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

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.