2-D periodic structures. A numerical study

Giuseppe Rocchetta,Geminiano Mancusi

doi:10.1108/prr-07-2018-0021

Abstract

Purpose Within the context of 2D square lattices, searching for the existence of band gaps assumes a great interest owing to many possible fields of application: from energy absorption devices to noise and vibration controllers, as well as advanced strategies for the seismic isolation. Design/methodology/approach The underlying microstructure may influence the mechanical response of 2D square lattices according to a complex interplay between different factors. A first one is related to the so-called “size-effect”. A second one relates, instead, to the mass density distribution. Findings It has been observed that lumped masses may induce additional band gaps to appear and may magnify their width. Finally, an additional factor deals with the inner damping characteristics of the constituent materials, which usually are polymer-based. Originality/value This study focuses on the first factor from a specific perspective: to investigate the influence of the size effect on the existence and properties of frequency band gaps.

Highlights

The study of the dynamic properties of a 2D lattice (Zhou et al, 2009; Wang et al, 2009; Martinsson and Movchan, 2003; Phani et al, 2006; Zhen et al, 2008; Gaofeng and Zhifei, 2010)is usually based on few assumptions
This study focuses on the first factor from a specific perspective: to investigate the influence of the size effect on the existence and properties of frequency band gaps
By virtue of the Bloch theorem, the hypothesis of infinite lattice points allows to restrict the study to the representative unit cell (RUC)

Summary

Introduction

The study of the dynamic properties of a 2D lattice (Zhou et al, 2009; Wang et al, 2009; Martinsson and Movchan, 2003; Phani et al, 2006; Zhen et al, 2008; Gaofeng and Zhifei, 2010)is usually based on few assumptions. Originality/value – This study focuses on the first factor from a specific perspective: to investigate the influence of the size effect on the existence and properties of frequency band gaps. Keywords 2D lattice structures, Frequency band gaps, RUC

Results

Conclusion