Abstract:
In this paper, we consider the processes of propagation of coupled harmonic waves of temperature increment, translational and spinor displacements along the axis of a thermally insulated cylindrical waveguide. The waveguide material is assumed to be semi-isotropic thermoelastic micropolar solid. We study the representations of absolute vector fields of translational and spinor displacements by using a system of vortex vector and scalar potentials that ensure the coupling of vector partial differential equations.The equations obtained after substituting Helmholtz representations into the original system of dynamic equations of a semi-isotropic micropolar thermoelastic continuum are investigated. The system of differential equations is divided into a triplet system for scalar potentials of temperature increment, translational and spinor displacements, and a doublet system for vortex potentials included in the Helmholtz decompositions of the translational and spinor displacement vectors. The obtained scalar and vortex vector potentials allow us to determine the fields of translational and spinor displacements vectors and to restore the force and couple stresses.
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