On Elastic Oscillations of a Thick-Walled Cylindrical Shell Subjected to Initial Finite Twist

This paper is concerned with the natural vibrations of a rubber-like, thick-walled tube which is prestressed by an initial finite twist about the axis of the tube. The analysis is based on a rigorous theory of finite elasticity and the extended theory of small displacements superposed on large elastic deformations. Numerical results are obtained for tubes made of a neo-Hookean material. The fundamental frequency of the vibrations is found to depend on the prestressed state of the tube. In particular, when the tube becomes unstable under the initial twist, then the corresponding fundamental frequency ceases to be real-valued. When this happens, the problem becomes identical with that of torsional instability of similar tubes which was investigated earlier both analytically and experimentally.