Local resonance phononic band gaps in modified two-dimensional lattice materials

In this paper, modified two-dimensional periodic lattice materials with local resonance phononic band gaps are designed and investigated. The design concept is to introduce some auxiliary structures into conventional periodic lattice materials. Elastic wave propagation in this kind of modified two-dimensional lattice materials is studied using a combination of Bloch's theorem with finite element method. The calculated frequency band structures of illustrative modified square lattice materials reveal the existence of frequency band gaps in the low frequency region due to the introduction of the auxiliary structures. The mechanism underlying the occurrence of these frequency band gaps is thoroughly discussed and natural resonances of the auxiliary structures are validated to be the origin. The effect of geometric parameters of the auxiliary structures on the width of the local resonance phononic band gaps is explored. Finally, a conceptual broadband vibration-insulating structure based on the modified lattice materials is designed and its capability is demonstrated. The present work is anticipated to be useful in designing structures which can insulate mechanical vibrations within desired frequency ranges.