Wave propagation in fractal-inspired self-similar beam lattices

Qi Jian Lim,Eng Huat Khoo,Katia Bertoldi,Soo Jin Adrian Koh,Pai Wang

doi:10.1063/1.4936564

Abstract

We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices. While the response of the triangular lattice is characterized by a locally resonant band gap, both Bragg-type and locally resonant gaps are found for the hierarchical lattice. Therefore, our results demonstrate that structural hierarchy can be exploited to introduce an additional type of band gaps, providing a robust strategy for the design of lattice-based metamaterials with hybrid band gap properties (i.e., possessing band gaps that arises from both Bragg scattering and localized resonance).

Highlights

We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices
Band gaps are generated by Bragg-type scattering, whereas in acoustic metamaterials, localized resonances within the medium are exploited to attenuate the propagation of waves
We focus on the dynamic response of fractal-like triangular beam lattices and investigate both numerically and experimentally the effect of hierarchy on the propagation of small amplitude elastic waves

Summary

Introduction

We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices. Band gaps are generated by Bragg-type scattering, whereas in acoustic metamaterials, localized resonances within the medium are exploited to attenuate the propagation of waves.

Results

Conclusion