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Simulation of plate bending vibration problems by the meshless backward substitution method.

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Title: Simulation of plate bending vibration problems by the meshless backward substitution method.
Authors: Xu, Yitong1,2 (AUTHOR), Lin, Ji1,2 (AUTHOR) linji@hhu.edu.cn, Lu, Jun3 (AUTHOR), Reutskiy, Sergiy4 (AUTHOR)
Source: Computers & Mathematics with Applications. Sep2025, Vol. 194, p202-213. 12p.
Subjects: Vibration (Mechanics), Meshfree methods, Numerical solutions to equations, Structural analysis (Engineering), Iterative methods (Mathematics), Boundary value problems, Collocation methods
Abstract: In this paper, the meshless backward substitution method is proposed for the first time to solve the fourth-order plate bending vibration problems. The numerical solution consists of approximation from the boundary conditions and the revised basis functions which satisfying the homogeneous conditions with weighted parameters which are obtained from the governing equations by the collocation method. Then the key issues are the organization of initial approximation and the revised basis function derived from the traditional basis functions. To demonstrate the accuracy and validity of the proposed method, several numerical examples are conducted and compared with existing methods in literature. The obtained results from numerical experiments confirm the potential of the proposed method in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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: 187340704
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Simulation of plate bending vibration problems by the meshless backward substitution method.
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  Data: <searchLink fieldCode="AR" term="%22Xu%2C+Yitong%22">Xu, Yitong</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lin%2C+Ji%22">Lin, Ji</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> linji@hhu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lu%2C+Jun%22">Lu, Jun</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Reutskiy%2C+Sergiy%22">Reutskiy, Sergiy</searchLink><relatesTo>4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Sep2025, Vol. 194, p202-213. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Vibration+%28Mechanics%29%22">Vibration (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+equations%22">Numerical solutions to equations</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+analysis+%28Engineering%29%22">Structural analysis (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Collocation+methods%22">Collocation methods</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, the meshless backward substitution method is proposed for the first time to solve the fourth-order plate bending vibration problems. The numerical solution consists of approximation from the boundary conditions and the revised basis functions which satisfying the homogeneous conditions with weighted parameters which are obtained from the governing equations by the collocation method. Then the key issues are the organization of initial approximation and the revised basis function derived from the traditional basis functions. To demonstrate the accuracy and validity of the proposed method, several numerical examples are conducted and compared with existing methods in literature. The obtained results from numerical experiments confirm the potential of the proposed method in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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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      – Type: doi
        Value: 10.1016/j.camwa.2025.06.019
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 202
    Subjects:
      – SubjectFull: Vibration (Mechanics)
        Type: general
      – SubjectFull: Meshfree methods
        Type: general
      – SubjectFull: Numerical solutions to equations
        Type: general
      – SubjectFull: Structural analysis (Engineering)
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Collocation methods
        Type: general
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      – TitleFull: Simulation of plate bending vibration problems by the meshless backward substitution method.
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            NameFull: Xu, Yitong
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            NameFull: Lin, Ji
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            NameFull: Lu, Jun
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            NameFull: Reutskiy, Sergiy
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          Dates:
            – D: 15
              M: 09
              Text: Sep2025
              Type: published
              Y: 2025
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              Value: 194
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            – TitleFull: Computers & Mathematics with Applications
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