Design And Optimization Of Phononic Crystal Band Gap Characteristics

Phononic crystals are periodic composite materials with elastic band gap,and the elastic waves in the band gap frequency range are forbidden to propagate.This characteristic of the phononic crystals makes it possible to artificially manipulate the propagation of the elastic waves.As a new type of artificial structure,it has the characteristics such as small size,strong pertinence and strong frequency range designability.Therefore,it has a wide application prospect in the fields of aerospace,mechnical power,transportation,medicine and human life.In recent years,the topological optimization design of phononic crystals has become a research hotspot,it will be another great progress in the development and application of materials to obtain new crystal materials through band gap design.Based on the Evolutionary Algorithm,the topological structure and material parameters which affect the band gap characteristics of phononic crystals are optimized in this paper.The main contents include the following aspects:Firstly,the band gap optimization model of solid-solid phononic crystals is established,and the effect of topological configuration and material parameters on the band gap is discussed.By introducing the mixed variable into the Genetic Algorithm,the microstructure of phononic crystals with wide and low frequency band gap was designed by taking the material parameters and topological configuration that affect the characteristics of phononic crystals as common design variables.The results show that both the parameters have significant effects on the bandgap characteristics.The effect of density can make the lower boundary of the bandgap move to low frequency,and the effect of elastic modulus can make the upper boundary move to high frequency.At the same time,the larger the difference between the parameters of the scatterer and the matrix material,the easier to produce a wider bandgap.Secondly,the optimization model of phononic crystals based on multiphase material microstructures is established,and the effects of traditional Bragg scattering phononic crystals and locally resonant phononic crystals on the bandgap are discussed.By introducing the pseudo-density variable,a two-stage Genetic Algorithm is applied to optimize the topology of the phononic crystals with three-phase materials.The phononic crystal configurations with maximum relative bandwidth,maximum absolute bandwidth and maximum bandgap at specific frequencies are obtained.The results show that,the three-phase materials can obtain better broadband phononic crystals even under rough mesh conditions compared with the two-phase materials.what's more,the three-phase materials are more likely to open wider band gap in lower frequency.Finally,a multi-objective optimization model of phononic crystals based on three-phase materials is established,and various performance requirements in the design of phononic crystals are analyzed.Based on the Non-dominated Sorting Genetic Algorithm(NSGA-II)with elitist strategy,the multi-objective topological optimization designs of two-dimensional three-phase material phononic crystals were carried out,and the Pareto optimal solutions with different objectives were obtained.The results show that the three-phase materials can significantly increase the design space.And on this basis,the phononic crystals with various characteristics can be obtained by multi-objective optimization design.