On the dispersion relations for an inhomogeneous waveguide with attenuation


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Abstract

Some general laws concerning the structure of dispersion relations for solid inhomogeneous waveguides with attenuation are studied. An approach based on the analysis of a first-order matrix differential equation is presented in the framework of the concept of complex moduli. Some laws concerning the structure of components of the dispersion set for a viscoelastic inhomogeneous cylindrical waveguide are studied analytically and numerically, and the asymptotics of components of the dispersion set are constructed for arbitrary inhomogeneity laws in the low-frequency region.

About the authors

A. O. Vatul’yan

South Federal University

Author for correspondence.
Email: vatulyan@math.rsu.ru
Russian Federation, ul. Mil’chakova 8a, Rostov-on-Don, 344090

V. O. Yurlov

South Mathematical Institute

Email: vatulyan@math.rsu.ru
Russian Federation, ul. Markusa 22, Vladikavkaz, 362027

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