On Determination of Wave Velocities through the Eigenvalues of Material Objects

The statement of the eigenvalue problem for a tensor–block matrix of any order and of any<br />even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix<br />are invariant quantities. Therefore, in this work, our goal is to fi...

Full description

Bibliographic Details
Main Authors:	Mikhail U. Nikabadze, Sergey A. Lurie, Hovik A. Matevossian, Armine R. Ulukhanyan
Format:	Article
Language:	English
Published:	MDPI AG 2019-04-01
Series:	Mathematical and Computational Applications
Subjects:	eigentensor tensor-operator tensor–block matrix operator tensor–block matrix wave velocities dispersion tensor symbol of anisotropy velocity tensor
Online Access:	https://www.mdpi.com/2297-8747/24/2/39

id	doaj-d999bfa555f9457eb4c3cf1fc283f268
record_format	Article
spelling	doaj-d999bfa555f9457eb4c3cf1fc283f2682020-11-24T21:44:36ZengMDPI AGMathematical and Computational Applications2297-87472019-04-012423910.3390/mca24020039mca24020039On Determination of Wave Velocities through the Eigenvalues of Material ObjectsMikhail U. Nikabadze0Sergey A. Lurie1Hovik A. Matevossian2Armine R. Ulukhanyan3Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, RussiaFederal Research Center "Computer Science and Control", Russian Academy of Sciences, Vavilov str., 40, 119333 Moscow, RussiaFederal Research Center "Computer Science and Control", Russian Academy of Sciences, Vavilov str., 40, 119333 Moscow, RussiaDepartment of Computational Mathematics and Mathematical Physics, Bauman Moscow State Technical University, 105005 Moscow, RussiaThe statement of the eigenvalue problem for a tensor–block matrix of any order and of any<br />even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix<br />are invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities of<br />wave propagation of some medias through the eigenvalues of the material objects. In particular, we<br />consider the classical and micropolar materials with the different anisotropy symbols and for them<br />we determine the expressions for the velocities of wave propagation through the eigenvalues of the<br />material objects.https://www.mdpi.com/2297-8747/24/2/39eigentensortensor-operatortensor–block matrix operatortensor–block matrixwave velocitiesdispersion tensorsymbol of anisotropyvelocity tensor
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mikhail U. Nikabadze Sergey A. Lurie Hovik A. Matevossian Armine R. Ulukhanyan
spellingShingle	Mikhail U. Nikabadze Sergey A. Lurie Hovik A. Matevossian Armine R. Ulukhanyan On Determination of Wave Velocities through the Eigenvalues of Material Objects Mathematical and Computational Applications eigentensor tensor-operator tensor–block matrix operator tensor–block matrix wave velocities dispersion tensor symbol of anisotropy velocity tensor
author_facet	Mikhail U. Nikabadze Sergey A. Lurie Hovik A. Matevossian Armine R. Ulukhanyan
author_sort	Mikhail U. Nikabadze
title	On Determination of Wave Velocities through the Eigenvalues of Material Objects
title_short	On Determination of Wave Velocities through the Eigenvalues of Material Objects
title_full	On Determination of Wave Velocities through the Eigenvalues of Material Objects
title_fullStr	On Determination of Wave Velocities through the Eigenvalues of Material Objects
title_full_unstemmed	On Determination of Wave Velocities through the Eigenvalues of Material Objects
title_sort	on determination of wave velocities through the eigenvalues of material objects
publisher	MDPI AG
series	Mathematical and Computational Applications
issn	2297-8747
publishDate	2019-04-01
description	The statement of the eigenvalue problem for a tensor–block matrix of any order and of any<br />even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix<br />are invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities of<br />wave propagation of some medias through the eigenvalues of the material objects. In particular, we<br />consider the classical and micropolar materials with the different anisotropy symbols and for them<br />we determine the expressions for the velocities of wave propagation through the eigenvalues of the<br />material objects.
topic	eigentensor tensor-operator tensor–block matrix operator tensor–block matrix wave velocities dispersion tensor symbol of anisotropy velocity tensor
url	https://www.mdpi.com/2297-8747/24/2/39
work_keys_str_mv	AT mikhailunikabadze ondeterminationofwavevelocitiesthroughtheeigenvaluesofmaterialobjects AT sergeyalurie ondeterminationofwavevelocitiesthroughtheeigenvaluesofmaterialobjects AT hovikamatevossian ondeterminationofwavevelocitiesthroughtheeigenvaluesofmaterialobjects AT arminerulukhanyan ondeterminationofwavevelocitiesthroughtheeigenvaluesofmaterialobjects
_version_	1725909192788672512

On Determination of Wave Velocities through the Eigenvalues of Material Objects

Similar Items