Geodesic
On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 4, pp. 454-463.

Voir la notice de l'article provenant de la source Math-Net.Ru

Coupled equations of hemitropic thermoelastic micropolar continuum formulated in terms of displacement vector, microrotation vector and temperature increment are considered. Thermodiffusion mechanism of heat transport is assumed. Hemitropic thermoelastic constitutive constants are reduced to a minimal set retaining hemitropic constitutive behaviour. Coupled plane waves propagating in thermoelastic media are studied. Spatial polarizations of the coupled plane waves are determined. Bicubic equations for wavenumbers are obtained and then analyzed. Three normal complex wavenumbers for plane waves are found. Equations relating to the complex amplitudes of displacements, microrotations and temperature increment are obtained. Athermal plane waves propagation is also discussed. It is shown that polarization vectors and the wave vector are mutually orthogonal. Wavenumbers are found as roots of a biquadratic equation. For athermal plane wave depending on the case two or single real normal wavenumbers are obtained. 
@article{ISU_2019_19_4_a7,
     author = {V. A. Kovalev and Yu. N. Radayev},
     title = {On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {454--463},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2019_19_4_a7/}
}
TY  - JOUR
AU  - V. A. Kovalev
AU  - Yu. N. Radayev
TI  - On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2019
SP  - 454
EP  - 463
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2019_19_4_a7/
LA  - ru
ID  - ISU_2019_19_4_a7
ER  - 
%0 Journal Article
%A V. A. Kovalev
%A Yu. N. Radayev
%T On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2019
%P 454-463
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2019_19_4_a7/
%G ru
%F ISU_2019_19_4_a7
V. A. Kovalev; Yu. N. Radayev. On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 4, pp. 454-463. http://geodesic.mathdoc.fr/item/ISU_2019_19_4_a7/

[1] G. A. Maugin, Non-Classical Continuum Mechanics. A Dictionary, Advanced Structured Materials, 51, Springer, Singapore, 2017, 259 pp. | DOI | MR | Zbl

[2] W. Nowacki, Theory of Asymmetric Elasticity, Pergamon Press, Oxford–New York–Toronto–Sydney–Paris–Frankfurt, 1986, 383 pp. | MR | Zbl

[3] J. Dyszlewicz, Micropolar Theory of Elasticity, Lecture Notes in Applied and Computational Mechanics, Springer Science Business Media, Berlin–Heidelberg, 2012, 345 pp. | MR

[4] Yu. N. Radayev, “The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories”, J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 22:3 (2018), 504–517 (in Russian) | DOI | Zbl

[5] W. Nowacki, Theory of Elasticity, Mir, M., 1975, 872 pp. (in Russian)

[6] W. Nowacki, Problems of Thermoelasticity, USSR Academy of Sciences, M., 1962, 364 pp. (in Russian)

[7] W. Nowacki, Dynamic Problems of Thermoelasticity, Mir, M., 1970, 256 pp. (in Russian)

[8] V. A. Kovalev, Yu. N. Radayev, Waves Problem of Field Theory and Thermomechanics, Izd-vo Sarat. un-ta, Saratov, 2010, 328 pp. (in Russian)

[9] J. B. Witham, Linear and Nonlinear Waves, Mir, M., 1977, 622 pp. (in Russian)

[10] L. M. Brekhovskikh, V. V. Goncharov, Introduction to Continuum Mechanics (in Application to Theory of Waves), Nauka, M., 1982, 336 pp. (in Russian)

[11] Z. Wesolowski, Dynamic Problems of Nonlinear Elasticity, Naukova Dumka, Kiev, 1981, 216 pp. (in Russian)

[12] A. K. Sushkevich, Foundations of Higher Algebra, ONTI, L., 1937, 476 pp. (in Russian)

[13] Y. N. Radayev, “Hyperbolic Theories and Applied Problems of Solid Mechanics”, Actual Problems of Mechanics, Int. Conf., Dedicated to L. A. Galin 100th Anniversary, Theses of reports (September, 20–21, 2012, Moscow), M., 2012, 75–76 (in Russian)