#### Vol. 12, No. 4, 2017

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Localized bulging of rotating elastic cylinders and tubes

### Juan Wang, Ali Althobaiti and Yibin Fu

Vol. 12 (2017), No. 4, 545–561
##### Abstract

We investigate axially symmetric localized bulging of an incompressible hyperelastic circular solid cylinder or tube that is rotating about its axis of symmetry with angular velocity $\omega$. For such a solid cylinder, the homogeneous primary deformation is completely determined by the axial stretch ${\lambda }_{z}$, and it is shown that the bifurcation condition is simply given by $d\omega ∕d{\lambda }_{z}=0$ if the resultant axial force $F$ is fixed. For a tube that is shrink-fitted to a rigid circular cylindrical spindle, the azimuthal stretch ${\lambda }_{a}$ on the inner surface of the tube is specified and the deformation is again completely determined by the axial stretch ${\lambda }_{z}$ although the deformation is now inhomogeneous. For this case it is shown that with $F$ fixed the bifurcation condition is also given by $d\omega ∕d{\lambda }_{z}=0$. When the spindle is absent (the case of unconstrained rotation), we also allow for the possibility that the tube is additionally subjected to an internal pressure $P$. It is shown that with $P$ fixed, and $\omega$ and $F$ both viewed as functions of ${\lambda }_{a}$ and ${\lambda }_{z}$, the bifurcation condition for localized bulging is that the Jacobian of $\omega$ and $F$ should vanish. Alternatively, the same bifurcation condition can be derived by fixing $\omega$ and setting the Jacobian of $P$ and $F$ to zero. Illustrative numerical results are presented using the Ogden and Gent material models.

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