Analysis Of The Acoustic Characteristics Of A Pentamode Metamaterial And Its Structural Parameters Of Microstructures

Metamaterials is one of the hot topics in the state-of-the-art of materials, and it has broad prospects in fields such as national defense, aerospace, new energy and so on. Pentamode metamaterials (PM materials) are novel artificial metamaterials, and five eigenvalues of their elastic modulus matrix are zero or smaller than the other one. Hence the bulk modulus of the material is extremely larger compared to the shear modulus and the elastic properties of the material are similar to liquids. PM materials can be used to manufacture acoustic cloaks and acoustic lens with great prospect, which have received great attention from scientific community.Investigations on the acoustic properties of PM materials are indispensable parts in researches on PM materials. There have been many proven methods which are available to study the acoustic characteristics of the periodic structures, so far, such as plane wave expansion method, multiple scattering method, finite element method and so forth. Finite element method is used in this thesis to analyze the acoustic properties of PM materials.Firstly, the quasi-static analysis method of homogenization and dynamic analysis method of dispersion characteristics are introduced, and then, on the one hand, the homogenization method is used to analyze the quasi-static effective elastic material parameters, on the other hand, the dispersion properties of the periodic microstructures are researched to evaluate the dynamic effective elastic material parameters. Secondly, the effects of structural parameters of periodic microstructures on the velocity variation of acoustic wave propagation in the metamaterials are discussed by means of a number of numerical examples. Then, for the sake of designing pentamode metamaterials with anisotropic acoustic properties, three schemes for adjusting the parameters of microstructures are put forwards, and then their abilities to obtain the anisotropic acoustic properties are compared by analyzing the relationship between the ratio of compression wave velocities in orthogonal directions and the corresponding adjustment parameters of microstructures. As a result, it is illustrated that changing the shape ratio of cubic frames inside microstructures is the best method of obtaining the anisotropic acoustic properties, by which the ratio of compression wave velocities can not only be adjusted in a large scale, but also the ratio of compression wave velocities has a good linear relationship with the adjustment parameter. Finally, the velocity and velocity ratio of the unit cell with different material parameters are calculated and compared, the results show that the change of material parameters only affect the velocity of PM materials, but not affect the velocity ratio or the adjustment ability of microstructures for the anisotropic acoustic properties.