In-Plane Vibration Analysis of Rectangular Plates with Elastically Restrained Boundaries Using Differential Quadrature Method of Variational Weak Form.
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| Title: | In-Plane Vibration Analysis of Rectangular Plates with Elastically Restrained Boundaries Using Differential Quadrature Method of Variational Weak Form. |
|---|---|
| Authors: | Wang, Xianke1 (AUTHOR), Zhou, Weipeng2,3 (AUTHOR) weipengzhou2025@163.com, Yi, Shichao1,3,4 (AUTHOR), Li, Sen4,5 (AUTHOR) |
| Source: | Materials (1996-1944). Jul2025, Vol. 18 Issue 14, p3250. 17p. |
| Subjects: | Rectangular plates (Engineering), Differential quadrature method, Variational approach (Mathematics), Vibration (Aeronautics), Functionally gradient materials, Frequency response, Eigenvalues, Boundary value problems |
| Abstract: | An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated. [ABSTRACT FROM AUTHOR] |
| Copyright of Materials (1996-1944) is the property of MDPI 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: 186929059 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: In-Plane Vibration Analysis of Rectangular Plates with Elastically Restrained Boundaries Using Differential Quadrature Method of Variational Weak Form. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wang%2C+Xianke%22">Wang, Xianke</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhou%2C+Weipeng%22">Zhou, Weipeng</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> weipengzhou2025@163.com</i><br /><searchLink fieldCode="AR" term="%22Yi%2C+Shichao%22">Yi, Shichao</searchLink><relatesTo>1,3,4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Sen%22">Li, Sen</searchLink><relatesTo>4,5</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Materials+%281996-1944%29%22">Materials (1996-1944)</searchLink>. Jul2025, Vol. 18 Issue 14, p3250. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Rectangular+plates+%28Engineering%29%22">Rectangular plates (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+quadrature+method%22">Differential quadrature method</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+approach+%28Mathematics%29%22">Variational approach (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Vibration+%28Aeronautics%29%22">Vibration (Aeronautics)</searchLink><br /><searchLink fieldCode="DE" term="%22Functionally+gradient+materials%22">Functionally gradient materials</searchLink><br /><searchLink fieldCode="DE" term="%22Frequency+response%22">Frequency response</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Materials (1996-1944) is the property of MDPI 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: BibEntity: Identifiers: – Type: doi Value: 10.3390/ma18143250 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 3250 Subjects: – SubjectFull: Rectangular plates (Engineering) Type: general – SubjectFull: Differential quadrature method Type: general – SubjectFull: Variational approach (Mathematics) Type: general – SubjectFull: Vibration (Aeronautics) Type: general – SubjectFull: Functionally gradient materials Type: general – SubjectFull: Frequency response Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Boundary value problems Type: general Titles: – TitleFull: In-Plane Vibration Analysis of Rectangular Plates with Elastically Restrained Boundaries Using Differential Quadrature Method of Variational Weak Form. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wang, Xianke – PersonEntity: Name: NameFull: Zhou, Weipeng – PersonEntity: Name: NameFull: Yi, Shichao – PersonEntity: Name: NameFull: Li, Sen IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 07 Text: Jul2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 19961944 Numbering: – Type: volume Value: 18 – Type: issue Value: 14 Titles: – TitleFull: Materials (1996-1944) Type: main |
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