Geometric Localization of Waves on Thin Elastic Structures

I this talk, I will consider the propagation of waves on thin elastic structures with varying curvature profiles using the semiclassical WKB approximation.  Using concrete examples of a curved rod and a singly curved shell, I will discuss how a varying curvature profile can be used to trap waves at points where the absolute curvature of the structure has a minimum.  The excellent agreement between our numerical experiments and the semiclassical results hinges on the vanishing of two extra phases that arise in the semiclassical quantization rule.  Our findings open up novel ways to fine-tune the acoustic and vibrational properties of thin elastic structures.