Wave numbers of harmonic plane waves of translational and spinor displacements in a semiisotropic thermoelastic solid

In present paper the propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semiisotropic thermoelastic solid is discussed. Characteristic equations for the wave numbers of plane harmonic coupled thermoelastic longitudinal (bicubic equation) and transverse waves (biquartic equation that naturally splits into two quartic algebraic equations) are obtained and analyzed. For a longitudinal wave, the complex amplitudes of the temperature increment, translational and spinor displacements are also coupled, contrary to a transverse wave. Algebraic forms containing multivalued complex square and cubic radicals for the wave numbers of transverse waves are derived by using the Wolfram Mathematica 13 symbolic computing system.