Plane Thermoelastic Waves in Ultrahemitropic Micropolar Solid

Abstract

In the present paper we consider problems related to propagation of plane time-harmonic coupled waves of temperature increment, translational and spinor displacements in an ultrahemitropic micropolar thermoelastic solid and investigation their wavenumbers. The ultrahemitropic model is derived from hemitropic. A closed coupled partial differential equations for the temperature increment and displacements are discussed. Terms of the partial differential equations of coupled micropolar thermoelasticity are compared with respect to micropolar characteristic length scale. The characteristic equations for the wavenumbers of plane harmonic coupled thermoelastic longitudinal (bicubic equation) and transverse (biquadratic equation) waves are found and solved. For a longitudinal wave the complex amplitudes of the temperature increment, translational and spinor displacements are also coupled, contrary to an athermal (or cold) transverse wave. The thermal part can not be eliminated from a thermoelastic longitudinal wave, whereas the transverse wave is intrinsically athermal and is called as cold. Algebraic radical expressions for the roots of the characteristic equations are obtained and normal wavenumbers with a positive real parts are discriminated.