Torsional wave band gap properties in a circular plate of a two-dimensional generalized phononic crystal

Lei Zhao,Shanjun Liang,Haisheng Shu,Jie Zhu,Xiaona Shi,Wanyue Ren,Shuowei An

doi:10.1063/1.5027600

Abstract

The torsional wave band gap properties of a two-dimensional generalized phononic crystal (GPC) are investigated in this paper. The GPC structure considered is consisted of two different materials being arranged with radial and circumferential periodicities simultaneously. Based on the viewpoint of energy distribution and the finite element method, the power flow, energy density, sound intensity vector together with the stress field of the structure excited by torsional load are numerically calculated and discussed. Our results show that, the band gap of Bragg type exists in these two-dimensional composite structures, and the band gap range is mainly determined by radial periodicity while the circumferential periodicity would result in some transmission peaks within the band gap. These peaks are mainly produced by two different mechanisms, the energy leakage occurred in circumferential channels and the excitation of the local eigenmodes of certain scatterers. These results may be useful in torsional vibration control for various rotational parts and components, and in the application of energy harvesting, etc.

Highlights

As a part of the quasi periodic structures, we have extended the traditional concept of phononic crystal to a more general case, i.e., the generalized phononic crystal.[11]
A kind of generalized phononic crystal (GPC) structure with both radial and circumferential periodicities is investigated from the angle of energy distribution in this paper
Dynamic model is presented and some important physical fields associated with energy such as the power flow, energy density and the sound intensity vector are calculated numerically using the finite element method

Summary

INTRODUCTION

The traditional theory of phononic crystals becomes more and more mature in recent years which makes the concept of phononic crystal show great application prospect in relevant fields such as elastic wave control, sound and vibration reduction etc.[1,2,3] More recently, the quasi periodic structures receive people’s attention.[4,5] It has been manifested that band gap of elastic wave can be produced by these special structures.[6,7,8] And that, some new properties may be in existence, for example, the phenomenon of energy localization in a circular phononic/photonic crystal without defect.[9,10]. As a part of the quasi periodic structures, we have extended the traditional concept of phononic crystal to a more general case, i.e., the generalized phononic crystal.[11] Through the investigation of a GPC plate and cylindrical shell with radial periodicity only, similar phononic band gaps are manifested numerically and experimentally.[11,12,13] It should be noted that, the frequently-used Bloch theorem is not applicable to these special structures involving material periodicities along curvilinear coordinates.[14,15,16] To characterize the band gap behaviors and wave propagation properties in those structures with one dimensional periodicity (radial periodicity), it is more suitable to combine the transfer matrix method and the concept of localized factor.[17,18,19,20].

MODEL AND METHOD

EXISTENCE AND FORMING MECHANISM OF THE BAND GAP

ENERGY DISTRIBUTION AND FLOW AT NON-PEAK FREQUENCY IN THE BAND GAP

ENERGY DISTRIBUTION AND FLOW AT PEAK FREQUENCY IN THE BAND GAP

CONCLUSIONS