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On the Problem of Eigenvalues of Material Tensor Objects and Wave Velocities

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Abstract

We formulate the eigenvalue problem for a tensor-block matrix of any order and of any even rank. It is well known that the eigenvalues of the tensor and the tensor-block matrix are invariant quantities. Therefore, in this work, our purpose is to find the expression for the wave velocities of some media through the eigenvalues of the material objects. In particular, the classical and micropolar materials with the different anisotropy symbols are considered, and the expressions for the wave velocities through the eigenvalues of the material objects are given.

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Funding

This work was supported by 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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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    M. Nikabadze

  2. Bauman Moscow State Technical University, Moscow, 107005, Russia

    M. Nikabadze & A. Ulukhanyan

  3. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, 119333, Russia

    S. Lurie & H. Matevossian

  4. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040, Russia

    S. Lurie

  5. Moscow Aviation Institute, Moscow, 125993, Russia

    H. Matevossian

Authors
  1. M. Nikabadze
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  2. S. Lurie
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  3. H. Matevossian
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  4. A. Ulukhanyan
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Correspondence to M. Nikabadze, S. Lurie, H. Matevossian or A. Ulukhanyan.

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Nikabadze, M., Lurie, S., Matevossian, H. et al. On the Problem of Eigenvalues of Material Tensor Objects and Wave Velocities. Lobachevskii J Math 40, 992–1009 (2019). https://doi.org/10.1134/S1995080219070151

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  • DOI: https://doi.org/10.1134/S1995080219070151

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