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Application of Eigenvalue Problems Under the Study of Wave Velocity in Some Media

  • Mikhail NikabadzeEmail author
  • Armine Ulukhanyan
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 120)

Abstract

The wave velocities in some media under different types of anisotropy are estimated applying the eigenvalue problem of material tensors. In this connection, the canonical representations of material tensors, as well as kinematic and dynamic conditions on the strong discontinuity surface are given. Using them the problem of finding the wave velocities is reduced to the eigenvalue problem for the corresponding dispersion tensor. In addition, dispersion equations for determining the wave velocities are obtained. In particular, classical and micropolar materials with different symbols of anisotropy (structure) are considered and the wave velocities through the eigenvalues of material tensors are found.

Keywords

Wave velocity Eigenvalues of material tensors Anisotropy symbol Micropolar medium Tensor-block matrix 

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Notes

Acknowledgements

This work was supported by the Shota Rustaveli National Science Foundation (project no. DI-2016-41) and the Russian Foundation for Basic Research (project no. 18–29– 10085–mk).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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