ON THE WELL-POSEDNESS AND STABILITY FOR CARBON NANOTUBES AS COUPLED TWO TIMOSHENKO BEAMS WITH FRICTIONAL DAMPINGS

Aissa Guesmia

doi:10.11948/20230065

2024 Volume 14 Issue 5

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Aissa Guesmia. ON THE WELL-POSEDNESS AND STABILITY FOR CARBON NANOTUBES AS COUPLED TWO TIMOSHENKO BEAMS WITH FRICTIONAL DAMPINGS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2572-2621. doi: 10.11948/20230065

Citation:

Aissa Guesmia. ON THE WELL-POSEDNESS AND STABILITY FOR CARBON NANOTUBES AS COUPLED TWO TIMOSHENKO BEAMS WITH FRICTIONAL DAMPINGS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2572-2621. doi: 10.11948/20230065

ON THE WELL-POSEDNESS AND STABILITY FOR CARBON NANOTUBES AS COUPLED TWO TIMOSHENKO BEAMS WITH FRICTIONAL DAMPINGS

Aissa Guesmia^1,

1.
Institut Elie Cartan de Lorraine, UMR 7502, Université de Lorraine, 3 Rue Augustin Fresnel, BP 45112, 57073 Metz Cedex 03, France

Author Bio: Email: aissa.guesmia@univ-lorraine.fr(A. Guesmia)
Fund Project: Not applicable

Abstract

Abstract

The objective of this paper is to study the well-posedness and stability questions for double wall carbon nanotubes modeled as linear one-dimensional coupled two Timoshenko beams in a bounded domain under frictional dampings. First, we prove the well-posedness of our system by applying the semigroups theory of linear operators. Second, we show several strong, non-exponential, exponential, polynomial and non-polynomial stability results depending on the number of frictional dampings, their position and some connections between the coefficients. In some cases, the optimality of the polynomial decay rate is also proved. The proofs of these stability results are based on a combination of the energy method and the frequency domain approach.
- Coupled Timoshenko beams /
- well-posedness /
- asymptotic behavior /
- semigroups theory /
- energy method /
- frequency domain approach
MSC: 35B40, 35L45, 74H40, 93D20, 93D15

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References

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