A Study Of Elastic Wave Propagation Properties Of Functionally Graded Piezoelectric Metamaterials

Phononic crystals and metamaterials are artificial periodic structures that can achieve physical properties not common in nature,such as negative density,negative refraction,stealth,band gap,etc.Based on the band gap characteristics of metamaterials,combined with local resonance units,a multifunctional sub-wavelength low-frequency vibration and noise reduction metamaterial can be designed,which has important academic value and wide application prospects in the field of civil engineering.At the same time,the study of the topological properties of metamaterials has aroused widespread interest.The edge state is topologically protected,suppresses defect backscattering and has a certain robustness,and can accurately guide the propagation of mechanical waves,which makes metamaterials have broad application prospects in many fields such as energy harvesting,directional waveguides,and non-destructive testing.Based on this,this paper focuses on two aspects of gradient piezoelectric metamaterials and surface wave topological metamaterials.The details are as follows:(1)By regulating the negative capacitance in the shunt circuit,the piezoelectric metamaterials with gradient and disordered arrays can be programmed.The dispersion relation of the gradient piezoelectric metamaterial beam is calculated by the transfer matrix method.Compared with the periodic piezoelectric beam,the gradient piezoelectric beam can achieve a wider attenuation frequency range,and it is found that it increases with the increase of the negative capacitance ratio.The frequency-space spectrum of the gradient piezoelectric beam was obtained by Fourier transform,and the force-elastic wave rainbow phenomenon was discovered,which can effectively slow down the behavior of flexural wave propagation.The attenuation behavior of bending waves in gradient and disorderly piezoelectric metamaterial sheets in a 2D system was further investigated,with the latter having a wider average bandwidth than the former.(2)In this chapter,a new type of piezoelectric local resonance metamaterial is constructed,and based on the principle of energy band folding,Dirac points appear in the high symmetry points of its energy bands.Changing the capacitance parameters of the shunt circuit can destroy the spatial symmetry of the crystal cell and make the topological phase transition of the structure.Then the SSH model is constructed,and the displacement at the interface can be locally enhanced by applying the excitation of specific frequency.In addition,a gradient SSH piezoelectric local resonance metamaterial structure is designed by combining the concept of topology and gradient.The elastic wave propagation characteristics of the structure with periodic structure,periodic SSH structure,gradient SSH structure and gradient structure are analyzed in frequency domain and time domain respectively.It can be found that compared with periodic SSH structure and periodic structure,the corresponding gradient SSH structure and gradient structure can obtain a wider attenuation frequency range and produce rainbow effect.At the same time,the gradient SSH structure and periodic SSH structure have the characteristics of localization in energy collection,and can obtain higher energy compared with the corresponding gradient structure and periodic structure,which shows the advantages of topology in energy collection.(3)A novel two-dimensional surface wave metamaterial with C_3v symmetry is designed based on the acoustic cone method,and a low-frequency Dirac cone is formed at the high symmetry point of the irreducible Brillouin zone.By rotating the Angle of the resonance unit,the spatial symmetry of the system can be broken and the degeneracy of Dirac point can be opened,thus valley topological materials of two different topological systems can be obtained.By synthesizing a new heterogeneous structure from two topological materials and calculating its projected energy band,the existence of valley Hall topological edge state in the system can be found effectively,and the anti-scattering and robustness of valley hall topological edge state surface waves can be found by studying its propagation behavior.Based on this,a gradient surface wave topological metamaterial was designed and the topological rainbow effect was found.This design can transform the elastic edge state into local standing wave,which makes the structure have a broader application prospect in civil vibration field.