Study On Elastic Wave Propagation In Metamaterial Lattices And Metamaterial Plates

Acoustic elastic metamaterials are man-made periodic elastic composite materials which can offer the possibility to manipulate elastic wave propagating in the subwavelength scale through local resonance mechanism.Elastic metamaterials are materials that may have negative effective mass or negative effective modulus.The existing researches show that the unusual properties of acoustic metamaterial result from the manmade microstructures embedded in host material.The existence of these microstructures makes the classical continuum theory no longer suitable for metamaterials.Therefore,it is necessary to establish a mechanical model to describe the mechanical behavior of metamaterials.Firstly,we start with the discrete spring-mass model and build the continuum model of the metamaterial crystal lattice from one to two dimensions.Then,the in-plane and out-of-plane vibration of the metamaterial plate are studied.The specific research contents and the innovative conclusions are as follows:(1).The continuum models of one dimensional acoustic metainaterials with monatomic and diatomic discrete crystal lattice are studied.The dispersive relation of lattice wave in one-dimensional crystal lattice of metamaterial is established and.compared with that of the classic material.Then,the continuum models of the metamaterial are studied which lead to the classical continuum model,the stain gradient continuum model and the nonlocal gradient continuum model based on different assumptions.The advantages and disadvantages of the above continuum models are discussed based on numerical results.(2).The classical continuum model,the stain gradient continuum model and the nonlocal gradient continuum model are derived for the 9-cell square metamaterial discrete crystal lattice.Then,based on the Cosserat continuum theory and taken the rotation interactions into consideration between particles,the Cosserat continuum model for the 7-cell hexagonal discrete crystal lattice is derived.The dispersive curves as well as the above continuum models are discussed based on numerical results.(3).The propagation of the in-plane guided waves of metamaterial plate with periodically arranged resonators is studied.The propagation of guided waves of metamaterial plate is obviously different from that of classical material plate due to the periodically arranged resonators.In order to describe the influence of the periodically arranged resonators on the propagation of the in-plane guided waves,additional fields are introduced to describe the deformation characteristics of the microstructure,then the total kinetic energy and deformation potential energy of the single cell are established from the scope of energy,and the governing equations of the in-plane guided waves are derived by using the periodic interface conditions of adjacent cells,and the dispersion characteristics of the guided waves are further studied.(4).The propagation of the out-of-plane guided waves of metamaterial plate with periodically arranged resonators is studied.The out-of-plane guided wave refers that the vibration displacement is perpendicular to the wave propagation plane.In this case it leads to symmetry modes and anti-symmetric modes along the thickness direction of the plate,which is not present in the in-plane guided waves.We introduce additional fields to describe microstructure deformation for symmetric and anti-symmetric modes and derive the dispersion equations of the symmetric and antisymmetric modes,respectively.The following results are obtained through the above research.Firstly.for metamaterial crystal lattice,the nonlocal strain gradient continuum model can better describe the dispersive characteristics of the metamaterial crystal lattice than the multi-displacement continuum model and the strain gradient continuum model.Besides,by adjusting the nonlocal parameters,it can help gain a larger frequency range and better description with the dispersion characteristics of the metamaterial crystal lattice.Secondly,the microstructure effect of metamaterial plate can be well described by introducing additional fields that describe the microstructure deformation.The dispersion characteristics of in-plane and out-of-plane guided waves can be better described.