Free Vibration of Functionally Graded Graphene Nanoplatelets–Reinforced Saturated Porous Cylindrical Shell Panel.

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Title: Free Vibration of Functionally Graded Graphene Nanoplatelets–Reinforced Saturated Porous Cylindrical Shell Panel.
Authors: Zheng, Honglong1 (AUTHOR), Liu, Ling1 (AUTHOR) d526liu@126.com, Wei, Bowen2 (AUTHOR) weibowen1984@gmail.com
Source: International Journal of Structural Stability & Dynamics. 7/15/2026, Vol. 26 Issue 15, p1-34. 34p.
Subjects: Free vibration, Cylindrical shells, Finite element method, Functionally gradient materials, Micromechanics, Urethane foam, Graphene, Genetic algorithms
Abstract: This study investigates the free vibration behavior of cylindrical shell panel nanocomposite foams composed of polyurethane (PU) integrated with graphene nanoplatelets (GNPs). The analysis highlights the critical role of agglomeration effects and the adoption of an appropriate micromechanical model. Accordingly, this work presents, for the first time, a modified Halpin–Tsai model that incorporates experimental data and employs a genetic algorithm (GA) to extract the exponential shape factor, optimizing the model's alignment with experimental results. Given the significance of GNP flake size, the study systematically examines its influence on the vibration characteristics. Three commercially available GNP types, with flake sizes of 24, 5, and 1. 5 μ m , are analyzed. To more accurately capture practical conditions, a saturated porous material model based on the Biot constitutive law is employed as an alternative to the conventional Hooke's law to characterize the closed-cell structure of PU foam. The governing equations of motion are formulated using Hamilton's principle, grounded in the first-order shear deformation theory (FSDT) plate theory and implemented through the finite element method (FEM). This research presents a comprehensive parametric investigation, examining for the first time the influence of geometric parameters, porosity characteristics, GNP weight fractions, and reinforcement configurations (X, O, U, and V patterns) on the vibration response of nanocomposite structures. For variations in weight fraction, GNP-5 and GNP-24 demonstrated an initial increase in natural frequency; however, beyond a certain threshold, the added mass surpassed the stiffness enhancement, leading to a reduction in natural frequency. In contrast, GNP-1.5 exhibited a lower natural frequency compared to pure PU. [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.)
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  Label: Title
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  Data: Free Vibration of Functionally Graded Graphene Nanoplatelets–Reinforced Saturated Porous Cylindrical Shell Panel.
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  Data: <searchLink fieldCode="AR" term="%22Zheng%2C+Honglong%22">Zheng, Honglong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Ling%22">Liu, Ling</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> d526liu@126.com</i><br /><searchLink fieldCode="AR" term="%22Wei%2C+Bowen%22">Wei, Bowen</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> weibowen1984@gmail.com</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>. 7/15/2026, Vol. 26 Issue 15, p1-34. 34p.
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  Data: <searchLink fieldCode="DE" term="%22Free+vibration%22">Free vibration</searchLink><br /><searchLink fieldCode="DE" term="%22Cylindrical+shells%22">Cylindrical shells</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Functionally+gradient+materials%22">Functionally gradient materials</searchLink><br /><searchLink fieldCode="DE" term="%22Micromechanics%22">Micromechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Urethane+foam%22">Urethane foam</searchLink><br /><searchLink fieldCode="DE" term="%22Graphene%22">Graphene</searchLink><br /><searchLink fieldCode="DE" term="%22Genetic+algorithms%22">Genetic algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study investigates the free vibration behavior of cylindrical shell panel nanocomposite foams composed of polyurethane (PU) integrated with graphene nanoplatelets (GNPs). The analysis highlights the critical role of agglomeration effects and the adoption of an appropriate micromechanical model. Accordingly, this work presents, for the first time, a modified Halpin–Tsai model that incorporates experimental data and employs a genetic algorithm (GA) to extract the exponential shape factor, optimizing the model's alignment with experimental results. Given the significance of GNP flake size, the study systematically examines its influence on the vibration characteristics. Three commercially available GNP types, with flake sizes of 24, 5, and 1. 5 μ m , are analyzed. To more accurately capture practical conditions, a saturated porous material model based on the Biot constitutive law is employed as an alternative to the conventional Hooke's law to characterize the closed-cell structure of PU foam. The governing equations of motion are formulated using Hamilton's principle, grounded in the first-order shear deformation theory (FSDT) plate theory and implemented through the finite element method (FEM). This research presents a comprehensive parametric investigation, examining for the first time the influence of geometric parameters, porosity characteristics, GNP weight fractions, and reinforcement configurations (X, O, U, and V patterns) on the vibration response of nanocomposite structures. For variations in weight fraction, GNP-5 and GNP-24 demonstrated an initial increase in natural frequency; however, beyond a certain threshold, the added mass surpassed the stiffness enhancement, leading to a reduction in natural frequency. In contrast, GNP-1.5 exhibited a lower natural frequency compared to pure PU. [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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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1142/S0219455426501300
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 34
        StartPage: 1
    Subjects:
      – SubjectFull: Free vibration
        Type: general
      – SubjectFull: Cylindrical shells
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Functionally gradient materials
        Type: general
      – SubjectFull: Micromechanics
        Type: general
      – SubjectFull: Urethane foam
        Type: general
      – SubjectFull: Graphene
        Type: general
      – SubjectFull: Genetic algorithms
        Type: general
    Titles:
      – TitleFull: Free Vibration of Functionally Graded Graphene Nanoplatelets–Reinforced Saturated Porous Cylindrical Shell Panel.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Zheng, Honglong
      – PersonEntity:
          Name:
            NameFull: Liu, Ling
      – PersonEntity:
          Name:
            NameFull: Wei, Bowen
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          Dates:
            – D: 15
              M: 07
              Text: 7/15/2026
              Type: published
              Y: 2026
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              Value: 02194554
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              Value: 26
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              Value: 15
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            – TitleFull: International Journal of Structural Stability & Dynamics
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