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In this paper we study the motion of a finite composite cylindrical annulusmade of generalized neo-Hookean solids that is subject to periodic shearloading on the inner boundary. Such a problem has relevance to several problemsof technological significance, for example blood vessels can be idealized asfinite anisotropic composite cylinders. Here, we consider the annulus to becomprised of an isotropic material, namely a generalized neo-Hookean solid andstudy the effects of annular thickness on the stress distribution within theannulus. We solve the governing partial differential equations and examine thestress response for the strain hardening and strain softening cases of thegeneralized neo-Hookean model. We also solve the problem of the annular regionbeing infinite in length, that reduces the problem to a partial differentialequation in only time and one spatial dimension. When the thickness of theannulus is sufficiently large, the solutions to the problems exhibit veryinteresting boundary layer structure in that the norm of the strain has a largegradient in a narrow region adjacent to one of the boundaries, with the strainbeing relatively uniform outside the narrow region. We also find that beyond adistance of two times the annular wall thickness from the ends of the cylinderthe solutions for the infinite length cylinder match solutions for the finitelength cylinder implying that end effects are not felt in most of the length ofa sufficiently long annulus.

Motion of a finite composite cylindrical annulus comprised of nonlinear elastic solids subject to periodic shear