Geodesic
On plane thermoelastic waves in hemitropic micropolar~continua
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 3, pp. 464-474.

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

The paper deals with the coupled heat transport and dynamic equations of the hemitropic thermoelastic micropolar continuum formulated in terms of displacements, microrotations and temperature increment which are to be determined in applied problems. The mechanism of thermal conductivity is considered as simple thermodiffusion. Hemitropic constitutive constants are reduced to a minimum set nevertheless retaining hemitropic constitutive behaviour and thermoelastic semi-isotropy. Solutions of thermoelastic coupled equations in the form of propagating plane waves are studied. Their spatial polarizations are determined. An algebraic bicubic equation for the determination of wavenumbers is obtained. It is found that for a coupled thermoelastic wave actually there are exactly three normal complex wavenumbers. Athermal wave is also investigated. Spatial polarizations in this case form (together with the wave vector) a spatial trihedron of mutually orthogonal directions. For an athermal wave there are (depending on the case) either two real normal wavenumbers or single wavenumber.
Keywords: hemitropic, thermoelastic, plane wave, wavenumber, polarization, athermal wave.
Mots-clés : micropolar, complex amplitude 
@article{VSGTU_2019_23_3_a4,
     author = {Yu. N. Radayev and V. A. Kovalev},
     title = {On plane thermoelastic waves in hemitropic micropolar~continua},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {464--474},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a4/}
}
TY  - JOUR
AU  - Yu. N. Radayev
AU  - V. A. Kovalev
TI  - On plane thermoelastic waves in hemitropic micropolar~continua
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2019
SP  - 464
EP  - 474
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a4/
LA  - en
ID  - VSGTU_2019_23_3_a4
ER  - 
%0 Journal Article
%A Yu. N. Radayev
%A V. A. Kovalev
%T On plane thermoelastic waves in hemitropic micropolar~continua
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2019
%P 464-474
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a4/
%G en
%F VSGTU_2019_23_3_a4
Yu. N. Radayev; V. A. Kovalev. On plane thermoelastic waves in hemitropic micropolar~continua. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 3, pp. 464-474. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a4/

[1] Nowacki W., Theory of Asymmetric Elasticity, Pergamon Press, Oxford, 1986, viii+383 pp. | Zbl

[2] Radayev Y. N., “The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 22:3 (2018), 504–517 (In Russian) | DOI

[3] Nowacki W., Theory of micropolar elasticity, International Centre for Mechanical Sciences. Courses and Lectures, 25, Springer-Verlag, Wien, 1972, 286 pp | DOI | Zbl

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

[5] Sushkevich A. K., Foundations of Higher Algebra, ONTI, Moscow, Leningrad, 1937, 476 pp. (In Russian)

[6] Radayev Y. N., “Hyperbolic theories and applied problems of solid mechanics”, “Actual Problems of Mechanics”, Int. Conf., Dedicated to L. A. Galin 100th Anniversary (September, 20-21, 2012. Moscow), Book of Abstracts, IPMech RAS, Moscow, 2012, 75–76 (In Russian)