Shear (Mechanics), Eigenfrequencies, Boundary value problems
Abstract: Although some third-order shear deformation plate theories, including Levinson plate theory (LPT) and Reddy plate theory (RPT), are available, their computational complexity limits their application. Based on LPT, a single-variable third-order shear deformation theory, named the simplified LPT, is proposed by requiring vanishing torsional deformation along the thickness direction. The LPT is described by a sixth-order partial differential equation (PDE), whereas the simplified LPT is described by a fourth-order PDE, similar to that of classical plate theory (CPT). Following the CPT, the twisting moments are converted into shear forces in the boundary conditions of the simplified LPT. To further demonstrate the effectiveness of the simplified LPT, the free vibration analysis of Lévy-type plates is conducted, where two opposite edges are simply supported (or guided) while the remaining two edges are subject to arbitrary boundary conditions. Using the Lévy approach, the natural frequencies based on the CPT, Mindlin plate theory, LPT, RPT, and simplified LPT are compared. The numerical results indicate that the simplified LPT is effective and can be applied to thin, moderately thick, and thick plates. Consideration of shear deformation brings the results of the simplified LPT closer to those of LPT and RPT. [ABSTRACT FROM AUTHOR]
Copyright of Acta Mechanica 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.)
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DbLabel: Engineering Source
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  Data: A novel single-variable third-order shear deformation theory for free vibration of rectangular plates.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Ya-Wei%22">Wang, Ya-Wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Long%2C+Fei%22">Long, Fei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Xian-Fang%22">Li, Xian-Fang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xfli@csu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Dec2025, Vol. 236 Issue 12, p7057-7082. 26p.
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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="%22Shear+%28Mechanics%29%22">Shear (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfrequencies%22">Eigenfrequencies</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Although some third-order shear deformation plate theories, including Levinson plate theory (LPT) and Reddy plate theory (RPT), are available, their computational complexity limits their application. Based on LPT, a single-variable third-order shear deformation theory, named the simplified LPT, is proposed by requiring vanishing torsional deformation along the thickness direction. The LPT is described by a sixth-order partial differential equation (PDE), whereas the simplified LPT is described by a fourth-order PDE, similar to that of classical plate theory (CPT). Following the CPT, the twisting moments are converted into shear forces in the boundary conditions of the simplified LPT. To further demonstrate the effectiveness of the simplified LPT, the free vibration analysis of Lévy-type plates is conducted, where two opposite edges are simply supported (or guided) while the remaining two edges are subject to arbitrary boundary conditions. Using the Lévy approach, the natural frequencies based on the CPT, Mindlin plate theory, LPT, RPT, and simplified LPT are compared. The numerical results indicate that the simplified LPT is effective and can be applied to thin, moderately thick, and thick plates. Consideration of shear deformation brings the results of the simplified LPT closer to those of LPT and RPT. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Acta Mechanica 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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        Value: 10.1007/s00707-025-04504-5
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      – Code: eng
        Text: English
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        PageCount: 26
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    Subjects:
      – SubjectFull: Free vibration
        Type: general
      – SubjectFull: Rectangular plates (Engineering)
        Type: general
      – SubjectFull: Shear (Mechanics)
        Type: general
      – SubjectFull: Eigenfrequencies
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      – SubjectFull: Boundary value problems
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            – D: 01
              M: 12
              Text: Dec2025
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