Well-Posedness and the Family of Global Attractors for Higher-Order Coupled Beam Models with Higher-Order Fractional Energy Damping.
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| Title: | Well-Posedness and the Family of Global Attractors for Higher-Order Coupled Beam Models with Higher-Order Fractional Energy Damping. |
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| Authors: | Lv, Penghui1 18487279097@163.com, Lin, Guoguang2 gglin@ynu.edu.cn |
| Source: | IAENG International Journal of Applied Mathematics. May2026, Vol. 56 Issue 5, p1633-1645. 13p. |
| Subjects: | Damping (Mechanics), Structural dynamics, Energy dissipation, Stability (Mechanics), Invariant manifolds, Mathematical models |
| Abstract: | This study investigates the mathematical behavior of advanced coupled beam systems that incorporate higherorder and fractional energy-damping effects. These models describe how interconnected elastic beams vibrate and gradually dissipate energy through complex damping mechanisms. Understanding these dynamics is essential for designing stable structures in engineering and materials science. The current research aims to demonstrate that the governing equations are mathematically well-behaved and that their longterm behavior can be predicted using attractor theory. We examined the well-posedness and long-time dynamics of a class of higher-order (m1;m2)-coupled beam systems with higher-order fractional energy damping. In this study, new critical exponents are established: p1α1 ≡... + (with p1α1 > p* = ..., q1α1;α2 ≡ ... + (with q1α1;α2 > q* = ..., p2α1;α2 ≡ ...+ (with p2α1;α2 > p* = N ..., q2α2 ≡ ...+ (with q2α2 > q* = .... These exponents depend on m1 ∊ N+;m2 ∊ N+, and 2/3 ≤ α1; α2 ≤ 1. We demonstrate that for 1 ≤ p1 < p1α1, 1 ≤ q1 < q1α1;α2 ; 1 ≤ p2 < p2α1;α2 ; 1 ≤ q2 < q2α2, the following observation was established: (i) the initialboundary value problem (IBVP) of equations admits a unique solution in different spaces; (ii) the related solution semigroup possesses a family of global attractors. A definition and proof process are proposed for the family of global attractors, which enriches related conclusions for higher-order coupled beam models. These results extend existing theories for nonlocal and coupled beam models and provide a rigorous mathematical foundation for future applications in higher-order structural dynamics. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: 193517524 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Well-Posedness and the Family of Global Attractors for Higher-Order Coupled Beam Models with Higher-Order Fractional Energy Damping. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lv%2C+Penghui%22">Lv, Penghui</searchLink><relatesTo>1</relatesTo><i> 18487279097@163.com</i><br /><searchLink fieldCode="AR" term="%22Lin%2C+Guoguang%22">Lin, Guoguang</searchLink><relatesTo>2</relatesTo><i> gglin@ynu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. May2026, Vol. 56 Issue 5, p1633-1645. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Damping+%28Mechanics%29%22">Damping (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+dynamics%22">Structural dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+%28Mechanics%29%22">Stability (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Invariant+manifolds%22">Invariant manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study investigates the mathematical behavior of advanced coupled beam systems that incorporate higherorder and fractional energy-damping effects. These models describe how interconnected elastic beams vibrate and gradually dissipate energy through complex damping mechanisms. Understanding these dynamics is essential for designing stable structures in engineering and materials science. The current research aims to demonstrate that the governing equations are mathematically well-behaved and that their longterm behavior can be predicted using attractor theory. We examined the well-posedness and long-time dynamics of a class of higher-order (m1;m2)-coupled beam systems with higher-order fractional energy damping. In this study, new critical exponents are established: p1α1 ≡... + (with p1α1 > p* = ..., q1α1;α2 ≡ ... + (with q1α1;α2 > q* = ..., p2α1;α2 ≡ ...+ (with p2α1;α2 > p* = N ..., q2α2 ≡ ...+ (with q2α2 > q* = .... These exponents depend on m1 ∊ N+;m2 ∊ N+, and 2/3 ≤ α1; α2 ≤ 1. We demonstrate that for 1 ≤ p1 < p1α1, 1 ≤ q1 < q1α1;α2 ; 1 ≤ p2 < p2α1;α2 ; 1 ≤ q2 < q2α2, the following observation was established: (i) the initialboundary value problem (IBVP) of equations admits a unique solution in different spaces; (ii) the related solution semigroup possesses a family of global attractors. A definition and proof process are proposed for the family of global attractors, which enriches related conclusions for higher-order coupled beam models. These results extend existing theories for nonlocal and coupled beam models and provide a rigorous mathematical foundation for future applications in higher-order structural dynamics. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1633 Subjects: – SubjectFull: Damping (Mechanics) Type: general – SubjectFull: Structural dynamics Type: general – SubjectFull: Energy dissipation Type: general – SubjectFull: Stability (Mechanics) Type: general – SubjectFull: Invariant manifolds Type: general – SubjectFull: Mathematical models Type: general Titles: – TitleFull: Well-Posedness and the Family of Global Attractors for Higher-Order Coupled Beam Models with Higher-Order Fractional Energy Damping. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lv, Penghui – PersonEntity: Name: NameFull: Lin, Guoguang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 5 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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