Active Control Of Topological Properties On Elastic Wave Metamaterials

Phononic crystals are the composite structures in which the band gaps of acoustic or elastic waves can be found,in which the band structure is the basic feature.Researchers use various methods to adjust the band gap characteristics,in which most attention is focused on changing the filling ratio and structure types.Recently,the active control on the band gaps of phononic crystals and elastic waves has received considerable attention.It is an innovative research to use the negative capacitance circuit containing piezoelectric materials to realize the control of elastic wave.In addition,the topological properties of phononic crystals and acoustic metamaterials are also popular.Many researches on the topological properties of sound waves in phononic crystals have been performed.The topological immunity,topological edge states and interface states of acoustics have been realized.Inspired by these advances,it is necessary to consider the topological properties of flexural waves in solid structures.In this work,the topological properties of flexural waves in elastic wave metamaterials are studied.In this work,we first discuss the adjustment of controllable circuit on band gaps of elastic wave metamaterial beam in which the piezoelectric shunt circuits are attached periodically.After that,the unit cell is controlled actively,as well as the generation and disappearance are observed with active control system.Then,an elastic wave metamaterial beam with the interface is constructed to study the effect of the active control system on the band gap and interface localized state.The present part of this work is mainly to change the band gap or generate the interface state of the elastic wave metamaterial beam by adjusting the resistance and other parameters in the shunt circuit,after which the band gap characteristics and topological properties are analyzed.This section proves that the piezoelectric shunt circuit can effectively adjust the band gap characteristic,generate Dirac points and form the topological interface state.In previous investigations,it is found that the hexagonal cell is a common repeating unit with topological properties in acoustic periodic structure.Therefore,a hexagonal cell is designed.By attaching piezoelectric patches to the unit cell which can show the Dirac and Dirac-like points and connecting negative capacitance circuit to regulate the parameters of piezoelectric patches,we can realize the active control of the topological characteristics of flexural wave.Finally,we apply the two-dimensional Kagome structure and fabricate an active control system based on this structure by laying piezoelectric patches and connecting negative capacitance circuits.For this unit cell which can be controlled actively,the band structures are calculated when the electric circuits are open and connected and the controllable effect of the active control system on Dirac point is verified.Then,the symmetry of the unit cell is reduced,which results in the disappearance of the Dirac point.Then,the unit cells are periodically arrayed by two different ways to generate the elastic wave metamaterial plate with the topological interface state.During these studies,the topological concepts of physics and acoustics are introduced into the elastic wave metamaterial plate,which can obtain the topological properties and actively controllable characteristics of flexural waves.