Nonlinear three layer beam system: Well-posedness, asymptotic stability and numerical analysis

Soh Edwin Mukiawa; Cyril Dennis Enyi; Johnson D. Audu; Hasan A. Almutairi; Soh Edwin Mukiawa; Cyril Dennis Enyi; Johnson D. Audu; Hasan A. Almutairi

doi:10.3934/math.20251082

AIMS Mathematics

2025, Volume 10, Issue 10: 24389-24430. doi: 10.3934/math.20251082

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Nonlinear three layer beam system: Well-posedness, asymptotic stability and numerical analysis

1.
Department of Mathematics, College of Science, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi Arabia
2.
Mount Vernon Nazarene University, 800 Martinsburg Road Mount Vernon, OH 43050, United States of America
3.
Department of Mathematics and Natural Sciences, Prince Mohammed Bin Fahd University Alkhobar, 31952, Saudi Arabia

Received: 26 July 2025 Revised: 12 October 2025 Accepted: 16 October 2025 Published: 24 October 2025
MSC : 35D30, 35B35, 35L51, 74J30, 74S20

Our goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a nonlinear triple beam system commonly known as the Rao-Nakra beam model. We investigated the effects of non-linear frictional and external forces to the beam model. The Garlekin approximation and the multiplier methods were techniques applied to achieve our goals. Numerical approximations were also performed with the finite difference method to validate our theoritical findings.
- well-posedness,
- polynomial and exponential stability,
- numerical approximation,
- nonlinear Rao-Nakra beam
Citation: Soh Edwin Mukiawa, Cyril Dennis Enyi, Johnson D. Audu, Hasan A. Almutairi. Nonlinear three layer beam system: Well-posedness, asymptotic stability and numerical analysis[J]. AIMS Mathematics, 2025, 10(10): 24389-24430. doi: 10.3934/math.20251082

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Abstract

Our goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a nonlinear triple beam system commonly known as the Rao-Nakra beam model. We investigated the effects of non-linear frictional and external forces to the beam model. The Garlekin approximation and the multiplier methods were techniques applied to achieve our goals. Numerical approximations were also performed with the finite difference method to validate our theoritical findings.

References

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