Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics

A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms ${\displaystyle \underline{u}=(0,u_{\theta },0)}$, ${\displaystyle \underline{\phi }=({\phi }_r,0,{\phi }_z)}$ ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how ${\displaystyle \underline{u}}$ and ${\displaystyle \underline{\phi }}$ can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated body couple in an infinite space can be obtained from the solution of a pure stress problem.