Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Kovalev V. A., Radayev Y. N. On Wave Solutions of Dynamic Equations of Hemitropic Micropolar Thermoelasticity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 4, pp. 454-463. DOI: 10.18500/1816-9791-2019-19-4-454-463, EDN: EVFCSA

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.12.2019
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Russian
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Article
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539.374
EDN: 
EVFCSA

On Wave Solutions of Dynamic Equations of Hemitropic Micropolar Thermoelasticity

Autors: 
Kovalev Vladimir Aleksandrovich, Moscow City Government University of Management Moscow, Russia
Radayev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
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.

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Received: 
13.05.2019
Accepted: 
10.06.2019
Published: 
02.12.2019