Multi-Stop Band Wave Propagation in a Honeycomb Metamaterial With Embedded Resonators

Abstract

This work discusses the stop-band propagation properties of a honeycomb metamaterial hosting a periodic arrangement of highly tunable, infinite-dimensional resonators. The cellular material system architecture takes inspiration from lightweight honeycombs — due to their inherent periodicity, high flexural/shear stiffness — which host resonators with lumped masses exhibiting infinitely many frequencies and modes. These resonators are designed to possess high dynamic resilience and frequency/damping tunability. In the present work, two resonator architectures are investigated and compared, namely, (i) a cantilever with a tip mass, (ii) a spider-web-like structure with a central mass. Contrary to traditional approaches making use of discrete spring-mass-damper resonators, here the infinite-dimensional resonators are intentionally tailored for their potential of generating, in principle, infinitely many band gaps. The nondimensional dispersion curves are obtained via the Plane Wave Expansion method. By retaining the lowest modes of the two investigated resonators designs, the outcomes show the appearance of multiple band gaps whose bandwidth and central frequency depend on the mass ratio and the nondimensional stiffness of the resonators. Preliminary experimental results based on laser scanning vibrometry, and conducted on 3D printed honeycomb samples, corroborate the theoretical model and predictions.