Band gap formation in thin plates with a periodic array of resonators

Sahar Zouari,Julien Brocail,Jean-Michel Genevaux,Frédéric Ablitzer

doi:10.1051/meca/2016062

Abstract

A resonator assembly consisting of a two-dimensional periodic array (mass-screws) mounted to a thin homogenous plate was used to investigate the vibration characteristics of locally resonant (LR) phononic plates. The numeric simulations employed the finite element method to calculate the band structures of the proposed periodic plates and to analyze the effect of geometry parameters on the evolution of the flexural band gap behavior. To experimentally validate the predictions for these theoretical examinations, two measurements with the LR phononic plates were obtained with respective lattice constants a = 40 and 50 mm. The tested plate was clamped on one side to a shaking table to generate a plane wave, propagating in the Ox-direction. Obtained experimental measurements of the wave attenuation in this direction are in good agreement with the theoretical frequency of both complete and directional band gaps.

Highlights

The present paper proposes a two-dimensional (2D) locally resonant (LR) phononic plate composed of a thin homogeneous plate with an attached periodic array of resonators
The present study focused on the resonant frequency of the resonator and periodicity variations, and its impact on the flexural wave band gap behavior of the proposed periodic structure
The studied LR phononic plate consisted of a periodic array of resonators mounted to a thin homogeneous plate (Fig. 1a)

Summary

Introduction

The present paper proposes a two-dimensional (2D) LR phononic plate composed of a thin homogeneous plate with an attached periodic array of resonators (massscrews). This periodic structure allowed us to modify various geometric experimental parameters. The present study focused on the resonant frequency of the resonator and periodicity variations, and its impact on the flexural wave band gap behavior of the proposed periodic structure. A finite element method (FEM) was used. To investigate wave propagation in these LR plates. Band structures were calculated to predict band gaps characteristics. To experimentally validate our theoretical predictions, we used different lattice constants to measure the unidirectional excitation response of the LR phononic plates

Model and method

Experimental results

Conclusion