Uniform stability result of laminated beams with thermoelasticity of type Ⅲ

Tijani A. Apalara; Aminat O. Ige; Cyril D. Enyi; Mcsylvester E. Omaba; Tijani A. Apalara; Aminat O. Ige; Cyril D. Enyi; Mcsylvester E. Omaba

doi:10.3934/math.2023054

AIMS Mathematics

2023, Volume 8, Issue 1: 1090-1101. doi: 10.3934/math.2023054

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Research article

Uniform stability result of laminated beams with thermoelasticity of type Ⅲ

1.
Department of Mathematics, University of Hafr Al-Batin (UHB), Hafr Al-Batin 31991, Saudi Arabia
2.
Department of Mathematics, Lagos State University (LASU), Ojo 102101, Nigeria

Received: 26 July 2022 Revised: 24 September 2022 Accepted: 10 October 2022 Published: 17 October 2022
MSC : 74F05, 35B40, 93D20

In this work, we study the effect of heat conduction theories pioneered by Green and Naghdi, popularly called thermoelasticity of type Ⅲ, on the stability of laminated Timoshenko beams. Without the structural (interfacial slip) damping or any other forms of damping mechanisms, we establish an exponential stability result depending on the equality of wave velocities of the system. Our work shows that the thermal effect is strong enough to stabilize the system exponentially without any additional internal or boundary dampings. The result extends some of the developments in literature where structural damping (in addition to some internal or boundary dampings) is necessary to bring about exponential stability.
- laminated beams,
- thermoelasticity type Ⅲ,
- uniform stability,
- multiplier technique,
- structural damping,
- wave speeds
Citation: Tijani A. Apalara, Aminat O. Ige, Cyril D. Enyi, Mcsylvester E. Omaba. Uniform stability result of laminated beams with thermoelasticity of type Ⅲ[J]. AIMS Mathematics, 2023, 8(1): 1090-1101. doi: 10.3934/math.2023054

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Abstract

In this work, we study the effect of heat conduction theories pioneered by Green and Naghdi, popularly called thermoelasticity of type Ⅲ, on the stability of laminated Timoshenko beams. Without the structural (interfacial slip) damping or any other forms of damping mechanisms, we establish an exponential stability result depending on the equality of wave velocities of the system. Our work shows that the thermal effect is strong enough to stabilize the system exponentially without any additional internal or boundary dampings. The result extends some of the developments in literature where structural damping (in addition to some internal or boundary dampings) is necessary to bring about exponential stability.

References

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