Study On Low-frequency Broadband Properties Of Three-dimensional Pentamode Metamaterials

Manipulation of wave propagation is an extremely important basic scientific problem in the field of information science,and the use of natural materials to regulate the propagation of acoustic waves has strong limitations,which greatly limits the development of related disciplines.Therefore,there is an urgent need for a material with special physical properties that are not available in nature to achieve low frequency acoustic blocking.As a new type of artificial solid structure,the pentamode metamaterial can realize functions such as acoustic absorption and insulation,acoustic stealth and noise reduction,breaking the limitation of natural materials subject to the traditional mass action theory and effectively solving the problem of low-frequency acoustic modulation.At present,the research on pentamode metamaterial at home and abroad mainly focuses on their mechanical properties,and the research on their acoustic properties mainly focuses on the two-dimensional(2D)aspects,the research on the acoustic properties of three-dimensional(3D)pentamode metamaterial is less.In addition,underwater acoustic modulation devices are developing towards ultra-low frequency,so the study of low frequency acoustic modulation is particularly important.In this thesis,a multilayer cylinder-based structure is simulated and designed,and the energy band characteristics and pentamodal properties of the single-cell structure composed of this primitive element are analyzed based on the Bragg scattering mechanism and the local resonance mechanism,respectively.At the same time,in order to explore the simple structure as well as easy processing and fabrication of pentamode metamaterial,the structures of different lattice configurations are invoked and their energy band characteristics are analyzed to provide a reference for the realization of low-frequency acoustic modulation of 3D pentamode metamaterial.The work of this thesis is as follows.(1)The energy band characteristics and equivalent parameters of the 3D pentamode metamaterial are studied based on the Bragg scattering mechanism.A 3D multilayer cylindrical pentamode metamaterial with abundant adjustable parameters is designed,and the equivalent parameters and energy band characteristics are numerically modeled by the finite element method,the energy band characteristics and pentamode properties are analyzed by optimizing the geometrical structure parameters and material parameters of the structure.(2)Based on the principle of local resonance,the mechanism of low-frequency bandgap formation and the regulatory relationship of 3D pentamode metamaterial are elucidated.The design of the local resonance structural unit,the use of composite materials for the combination of its primitive elements,through the 3D space of the vibration pattern equivalent to the 2D plane space,the analysis of the equivalent 2D plane space is simplified to the analysis of the 1D equivalent “spring-mass” system,through the comparison of theoretical and simulation analysis,the relationship between structural parameters and low-frequency bandgap regulation is established.(3)A numerical calculation model of the energy band structure of 3D pentamode metamaterial based on different lattice structures is established.Based on the three lattice types of simple cubic,body-centered cubic and face-centered cubic,the simple Brillouin zone of different lattice structures are determined,and their simple Brillouin zone boundaries are solved numerically under Bloch periodic boundary conditions using the finite element method,in order to obtain phonon bandgaps with similarities to the ideal lattice structures.