Dynamics of locally damped Timoshenko systems

被引：2

作者：

Freitas, Mirelson M. ^{[1
]}

Almeida Junior, Dilberto S. ^{[2
]}

Santos, Mauro L. ^{[2
]}

Ramos, Anderson J. A. ^{[1
]}

Caljaro, Ronal Q. ^{[2
]}

机构：

[1] Fed Univ Para, Raimundo Santana St S-N, BR-68721000 Salinopolis, PA, Brazil

[2] Fed Univ, Inst Exact & Nat Sci, Doctoral Program Math, Belem, Para, Brazil

来源：

MATHEMATICS AND MECHANICS OF SOLIDS | 2023年 / 28卷 / 04期

关键词：

Timoshenko system; localized damping; global attractor; exponential attractor; quasi-stability; WAVE-EQUATION; EVOLUTION-EQUATIONS; DECAY-RATES; STABILITY; ENERGY;

D O I：

10.1177/10812865221101864

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we study the long-time dynamics of a Timoshenko system modeling vibrations of beams with non-linear localized damping mechanisms acting on both displacement and angular rotation and subjected to non-linear source terms. Using recent quasi-stability methods, we prove the existence of smooth finite dimensional global attractor, which is characterized as unstable manifold of the set of stationary solutions. Moreover, the existence of exponential attractors is shown. These aspects were not previously considered for the Timoshenko system with localized damping.

引用

页码：1012 / 1034

页数：23

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