Band Gap And Nonreciprocal Transmission Characteristics Of Granular Nonlinear Elastic Wave Metamaterials

In recent years,with the development of phononic crystals and elastic wave metamaterials,there are related applications in many technical fields.Elastic wave band gap,as a very important characteristic of phononic crystals,has received a lot of attention.Within the band gap,elastic waves cannot pass through phononic crystals.Up to now,studies about the nonlinear phononic crystals and elastic wave metamateirals are rather limited.Among them,the granular structure is a widely applied peridoc structures which is composed of elastic particles in contact with each other.It is also the main research object of this work.Another interesting characteristic of phononic crystals is the defect state.When there are point and line defects in the phononic crystal,the elastic wave will be localized at the point defect or can only propagate along the defect direction.Therefore,through changing the parameters of the phononic crystal structure and its defects,the propagation of elastic waves can be adjusted flexibly.On the other hand,inspired by electronic diodes,the concept of one-way transmission is introduced into the field of phononic crystals and elastic wave metamaterials,which can lead the design of a diode to realize the nonreciprocal transmission of nonlinear elastic waves.Firstly,the band gap characteristics of one-dimensional diatomic particle chain and the nonreciprocal transmission characteristics of nonlinear elastic waves are discussed.The incremental harmonic balance method is extended to nonlinear elastic wave metamaterials.The traditional calculation method of band gap in nonlinear periodic structure is improved.Then,the band gap of the diatomic particles chain is calculated and its influences are discussed.It is found that the position and width of the band gap can be changed by the different mass and amplitude ratios of the two kinds of particles,and then the nonlinear elastic wave can be tuned.In addition,a defect particle is introduced to design an elastic wave diode.The diode phenomenon is observed by numerical simulation and experiments and the nonreciprocal transmission of nonlinear elastic wave is realized.Secondly,we propose a curved diatomic particle chain.Compared with a straight chain,the curved one can satisfy the propagation of nonlinear elastic waves along the non-straight directions,which is not limited to a single straight direction.The band gap of the structure is calculated by the incremental harmonic balance method,and different effects on the band gap are discussed.On the other hand,a new type of diode structure is proposed and designed to realize the nonreciprocal transmission of nonlinear elastic waves in the diode.The numerical simulation and experimental results are consistent with theoretical predictions.This study provides a new application for phononic crystals and elastic wave metamaterials with nonlinear properties,which can realize the diode phenomenon of nonlinear elastic waves with tunable directions.Finally,we propose a digitally programmable elastic wave metamaterial,which is composed of two different components with the one direction transmission of elastic waves.There are four different coding modes,which are defined as ‘11','01',‘10' and‘00',respectively.Based on the difference of band gap positions and widths,different coded signals can be achieved within wide frequency regions.In addition,by changing the combination of the two components of the programable metamaterial,different transmission directions can be realized which makes the adjustment of nonlinear elastic waves more conveniently.