An Optimization Method for Design of Acoustic Metamaterial Structure

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.