Acoustic Metamaterial Design Method Based On Green Coordinate Transformation

With the continuous development of modern industry,the harm caused by low-frequency vibration is increasingly prominent.Due to the increasingly complex product structure,it is difficult to eliminate vibration and noise from the source,so it is necessary to regulate the acoustic wave in the propagation path.The raise of transformation acoustics and the research on acoustic metamaterial has made it possible to control the propagation of acoustic wave.Transformation acoustics links the spatial coordinate position change with the material physical parameter distribution.First,the propagation path of the acoustic wave in the physical space is planned,and the function mapping relationship corresponding to the space before and after the coordinate transformation is found.The material parameters after transformation are obtained by transformation acoustics and the corresponding acoustic metamaterial is finally designed.The acoustic metamaterial that satisfy transformation acoustics tend to have anisotropic material parameters and the anisotropy can be reduced by the conformal mapping property of Green coordinate transformation during coordinate transformation.As the new composite material,membrane-imbedded acoustic metamaterial possess some excellent mechanical properties which are not possessed by natural materials,and the equivalent elastic modulus of metamaterial can be changed by changing the material parameters of membrane to meet the anisotropy required for transformation acoustics.The material with isotropic density and orthogonal gradient elastic modulus is designed in this paper by the improvement of Norris transformation acoustics and the property of Green coordinate transformation's pseudo-conformal mapping in three-dimensional coordinate system.The asymptotic homogenization method is used to calculate the variation of equivalent elastic modulus of the membrane-imbedded acoustic metamaterial.The shape of the embedded membrane is changed to maintain the shear modulus which perpendicular to the membrane plane within a reasonable range.The anisotropic material that satisfy the transformation acoustics are achieved by imbedding membranes.The finite element analysis of the designed membrane-imbedded acoustic metamaterial is carried out to observe the propagation of acoustic wave in the material.It is proved that the propagation of acoustic wave can be controlled in the material,and the wave can maintain the plane wave characteristics.The genetic algorithm is used to optimize the model after Green coordinate transformation,the calculation error of the deformation gradient and the uneven distribution of the acoustic wave propagation displacement are reduced.The acoustic wave displacement cloud image shows that the acoustic wave propagation is improved in the acoustic metamaterial after genetic algorithm optimization.After the optimization of the genetic algorithm,the anisotropy of obtained material is further reduced,and finally the membrane-imbedded acoustic metamaterial with isotropic density and basic orthotropic elastic modulus is obtained,the difficulty of its implementation is reduced,and the acoustic wave can propagate according to the preset direction and path in the material,which has a good application prospect in the field of low frequency vibration and noise reduction.The multimode hyperboloid membrane-imbedded acoustic metamaterial is designed.The reflection in the shear direction is produced when acoustic wave propagating inside the material,and the propagation characteristics of the incident plane wave can be maintained at the exit.Combined with the nature of simple harmonics,the hyperbolic acoustic metamaterial can be applied to the study of the characteristics of unknown composite waves.