Zero-energy topological oppy edge modes have been demonstrated in families of kagome lattices with geometries that differ from the regular case composed of equilateral triangles. In this work, we explore the behavior of these systems in the limit of continuum elasticity, which is established when the ideal hinges that appear in the idealized models are replaced by ligaments capable of supporting bending deformation, as observed in realistic physical lattices. Under these assumptions, the oppy edge modes are preserved but shifted to finite frequencies, where they spectrally overlap with the acoustic bulk modes. The net result is the establishment of a relatively broad low-frequency regime over which the lattices display strong asymmetric wave transport capabilities. By simply varying the thickness of the ligament of the unit cell, we can obtain a variety of lattices with different localization capabilities. Through theoretical analysis and finite element simulations, we parametrically explore the localization capabilities of different configurations, thus establishing a qualitative relation between the topological descriptors of the unit cell and the effective global transmission properties of the lattice. Using simple elasticity arguments, we provide a mechanistic rationale for the observed range of behaviors. Our study has implications for the design of mechanical filters, structural logic components, and acoustic metamaterials for wave manipulation at large.
|Original language||English (US)|
|Title of host publication||Health Monitoring of Structural and Biological Systems XIII|
|Editors||Paul Fromme, Zhongqing Su|
|State||Published - 2019|
|Event||Health Monitoring of Structural and Biological Systems XIII 2019 - Denver, United States|
Duration: Mar 4 2019 → Mar 7 2019
|Name||Proceedings of SPIE - The International Society for Optical Engineering|
|Conference||Health Monitoring of Structural and Biological Systems XIII 2019|
|Period||3/4/19 → 3/7/19|
Bibliographical noteFunding Information:
The authors acknowledge the support of the National Science Foundation (NSF Grant No. EFRI-1741618).
© 2019 SPIE.
- Kagome lattice
- Topological floppy edge modes
- Topological metamaterials
- Wave propagation