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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, Volume 19, Issue 4, Pages 454–463
DOI: https://doi.org/10.18500/1816-9791-2019-19-4-454-463
(Mi isu821)
 

This article is cited in 1 scientific paper (total in 2 paper)

Scientific Part
Mechanics

On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity

V. A. Kovaleva, Yu. N. Radayevb

a Moscow City Government University of Management, 28 Sretenka St., Moscow 107045, Russia
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1 Vernadskogo Ave., Moscow 119526, Russia
Full-text PDF (382 kB) Citations (2)
References:
Abstract: 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.
Key words: hemitropic, micropolar, thermoelastic, plane wave, wavenumber, polarization, athermal wave.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation AAAA-A17-117021310381-8
Russian Foundation for Basic Research 18-01-00844_а
This work was in part financially supported by the Ministry of Science and Higher Education (State Registration Number AAAA-A17-117021310381-8) and by the Russian Foundation for Basic Research (project No. 18-01-00844 “Modeling of thermomechanical processes in complex media using the principle of thermomechanical orthogonality”).
Received: 13.05.2019
Accepted: 10.06.2019
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: Russian
Citation: V. A. Kovalev, Yu. N. Radayev, “On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity”, Izv. Saratov Univ. Math. Mech. Inform., 19:4 (2019), 454–463
Citation in format AMSBIB
\Bibitem{KovRad19}
\by V.~A.~Kovalev, Yu.~N.~Radayev
\paper On wave solutions of dynamic equations of hemitropic micropolar thermoelasticity
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2019
\vol 19
\issue 4
\pages 454--463
\mathnet{http://mi.mathnet.ru/isu821}
\crossref{https://doi.org/10.18500/1816-9791-2019-19-4-454-463}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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