  We propose wave and ray approaches for modelling mid- and high- frequency
structural vibrations through smoothed joints on thin shell cylindrical ridges.
The models both emerge from a simplified classical shell theory setting. The
ray model is analysed via an appropriate phase-plane analysis, from which the
fixed points can be interpreted in terms of the reflection and transmission
properties. The corresponding full wave scattering model is studied using the
finite difference method to investigate the scattering properties of an
incident plane wave. Through both models we uncover the scattering properties
of smoothed joints in the interesting mid-frequency region close to the ring
frequency, where there is a qualitative change in the dynamics from anisotropic
to simple geodesic propagation.
