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] |
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| Database: | Engineering Source |
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