Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type

IF 1.3 4区 数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-02-13 DOI:10.1155/2024/1615178
Mohammed M. Al-Gharabli, Shadi Al-Omari, Adel M. Al-Mahdi
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Abstract

In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations.
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利用科尔曼-古尔丁热力定律和变指数型非线性阻尼稳定饶-纳克拉夹层梁系统
本文探讨了热塑性 Rao-Nakra(三明治梁)梁方程中具有可变指数非线性阻尼的解的渐近行为。这种情况下的热传导遵循 Coleman-Gurtin 热定律,包括线性阻尼、傅里叶和 Gurtin-Pipkin 定律作为具体实例。通过使用乘法器方法,我们建立了一般能量衰减结果,指数衰减是其中一种特殊表现形式。这些发现扩展并概括了之前有关 Rao-Nakra 夹层梁方程的衰减结果。
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
Journal of Mathematics
Journal of Mathematics Mathematics-General Mathematics
CiteScore
2.50
自引率
14.30%
发文量
0
期刊介绍: Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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