  We consider the localization of elastic waves in thin elastic structures with
spatially varying curvature profiles, using a curved rod and a singly-curved
shell as concrete examples. Previous work on related problems have largely
focused on the localization of flexural waves on such structures. Here, using
the semiclassical/WKB approximation, we show that in addition to flexural
waves, extensional and shear waves also form localized, bound states around
points where the absolute curvature of the structure has a minimum. These
findings open up novel ways to fine-tune the acoustic and vibrational
properties of thin elastic structures, and raise the possibility of introducing
new phenomena not easily captured by effective models of flexural waves alone.

Soft Condensed Matter;Other Condensed Matter;Classical Physics