Regulation Of Band Gap And Topological Transport In Active Metamaterials

Elastic metamaterial is a new type of functional materials with periodic distribution of geometry and material parameters,which have new mechanical properties such as band gap,negative equivalent mass and negative equivalent stiffness.It has important academic value and application prospect in many fields of civil engineering,such as vibration isolation,earthquake resistance and noise reduction.In addition,the analogical Hall effect topological theory has been extended to the field of elastic wave.Elastic topological materials have an edge state at the cell interface,which can suppress the backscattering of defects,and has certain robustness due to the protection of topology.It can accurately guide and control the propagation of elastic wave,and has certain application value in the fields of structural detection,vibration isolation,noise reduction,and directional waveguide.However,the shortcomings of current research on topological metamaterials can be divided into two aspects:the band gap and topological states of most metamaterials are uncontrollable,the operating frequency range is narrow and the physical properties are single,which can't meet the practical engineering needs;In the field of elastic wave,the band gap of metamaterials is mostly due to Bragg scattering,and its operating frequency is usually in the range of medium and high frequency,so its application in civil engineering is greatly limited.Aiming at the above problems,this paper obtains the following research results:(1)A new type of one-dimensional granular crystal is designed.The contact stiffness between the particles is changed by changing the pre-compression on both ends of the crystal,and then the frequency range of band gap and topological properties of the granular crystal are adjusted.By combining the two structures with different topological properties together and changing the magnitude of the pre-compression,an adjustable interface states is obtained.The frequency response analysis of discrete and continuous models is used to obtain the corresponding frequency of interface states,and the transient analysis of discrete and continuous models is carried out by using state space method and finite element method,which further confirms the existence of interface states.(2)This article established a new kind of local resonance hybrid beam by introducing local resonance in periodic piezoelectric beam,which present a low frequency of acoustic branches and high frequency of optical branch in the band structure.Based on the band folding mechanism,two Dirac points are observed in the double-periodic band structure,and a low-frequency subwavelength band gaps are obtained by breaking the spatial symmetry of the cell.The regulation of shunt circuit is used to realize band inversion,and two kinds of microstructural models are established to form a heterostructure and excite the topological interface states.By combining the piezoelectric shunt circuit,the working frequency of the topological interface state can be tuned.(3)A new type of piezoelectric metamaterial plate is constructed in this paper,of which the system has C_3vsymmetry and a Dirac cone is observed at K point of the Brillouin region.By changing the parameters of the adjacent shunt-circuit,the spatial symmetry of the system is destroyed,so that the Dirac points open,close and open again,and the Berry curvature of the upper and lower valley states is reversed.Then,two kinds of piezoelectric metamaterial microstructure models with different topological properties are obtained.By combining metamaterials with different valley hall phases,we have constructed a variety of heterostructure plates,and analyzed the field distribution and the corresponding dispersion relations of the valley projection edge states at the boundary surface.Finally,by combining with the displacement mode shape,the ability of edge states to resist corners and defects is further analyzed,and the regulation mechanism of valley topological edge state transport in piezoelectric metamaterials is revealed.