The eigen value approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equation in a micropolar viscoelasitc medium for the anti- plane strain problem. An infinite space with concentrated force at the origin has been applied to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal microrotation, tangential displacement, tangential force stress and normal couple stress components have been obtained numerically and illustrated graphically to depict the effects of viscosity. A particular case of a micropolar elastic solid has also been deduced.
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