  A refined dynamic finite-strain shell theory for incompressible hyperelastic
materials was developed by the authors recently. In this paper, we first derive
the associated linearized incremental theory, and then use it to investigate
wave propagation in a fiber-reinforced hyperelastic tube that is subjected to
an axial pre-stretch and internal pressure. We obtain the dispersion relations
for both axisymmetric and non-axisymmetric waves and discuss their accuracy by
comparing them with the exact dispersion relations. The bending effect is also
examined by comparing the dispersion curves based on the present theory and
membrane theory, respectively. It is shown that the present theory is more
accurate than the membrane theory in studying wave propagation and the bending
effect plays an important role in some wave modes for relatively large
wavenumbers. The effects of the pressure, axial pre-stretch and fiber angle on
the dispersion relations are displayed. These results provide a theoretical
foundation for wave propagation in arteries, which can be used to determine
arterial properties.
