On the Problem of Eigenvalues of Material Tensor Objects and Wave Velocities
- Авторы: Nikabadze M.1,2, Lurie S.3,4, Matevossian H.3,5, Ulukhanyan A.2
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Учреждения:
- Lomonosov Moscow State University
- Bauman Moscow State Technical University
- Federal Research Center “Computer Science and Control”
- Institute of Applied Mechanics
- Moscow Aviation Institute
- Выпуск: Том 40, № 7 (2019)
- Страницы: 992-1009
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205089
- DOI: https://doi.org/10.1134/S1995080219070151
- ID: 205089
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Аннотация
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.
Об авторах
M. Nikabadze
Lomonosov Moscow State University; Bauman Moscow State Technical University
Автор, ответственный за переписку.
Email: nikabadze@mail.ru
Россия, Moscow, 119991; Moscow, 107005
S. Lurie
Federal Research Center “Computer Science and Control”; Institute of Applied Mechanics
Автор, ответственный за переписку.
Email: salurie@mail.ru
Россия, Moscow, 119333; Moscow, 125040
H. Matevossian
Federal Research Center “Computer Science and Control”; Moscow Aviation Institute
Автор, ответственный за переписку.
Email: hmatevossian@graduate.org
Россия, Moscow, 119333; Moscow, 125993
A. Ulukhanyan
Bauman Moscow State Technical University
Автор, ответственный за переписку.
Email: armine_msu@mail.ru
Россия, Moscow, 107005
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