Abstract
The deformation of a circular cylindrical elastic tube of finite wall thickness under rotation about its axis is considered. The angular speed (\(\omega\)) is analyzed as a function of an azimuthal deformation parameter at fixed axial extension for incompressible, isotropic, neo-Hookean elastic strain-energy function. Our aim is to investigate the bifurcation of the tube for the case of the prismatic bifurcation mode. We used the asymptotic WKB method for the solution of the eigenvalue problem. Although the dependency of \(\lambda _a\) (the ratio of the deformed inner radius to the un-deformed case) on the wall thickness (A/B) has a boundary layer structure, it depends on the mode numbers and the magnitude of the axial extension (\(\lambda _z\)). Finally, the eigenfunctions are obtained for \(\lambda _z=0.2,\,1,\,5\) and \(m=10,\,15,\,20\). We find that our derived asymptotic results are very similar to the counterpart numerical data.
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