Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Kovalev V. A., Murashkin E. V., Radayev Y. N. A mathematical theory of plane harmonic coupled thermoelastic waves in type-I micropolar continua. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 77-87. DOI: 10.18500/1816-9791-2014-14-1-77-87, EDN: SCSSSZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
Full text:
download
(downloads: 131)
Language: 
Russian
Heading: 
Mechanics
UDC: 
539.374
DOI: 
10.18500/1816-9791-2014-14-1-77-87
EDN: 
SCSSSZ

A mathematical theory of plane harmonic coupled thermoelastic waves in type-I micropolar continua

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

The present paper is devoted to an analysis of plane harmonic coupled thermoelastic waves of displacements, microrotations and temperature propagating in continua.The analysis is carried out in the framework of linear type-I (GNI/CTE) theory of thermoelastic micropolar continuum. Additional microrotations and moment stresses are taken into consideration. Propagating wave surfaces of weak discontinuities of displacements, microrotations, and temperature are studied by compatibility conditions technique due to Hadamard and Thomas. Wavenumbers (complex propagation constants (CPC)) of plane harmonic coupled thermoelastic waves are obtained. In order to determine the wavenumbers a bicubic and a biquadratic algebraic equations are derived for waves of displacements, microrotations, and temperature. Those equations are then analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal thermoelastic waves.

Key words: 
micropolar thermoelasticity
type-I continuum
weak discontinuity
longitudinal wave
transverse wave
wavenumber
frequency equation
References: 
  1. Cosserat E. et F. Theories of deformable bodies. Paris, Scientific Library A. Hermann et Fils, 1909, 242 p.
  2. Green A. E., Naghdi P. M. On undamped heat waves in an elastic solid. J. Therm. Stress. 1992, vol. 15, pp. 253–264.
  3. Green A. E., Naghdi P. M. Thermoelasticity without energy dissipation. J. Elasticity. 1993, vol. 31, pp. 189–208.
  4. Radayev Yu. N., Semenov D. A. Harmonic coupled CTE-thermoelastic waves in a free cylindrical waveguide. Vestn. Samar. Gos. Univ. Natural sciences ser., 2008, no. 8/1(67), pp. 411–459 (in Russian).
  5. Kovalev V. A., Radayev Yu. N., Semenov D. A. Coupled dynamic problems in hyperbolic thermoelasticity. Izv. Sarat. Univ. (N. S.), Ser. Math. Mech. Inform., 2009, vol. 10, iss. 4, pt. 2, pp. 94–128 (in Russian).
  6. Kovalev V. A., Radayev Yu. N. Wavenumbers of plane GNIII-thermoelastic waves and inequality, providing their normality. Izv. Sarat. Univ. (N. S.), Ser. Math. Mech. Inform., 2010, vol. 10, iss. 3, pp. 46–53 (in Russian).
  7. Kovalev V. A., Radayev Yu. N. Volnovye zadachi teorii polia i termomekhanika [Wave problems of field theory and thermomechanics]. Saratov, Saratov. Univ. Press, 2010, 328 p. (in Russian).
  8. Nowacki W. Theory of asymmetric elasticity. Oxford,Pergamon Press, 1986, 384 p. 
  9. Eringen А. С. Microcontinuum field theories. Vol. 1. Foundations and Solids. Berlin ; Heidelberg ; N. Y.,Springer, 1999, 325 p.
  10. Nowacki W. Theory of elasticity. Moscow, Mir, 1975, 872 p. (in Russian).
Received: 
11.08.2013
Accepted: 
10.01.2014
Published: 
28.02.2014
Short text (in English):
download
(downloads: 153)
  • 949 reads