  Soft materials can be designed with a functionally graded (FG) property for
specific applications. In this paper, we analyze the axisymmetric guided wave
propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is
subjected to a combined action of axial pre-stretch and pressure difference
applied to the inner and outer cylindrical surfaces. We consider both torsional
waves and longitudinal waves propagating in the FG cylinder made of
incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin
strain energy function but with the material parameters varying with the radial
coordinate in an affine way. The pressure difference generates an inhomogeneous
deformation field in the FG cylinder, which dramatically complicates the
superimposed wave problem described by the small-on-large theory. A
particularly efficient approach is hence employed which combines the
state-space formalism for the incremental wave motion with the approximate
laminate or multi-layer technique. Dispersion relations for the two types of
axisymmetric guided waves are then derived analytically. The accuracy and
convergence of the proposed approach is validated numerically. The effects of
the pressure difference, material gradient, and axial pre-stretch on both the
torsional and the longitudinal wave propagation characteristics are discussed
in detail through numerical examples. It is found that the frequency of
axisymmetric waves depends nonlinearly on the pressure difference and the
material gradient, and an increase in the material gradient enhances the
capability of the pressure difference to adjust the wave behavior in the FG
cylinder.
