Optimal stability for laminated beams with Kelvin–Voigt damping and Fourier’s law

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-28 DOI:10.3233/asy-231883

Victor Cabanillas Zannini, Teófanes Quispe Méndez, A.J.A. Ramos

引用次数: 0

Abstract

This article deals with the asymptotic behavior of a mathematical model for laminated beams with Kelvin–Voigt dissipation acting on the equations of transverse displacement and dimensionless slip. We prove that the evolution semigroup is exponentially stable if the damping is effective in the two equations of the model. Otherwise, we prove that the semigroup is polynomially stable and find the optimal decay rate when damping is effective only in the slip equation. Our stability approach is based on the Gearhart–Prüss–Huang Theorem, which characterizes exponential stability, while the polynomial decay rate is obtained using the Borichev and Tomilov Theorem.

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具有 Kelvin-Voigt 阻尼和傅里叶定律的层压梁的最佳稳定性

本文论述了一种层压梁数学模型的渐近行为，该模型的横向位移方程和无量纲滑移方程上存在开尔文-沃伊特耗散。我们证明，如果阻尼在模型的两个方程中有效，则演化半群是指数稳定的。否则，我们将证明半群是多项式稳定的，并找到当阻尼只对滑移方程有效时的最佳衰减率。我们的稳定性方法基于 Gearhart-Prüss-Huang 定理，该定理描述了指数稳定性，而多项式衰减率则通过 Borichev 和 Tomilov 定理获得。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.