Analysis Of Dynamic Mechanical Properties For Three-dimensional Membrane-imbedded Acoustic Metamaterial

With the rapid development of modern industry and aerospace industry,the requirements for material properties are getting better and better,so the composite materials have gained more and more applications because of their excellent mechanical properties.Metamaterial is one kind of composite materials and possess some properties which are not possessed by natural materials,what's more they often have more excellent mechanical properties than general composite materials.The membrane-imbedded acoustic metamaterial is a new type of metamaterial,it has a good application prospect in the field of low-frequency vibration and noise reduction.In addition,the membrane can regulate the equivalent elastic modulus of the material model in certain directions,so the material model can get the required anisotropic properties to achieve the control of wave propagation.The membrane-imbedded acoustic metamaterials can also be used to design new types of acoustic components due to this property.The analysis of mechanical properties for membrane-imbedded acoustic metamaterials can predict their mechanical properties,which contributes to the further research and popularization of membrane-imbedded acoustical metamaterials.In order to control the wave propagation,the transformation acoustics theory must be used to calculate and design the material parameters of the transformation medium,and it's also necessary to find out the relationship between the material parameter distribution and the coordinate transformation.The deformed material needs to have certain anisotropic mechanical properties to let the wave to propagate according to the preset path.The membrane-imbedded acoustic metamaterial can get the required anisotropy properties by adjusting the membrane parameters.Therefore,the membrane-imbedded acoustic metamaterial can be well applied to transformation acoustics.The static and dynamic finite element analysis of the membrane-imbedded acoustic metamaterial model is performed in this paper.The statically asymptotic homogenization analysis of the metamaterial model can be used to investigate the influence rule of membrane parameters on the model's equivalent elastic modulus in all directions.In the transformation acoustics calculation of the model transformation,the metamaterial model with a certain anisotropic property can be designed according to the rule.The finite element transient response analysis of the deformed metamaterial model was performed to observe the propagation of the plane wave and the plane wave characteristics in the metamaterial model.It was proved that the designed membrane-imbedded acoustic Metamaterials can well control the propagation of waves.The propagation characteristics of the plane wave cannot be strictly maintained at the corners of the model in the simulation results,and the equivalent elastic modulus has an error at this position.The error problem is produced in the process of coordinate transformation calculation,the error reasons are analyzed and the optimization law is proposed to reduce the error value.