Wavenumbers of Doublet and Triplet Plane Thermoelastic Wave in Ultraisotropic Micropolar Medium

Abstract

In this paper we consider problems related to propagation of coupled plane time-harmonic waves of temperature increment, translational and spinor displacements in an ultraisotropic micropolar thermoelastic solid and calculate their wavenumbers. The ultraisotropic model is derived from an isotropic solid as it’s simplification. The proposed model is characterized by constitutive tensors treated as those with constant components. A closed coupled system of second-order partial differential equations with respect to the temperature increment and displacement vectors is obtained. Characteristic equations for wavenumbers of plane harmonic coupled thermoelastic longitudinal (bicubic equation) and transverse (biquadratic equation) waves are found and analyzed. The longitudinal wave (as a triplet wave comprising translational displacements wave, spinor displacements wave, temperature wave) and cold transverse wave (as a doublet wave of translational and spinor displacements) propagating in an ultraisotropic micropolar thermoelastic solid are investigated. Algebraic expressions for the characteristic equations roots are found and normal wavenumbers are discriminated.