Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Kovalev V. A., Radayev Y. N. Cross-Coupled Type-III Thermoelastic Waves of a Given Azimuthal Number in a Waveguide under Sidewall Heat Interchanging. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 4, pp. 86-108. DOI: 10.18500/1816-9791-2011-11-4-86-108

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
21.12.2011
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Language: 
Russian
Heading: 
Mechanics
UDC: 
539.374
DOI: 
10.18500/1816-9791-2011-11-4-86-108

Cross-Coupled Type-III Thermoelastic Waves of a Given Azimuthal Number in a Waveguide under Sidewall Heat Interchanging

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: 

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves of a given azimuthal order propagating via a long cylindrical waveguide with circular cross-section. Sidewall of the waveguide is assumed free from tractions and permeable to heat. The study is carried out in the framework of coupled generalized theory of type-III thermoelasticity (GNIII) consistent with the fundamental principles of continuum thermomechanics. The type-III theory combines the both possible mechanisms of heat transfer: thermodiffusion and wave. Type-III generalized thermoelasticity includes classical thermoelasticity (GNI/CTE) and the theory of hyperbolic thermoelasticity (GNII) as limiting cases.The GNII-theory can be formulated as a field theory and differential field equations are of hyperbolic analytical type. Closed solution of the coupled linear GNIII-thermoelasticity partial differential equations satisfying the required boundary conditions on the surface of waveguide including convective heat interchanging condition is obtained by the separation of variables technique. For a given azimuthal number the frequency equation is derived. A numerical analysis of frequency equation is carried out by Mathematica. A scheme of frequency equation roots localization is proposed and wavenumbers of the coupled type-III thermoelastic waves of the first and seventh azimuthal numbers are computed. A numerical study of the coupled thermoelastic waves of the 70th azimutal number is also presented. Some aspects of numerical realization of the proposed approach are discussed.

Key words: 
thermomechanics
thermoelasticity
type-III thermoelasticity
frequency equation
waveguide
wavenumber
wave mode
azimuthal number
heat interchanging
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