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                <term xml:lang="en">WAVEGUIDE</term>
                <term xml:lang="en">REDUCTION</term>
                <term xml:lang="en">FINITE ELEMENT</term>
                <term xml:lang="en">MODE</term>
                <term xml:lang="en">VEERING</term>
                <term xml:lang="en">LEAKY</term>
                <term xml:lang="fr">ACOUSTIQUE</term>
                <term xml:lang="fr">GUIDE D'ONDES</term>
                <term xml:lang="fr">METHODE DES ELEMENTS FINIS</term>
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              <p>This paper presents a model reduction strategy for fast finite element analysis of continuously symmetric elastic waveguides. Accounting for continuous symmetry, the initial three-dimensional problem is first reduced to a two-dimensional quadratic eigenvalue problem based on a semi-analytical finite element method. This problem has to be solved repeatedly at multiple frequencies to determine the modal properties of the waveguide as functions of frequency (\textit{e.g.} dispersion curves). Although two-dimensional, such a problem becomes costly when the problem size increases. In this paper, a specific reduction basis is proposed to project the matrix operators of the eigenvalue problem. This reduced basis is built from complex eigenvectors computed at the maximum frequency of analysis, enriched by cut-off eigenvectors, and then post-processed through a QR decomposition. Numerical results are presented for three critical test cases, involving high-frequency viscoelastic loss, curve veering phenomena, or leakage loss respectively. The reduction method turns out to be simple to implement, fast, and accurate for the complex spectrum, including attenuated waves. The time needed to build the reduced model, prior to its solution, remains short (roughly equal to a single frequency iteration of the full model). Once reduced, the eigenvalue problem can be solved more than 50 times faster than the full eigenvalue problem.</p>
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