| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2023-0065 |
| ON THE WELL-POSEDNESS AND STABILITY FOR CARBON NANOTUBES AS COUPLED TWO TIMOSHENKO BEAMS WITH FRICTIONAL DAMPINGS |
| Aissa Guesmia |
| Keywords:Coupled Timoshenko beams, well-posedness, asymptotic behavior, semigroup theory, energy method, frequency domain approach. |
| 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. |
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