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Research Article | Open Access

Stability analysis for a Rao-Nakra sandwich beam equation with time-varying weights and frictional dampings

Adel M. Al-Mahdi1,2( ), Maher Noor3, Mohammed M. Al-Gharabli1,2, Baowei Feng4, Abdelaziz Soufyane5
Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
DCC-Math, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
Department of Mathematics and Statistics, University of Sharjah Sharjah, United Arab Emirates
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Abstract

In this paper, we studied the asymptotic behavior of solutions for a Rao-Nakra sandwich beam equation with time-varying weights and frictional damping terms acting complementarily in the domain. We studied the effect of the three damping on the asymptotic behavior of the energy function. Under nonrestrictive on the growth assumption on the frictional damping terms, we established exponential and general energy decay rates for this system by using the multiplier approach. The results generalized some earlier decay results on the Rao-Nakra sandwich beam equation.

Keywords

multilayer beammultiplier methodstability
CLC number: 35B40, 93D15, 93D20

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 12570-12587
DOI: 10.3934/math.2024615

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Cite this article:
Al-Mahdi AM, Noor M, Al-Gharabli MM, et al. Stability analysis for a Rao-Nakra sandwich beam equation with time-varying weights and frictional dampings. AIMS Mathematics, 2024, 9(5): 12570-12587. https://doi.org/10.3934/math.2024615

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Received: 16 January 2024
Revised: 18 March 2024
Accepted: 25 March 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)