## Computation of the torsional modes in an axisymmetric elastic layer

Mohamed Kara, Boubakeur Merouani, and Lahcène Chorfi

### Abstract

This paper is devoted to the numerical study of an eigenvalue problem modeling the torsional modes in an infinite and axisymmetric elastic layer. In the cylindrical coordinates $(r,z)$, without $\theta$, the problem is posed in a semi-infinite strip $\Omega=\mathbb{R}_+^* \times~]0,L[~$. For the numerical approximation, we formulate the problem in the bounded domain $\Omega_R=~]0,R[~\times~]0,L[~$. To this end, we use the localized finite element method, which links two representations of the solution: the analytic solution in the exterior domain $\Omega_R^\prime=~]R,+\infty[~\times~]0,L[$ and the numerical solution in the interior domain $\Omega_R$.

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### Key words

Torsional modes, spectra, localized finite elements

### AMS subject classifications

35P15, 65N30, 47A70

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