Wave Characteristics Of Two-dimensional Labyrinth Elastic Metamaterials

Metamaterials are a type of composite materials and structures composed of artificial unit cells in a certain order.Their properties are mainly determined by the structural characteristics and the order of the primitives.The abnormal behaviors of wave propagation can be obtained by careful design of the unit cells and their order.For elastic metamaterials formed by etching holes in solid matrix,the wave functions are mainly dependent on the structural parameters and the order of the unit cell.The labyrinth unit contains more bends,which can extend the wave propagation paths and promote the generation of sound band gaps.It can also be used to design acoustic metasurfaces,adjust the amplitude and phase of reflected/refracted sound waves,and achieve acoustic functions such as abnormal refraction and focusing.Inspired by this,this paper studies the propagation characteristics of elastic waves in two-dimensional labyrinth metamaterials(including phononic crystals,phononic crystal plates,and elastic metasurfaces).The main contents and conclusions include:(1)The band structure,response spectrum and iso-frequency curve of the two-dimensional labyrinth phononic crystal are calculated.Effects of the geometric parameters of the labyrinth unit(such as the number of bends,the width of the long arm and the width of the short arm)on the band gaps are invetigated.At the same time,3D printing technology is used to fabricate the labyrinth phononic crystal samples for experimental tests.The results show that: the labyrinth unit can be used to extend the propagation distance of elastic waves and induce complex vibration modes,which leads to the generation of low-frequency band gaps;the geometric parameters of the labyrinth unit significantly affect the width and position of the band gap;the experimental measurements and numerical results generally agree with each other.(2)Effects of the plate thickness on the band gap characteristics of two-dimensional labyrinth phononic crystal plates are discussed.Combined with iso-frequency curves,the directional propagation characteristics of flexural waves are analyzed.The results show that with the increase of the plate thickness,the order of corresponding band for the band edge is increasing,and the position of the band gap is also rising.By designing the labyrinth unit,directional transmission of flexural waves at different frequencies and in different directions can be achieved.(3)Based on the generalized Snell's law,the curved elastic metasurfaces are designed.By designing the geometric parameters of the labyrinth element,the phase of the refracted wave is adjusted,and the flexural wave is focused;Influences of the signal source,the number of elements,and the radius of curvature on focusing are analyzed.The results show that: the labyrinth element can be used to design curved metasurfaces with different curvatures and achieve the focusing of flexural waves;...