含机构位移模式的超材料低频宽带波动控制

Mechanism-based metamaterials for low-frequency broadband wave control

基于谐振微结构的超材料普遍存在有效工作带宽狭窄和工作频率位置受谐振子质量控制的问题,严重制约了弹性波超材料的应用推广.本文通过将机构位移模式引入超材料中,设计了由圆盘连杆机构组成的机构超材料,研究了其零频负刚度和双各向异性.通过同时引入机构位移模式和内部阻尼,在不增加整体质量的前提下,实现了局域谐振超材料的低频宽带振动控制.本文的研究探索了机构超材料中局部机构位移与整体超低频波动强耦合的机理,为工程结构的宽低频波动与振动控制提供了理论基础与设计指导.

Metamaterials with artificial microstructures possess negative dynamic effective properties that natural materials are unable to achieve,which greatly extend the design space of next generation materials and provide various new ideas for the control of low-frequency elastic waves.Compared with the Bragg scattering-based phononic crystals,elastic metamaterials can have extremely low-frequency bandgap that stops long-wavelength wave propagation.Simple mass-spring models can clearly explain the local resonance mechanism which introduces a negative effective mass density inside the band gap region.However,microstructure-based metamaterials rely on the local resonators and therefore,are usually confronted with the problems of narrow working bandwidth and fixed working frequency,which seriously restrict the application of elastic metamaterials in various engineering fields where structures with simultaneous lightweight and low-frequency vibration or wave controllability are much appreciated.Although the multi-resonator designs can enlarge the band gap region but it sacrifices the overall weight of the structure to achieve the desired broadband purpose.Mechanisms,which are collections of stiffer elements linked by flexible hinges that permit desired local deformation with zero potential energy,have proven to be the essential elements for the rational design of lightweight systems with novel functions and therefore,are particularly suitable for low frequency wave control.In this work,by introducing internal mechanism into the unit cells of elastic metamaterials,a new type of mechanismbased metamaterial is proposed.Firstly,a metamaterial consisting of springs,masses and disc-linkage mechanisms is designed to realize zero-frequency negative stiffness which contributes to the formation of an ultra-wide band gap starting from the quasi-static frequency to a cut-off frequency.Furthermore,a two-dimensional metamaterial consisting of springs,masses and double disc-linkage mechanisms is designed and bi-anisotropy,simultaneously anisotropic mass density and anisotropic modulus,are realized for the first time.Finally,by introducing both internal mechanism and internal damping into the spring-mass metamaterial,low-frequency broadband vibration isolation is realized without increasing the overall mass of the system.The advantages of the design over other multi-resonator designs are:Both translational and rotational resonances of the unit cell consisting of internal mechanism are utilized to generate two band gaps without additional resonant masses,while the damping in the unit cell provides the necessary dissipation to attenuate the waves in the pass band between the two band gaps and eventually,creates a continuous,wide wave attenuation zone.Both theoretical analyses and numerical simulations are carried out to study the physical mechanism behind the coupling effect of the local mechanism movements and the global wave propagations.Compared with microstructure-based metamaterials,the proposed mechanism-based metamaterials possess the advantage of broadband control of the low-frequency wave and vibration in lightweight engineering structures.The mass-spring-internal mechanism model also provides a powerful platform for studying abnormal elastic wave propagations in the low frequency region.The zero-frequency negative stiffness can be useful to realize extremely low frequency wave control and meta-damping while the bi-anisotropy properties are very critical for the interesting unidirectional wave propagation and super-resolution elastic wave imaging for the structural health monitoring and the non-destructive evaluation purposes.