A WKB approximation for the divergence-buckling instability of a travelling web.
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| Title: | A WKB approximation for the divergence-buckling instability of a travelling web. |
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| Authors: | Coman, Ciprian D.1 (AUTHOR) cdc3p@yahoo.com |
| Source: | Acta Mechanica. Jul2025, Vol. 236 Issue 7, p3873-3892. 20p. |
| Subjects: | WKB approximation, Computer simulation, Equations |
| Abstract: | A WKB method is proposed to analyse edge-buckling phenomena in a simplified model for axially moving, stretched thin elastic webs. The fourth-order bifurcation equation for this configuration is characterised by the presence of two turning points. Connection matrices for these points are constructed and their implication on determining the critical buckling values are discussed. In particular, we derive a transcendental eigenrelation for localised eigenmodes whose complexity depends on the order of the WKB approximation employed. When secondary boundary-layer effects are ignored, the eigenrelation can be solved with high accuracy using regular perturbation techniques. Although the inclusion of (bending) edge effects makes the eigenrelation less tractable analytically, it can still be efficiently solved with the help of standard numerical methods. Comparisons with direct numerical simulations and previously derived approximations are also presented. [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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 186309459 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A WKB approximation for the divergence-buckling instability of a travelling web. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Coman%2C+Ciprian+D%2E%22">Coman, Ciprian D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cdc3p@yahoo.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Jul2025, Vol. 236 Issue 7, p3873-3892. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22WKB+approximation%22">WKB approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A WKB method is proposed to analyse edge-buckling phenomena in a simplified model for axially moving, stretched thin elastic webs. The fourth-order bifurcation equation for this configuration is characterised by the presence of two turning points. Connection matrices for these points are constructed and their implication on determining the critical buckling values are discussed. In particular, we derive a transcendental eigenrelation for localised eigenmodes whose complexity depends on the order of the WKB approximation employed. When secondary boundary-layer effects are ignored, the eigenrelation can be solved with high accuracy using regular perturbation techniques. Although the inclusion of (bending) edge effects makes the eigenrelation less tractable analytically, it can still be efficiently solved with the help of standard numerical methods. Comparisons with direct numerical simulations and previously derived approximations are also presented. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00707-025-04375-w Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 3873 Subjects: – SubjectFull: WKB approximation Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Equations Type: general Titles: – TitleFull: A WKB approximation for the divergence-buckling instability of a travelling web. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Coman, Ciprian D. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00015970 Numbering: – Type: volume Value: 236 – Type: issue Value: 7 Titles: – TitleFull: Acta Mechanica Type: main |
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