Geometric localization of waves on thin elastic structures

Manu Mannattil, Christian D. Santangelo

Research output: Contribution to journalArticlepeer-review


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 studies on related problems have broadly focused on the localization of flexural waves on such structures. Here, using the semiclassical WKB approximation for multicomponent waves, 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. We also see excellent agreement between our numerical experiments and the semiclassical results, which 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 and raise the possibility of introducing new phenomena not easily captured by effective models of flexural waves alone.

Original languageEnglish (US)
Article number035001
JournalPhysical Review E
Issue number3
StatePublished - Mar 2024

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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