Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance.

Lin Li,Jun Li,Yu Fan,Zhou Jiang

doi:10.3390/ma11091656

Abstract

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

Highlights

Periodic structures feature frequency band gaps in which certain wave mode (Bloch wave modal shape) cannot propagate and the associated energy flow is forbidden [1,2,3].Such unique wave filtering characteristics can find applications in vibration reduction [4,5,6], energy focus [7] and even acoustic cloaking [8]
The creation of a Bragg or a local resonance (LR) band gap attributes to the frequency evolution of a single wave mode, as the results of interference generated by the interaction of incident and scattered waves at the unit-cell boundaries that periodically presented in space [9]
The question is how to identify the ‘effective’ band gap for the flexural and electric deformation. For this we propose the following indicator termed the Ratio of Single Wave (RSW): ratio of single wave (RSW) = MAC(φref, φfull ) =

Summary

Introduction

Periodic structures feature frequency band gaps ( termed the stop bands) in which certain wave mode (Bloch wave modal shape) cannot propagate and the associated energy flow is forbidden [1,2,3]. Such unique wave filtering characteristics can find applications in vibration reduction [4,5,6], energy focus [7] and even acoustic cloaking [8]. The Bragg band gaps appear around frequencies governed by the Bragg condition L = n(λ/2) where n is an integer, λ is the wavelength and L is the unit-cell length ( termed the lattice constant). This implies that the structural periodicity must be of the same order as the wavelength of the band-gap frequencies, as observed in periodic engineering structures such as truss beams [10], perforated plates [11], and stiffened cylinders [12]

Objectives

Results

Conclusion