Volume 38, pp. 303-316, 2011.

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 $\mathrm{\Omega }={\mathbb{R}}_{+}^{\ast }\times ]0,L[$. For the numerical approximation, we formulate the problem in the bounded domain ${\mathrm{\Omega }}_R=]0,R[\times ]0,L[$. To this end, we use the localized finite element method, which links two representations of the solution: the analytic solution in the exterior domain ${\mathrm{\Omega }}_R^{\prime }=]R,+\mathrm{\infty }[\times ]0,L[$ and the numerical solution in the interior domain ${\mathrm{\Omega }}_R$.

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Key words

Torsional modes, spectra, localized finite elements

AMS subject classifications

35P15, 65N30, 47A70