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On Determination of Wave Velocities through the Eigenvalues of Material Objects

1
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia
2
Department of Computational Mathematics and Mathematical Physics, Bauman Moscow State Technical University, 105005 Moscow, Russia
3
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Vavilov str., 40, 119333 Moscow, Russia
4
Institute of Applied Mechanics, Russian Academy of Sciences, Leningradsky prt 7, 125040 Moscow, Russia
5
Moscow Aviation Institute (National Research University), Volokolomskoe Shosse, 4, 125993 Moscow, Russia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(2), 39; https://doi.org/10.3390/mca24020039
Received: 26 January 2019 / Revised: 9 April 2019 / Accepted: 9 April 2019 / Published: 11 April 2019
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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Abstract

The statement of the eigenvalue problem for a tensor–block matrix of any order and of any
even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix
are invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities of
wave propagation of some medias through the eigenvalues of the material objects. In particular, we
consider the classical and micropolar materials with the different anisotropy symbols and for them
we determine the expressions for the velocities of wave propagation through the eigenvalues of the
material objects. View Full-Text
Keywords: eigentensor; tensor-operator; tensor–block matrix operator; tensor–block matrix; wave velocities; dispersion tensor; symbol of anisotropy; velocity tensor eigentensor; tensor-operator; tensor–block matrix operator; tensor–block matrix; wave velocities; dispersion tensor; symbol of anisotropy; velocity tensor
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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MDPI and ACS Style

Nikabadze, M.U.; Lurie, S.A.; Matevossian, H.A.; Ulukhanyan, A.R. On Determination of Wave Velocities through the Eigenvalues of Material Objects. Math. Comput. Appl. 2019, 24, 39.

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