An overview of geometric phases in elastic systems and their connection to topological invariants of elastic metamaterials

Mohit Kumar; Fabio Semperlotti

doi:10.1117/12.3010877

9 May 2024 An overview of geometric phases in elastic systems and their connection to topological invariants of elastic metamaterials

Mohit Kumar, Fabio Semperlotti

Author Affiliations +

Proceedings Volume 12951, Health Monitoring of Structural and Biological Systems XVIII; 129510V (2024) https://doi.org/10.1117/12.3010877
Event: SPIE Smart Structures + Nondestructive Evaluation, 2024, Long Beach, California, United States

Abstract

The geometric phase is an additional phase factor acquired by oscillating dynamical systems. It has emerged as an insightful parameter to understand the dynamic behavior in a variety of systems, from molecular physics to elastic waveguides. In more recent years, the geometric phase has been widely exploited in connections with the analysis of topological materials. The present article reviews the concept of geometric phase in elastic systems and its connection to the design of elastic topological metamaterials. Examples are presented to explain the theoretical basis of the geometric phase by using arguments of differential geometry and topology. These concepts are then applied to the analysis of a one-dimensional elastic topological metamaterial that possesses localized vibration modes immune to geometric perturbations.

Conference Presentation

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Mohit Kumar and Fabio Semperlotti "An overview of geometric phases in elastic systems and their connection to topological invariants of elastic metamaterials", Proc. SPIE 12951, Health Monitoring of Structural and Biological Systems XVIII, 129510V (9 May 2024); https://doi.org/10.1117/12.3010877

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