Research On Maximizing The Band Gap Of Phononic Crystals Under Uncertainty Based On BESO

The phononic crystals is a kind of artificial periodic composite material,and its special bandgap,negative refraction,self-collimation and other characteristics have attracted extensive attention and research.The range of frequencies in which an elastic wave cannot propagate in phononic crystals is called absolute bandgap.This property has broad application prospects in the field of vibration isolation and noise reduction.Therefore,this paper mainly studies the energy band structure diagram of phononic crystals.The calculation of the phononic crystals band structure,the maximization of adjacent band gap and the prediction and maximization of adjacent band gap under hybrid random interval uncertainties are studied in this paper.(1)The phononic crystals are generally composed of two or more materials and belongs to a non-homogeneous medium.Therefore,the calculation of the characteristic frequency of the phononic crystals are different from that of common material.In this paper,based on the theory of elastic wave,the lattice concept of solid physics,Bloch theorem,and the Finite Element Method,the characteristic frequency of periodic inhomogeneous medium is calculated.Although commercial software is available for calculating the energy band structure of phononic crystals,commercial software cannot handle this situation for intermediate density units that may occur in topology optimization.Therefore,the programmatical calculation of band structure of phononic crystals has its special significance in the theoretical exploration and research of phononic crystals.(2)Because of the finding of the special band gap in the periodic structure,compared with photonic crystals proposed before,the concept of phononic crystals was put forward.The frequency range of the band gap is mainly related to the lattice size,material properties and lattice structure.This paper mainly studies the structure of the lattice,and realizes the maximization of adjacent band gaps in phononic crystals based on the BESO method that is one of the topology optimization methods which can re-lay the material in structure,which is important for the regulation of the phononic crystals band gap.(3)There are uncertainties in the design,manufacturing,assembly and use phases of the product.Accurate estimation of the influence of uncertain factors on the function of the product will greatly enhance the competitiveness and reliability of the product.This paper mainly considers the influence of uncertain material parameter density p,Young's modulus E and Poisson's ratio v on the characteristic frequency of phononic crystals.Taking into account the uncertainty parameters in the initial stages of design.Based on random interval hybrid perturbation method and random interval moment method,the upper and lower bounds of mean and variance of phononic crystals characteristic frequency are calculated,and realized the maximization of adjacent band gaps in phononic crystals under hybrid random interval uncertainties based BESO method.Uncertain parameters are defined as the uncertainty of random and interval mixing,because in most cases,random uncertainty and interval uncertainty exist simultaneously.