Finite,free torsional oscillations of hollow circular cylinders made of a mooney material

Finite, free torsional oscillations of hollow circular cylinders of arbitrary wall thickness and of arbitrary length are investigated. The material of the cylinder is assumed to be homogeneous, isotropic, elastic and incompressible. The governing differential equations of motion are obtained by the use of finite elasticity theory. While the exact solution of the problem requires a rather unrealistic body force distribution in the axial direction, it is shown that, in the solutions corresponding to long tubes and hollow disks, the error introduced by ignoring the body force distribution is negligibly small for large wavelengths.