Abstract
Pentamode (PM) metamaterial is a kind of acoustic metamaterial generally designed from a general material and made by a periodic array of micro-truss structures. The paper presents an optimization method for the design of PM metamaterial structure, and this kind of structure has usually special physical properties to guide the acoustic wave to propagate according to the design path. In order to construct the optimization model, the micro-truss unit cell is firstly investigated deeply, and the relationship between the effective elastic modulus of PM materials and the structural parameters of micro-truss unit cells is established. With incorporating the transformation acoustics algorithm into the optimization process to predict the theoretic material parameters of the current design structure, the constraint of the material property in the design structure is converted into the rod size constraint of micro-truss. As a result, the design of PM material structures can be realized as a problem of structure size optimization, and the optimized result can meet the requirement of PM metamaterial property and the theory of transformation acoustics. And also, the total stability of the PM material structure is also ensured by the balance rod forces constraints in the optimization process. Finally, a numerical example of PM material structure is presented.
Highlights
Over the past few decades, people have developed interest in the study of superior properties and potential applications of optical and electromagnetic metamaterials
According to the transformation acoustic theory [6-7], the material property of the design structure relies on the coordinate transformation from an original domain to a current domain, which is given by the point-wise deformation X → x
An optimization method is presented for the design of a structure with PM materials
Summary
Over the past few decades, people have developed interest in the study of superior properties and potential applications of optical and electromagnetic metamaterials. The paper utilizes the PM material configuration proposed by Xu Bing [4] It adopts a symmetrical double cone rod structure and constitutes a micro-truss PM material, the symmetry of the micro-truss material cell makes it easy to design and optimize material parameters of structures. The design of this PM material structure is represented in Fig., where Fig. (a) is the initial design structure of the PM material, the shaded area is an annular area composed of the isotropic PM material with its material properties similar to surrounding fluids. Fig. is to describe the basic design process of the PM material structure, mainly by iteratively adjusting the micro truss size parameters to gradually change the wave propagation characteristics to meet the demand of the design. At Final, a numerical example of structural design of PM material is given
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