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This paper addresses the question of damage detection of cylindrical structures using finite element and periodic structure theory. The structure is modeled considering two waveguides connected through a coupling element, simulated as the defect. Wave characteristics in the waveguides are evaluated using a Wave Finite Element method (W.F.E.M) based on the analysis of the anomalies which affect the elastic wave travelling in the structure. Reflection and transmission coefficients of the wave modes which are incident to the coupling element are provided by a diffusion matrix. Then forced response of the pipe with and without transversal defect is predicted using wave decomposition. Numerical examples are given. These concern an isotropic pipe, for which dispersion curves are provided and diffusion coefficients in presence of a transversal and a longitudinal defect are predicted. [ABSTRACT FROM AUTHOR]