Coupled Harmonic Plane Waves in a Semi-Isotropic Thermoelastic Medium

The present paper deals with problems of propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The requisite constitutive and differential equations of semi-isotropic solids are revisited. Dispersion equation for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic algebraic equation) are obtained and analyzed. Dispersion equations for the transverse waves (equation of the 8th algebraic degree) are splitted into two algebraic quartic equations and then solved. For a longitudinal wave, the complex amplitudes of temperature increment, translational displacements and spin–vector are coupled, unlike a transverse wave. The roots of mentioned algebraic equations are calculated by using the Wolfram Mathematica 13 symbolic computing system. The normal wavenumbers with positive real part are discriminated.