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Mathematics. Mechanics. Informatics

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Kovalev V. A., Radaev Y. N., Revinsky R. A. Generalized Cross-Coupled Type-III Thermoelastic Waves Propagating via a Waveguide under Sidewall Heat Interchange. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 1, pp. 59-70. DOI: 10.18500/1816-9791-2011-11-1-59-70

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Generalized Cross-Coupled Type-III Thermoelastic Waves Propagating via a Waveguide under Sidewall Heat Interchange

Kovalev Vladimir Aleksandrovich, Moscow City Government University of Management Moscow, Russia
Radaev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Revinsky R. A., Saratov State University

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves propagation via a long cylindrical waveguide. The sidewall of the waveguide is assumed free from tractions and permeable to heat. The analysis is carried out in the framework of coupled generalized theory of GNIII- thermoelasticity consistent with the basic thermodynamic principles. The 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 GNIII-thermoelasticity equations satisfying the required boundary conditions on the surface of waveguide including convective heat interchanging condition has been obtained. The paper provides numerical analysis of frequency equation. A scheme of frequency equation roots localization is described and wavenumbers of the coupled thermoelastic waves of the first azimuthal order are computed.

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