Dynamic extension and twist of a non-linear elastic tube

The propagation of waves in a non-linear cylindrical elastic membrane is considered when one end is fixed and the other is subjected to a dynamic extension and twist. The governing equations are derived for a hyperelastic material with a general strain energy function. In order to obtain specific results the equations are specialised to deal with neo-Hookian materials and in this case we show that there are three real wave speeds in each direction along the cylinder. Numerical results are given and a limiting case considered which provides a check on these results.