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On Waves Processes in Transversally-Inhomogeneous Waveguides

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Modern Methods in Operator Theory and Harmonic Analysis (OTHA 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 291))

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Abstract

Different types of problems on wave propagation in transversally inhomogeneous cylindrical waveguides are considered. General properties of the dispersion set of inhomogeneous cylindrical waveguides are presented. Asymptotic formulas for the dispersion set branches in the vicinity of radial resonance points are constructed. A condition of solvability of inhomogeneous problems is built. Different models of materials are used for numerical testing of the asymptotic formulas. Dispersion relations for elastic, viscoelastic, electro-elastic and prestressed elastic waveguides are analyzed. The formulas allowing to estimate the influence of residual stresses on the radial resonances points are presented. The effect of various types of homogeneous boundary conditions on the structure of dispersion set is analysed.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, 344090, Russia

    Alexander Vatulyan & Victor Yurov

  2. Southern Mathematical Institute of the Vladikavkaz Scientific Centre of the RAS, Vladikavkaz, 362027, Russia

    Alexander Vatulyan & Victor Yurov

Authors
  1. Alexander Vatulyan
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  2. Victor Yurov
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Corresponding author

Correspondence to Victor Yurov .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey Karapetyants

  2. Department of Mathematics, Cinvestav, Santiago de Querétaro, Querétaro, Mexico

    Vladislav Kravchenko

  3. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

    Elijah Liflyand

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Vatulyan, A., Yurov, V. (2019). On Waves Processes in Transversally-Inhomogeneous Waveguides. In: Karapetyants, A., Kravchenko, V., Liflyand, E. (eds) Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics & Statistics, vol 291. Springer, Cham. https://doi.org/10.1007/978-3-030-26748-3_24

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