Band Gaps Optimization Of The One-dimensional Phononic Crystal Plates

Mechanical vibration and noise are widely occurred in the industrial production and people’s daily life.The suppression of harmful vibration and noise is an urgent problem in the engineering field.Lamb wave type acoustic metamaterials can generate elastic wave stop band,have the advantages of good acoustic absorption and acoustic rectification,these properties have attracted wide interest from researchers at home and abroad.As a periodic composite material with elastic wave stop band,based on its band gap characteristics,phononic crystal plates has potential engineering application value in artificially designing specific frequency band gap in vibration damping and noise reduction.Therefore,optimizing the band gaps of the phononic crystal plates,designing a lower band gap,and increasing the bandgap width are problems that we need to solve in the study of phononic crystal plate.Taking the one-dimensional phononic crystal plate as the research object,the band gaps properties of one-dimensional phononic crystal plates are studied based on the existing basic theory and research methods of phononic crystal plates.The Lamb wave band structure of the phononic crystal plates is obtained by finite element method,the band gaps of the phononic crystal plate is optimized by genetic algorithm,and the topology characteristics and band gap characteristics of the new cell structure obtained by topology optimization are analyzed.The main research content is as follows:(1)A one-dimensional solid-solid phononic crystal plate model is established.The band gap structures are calculated and compared using the finite element method and the plane wave expansion method.One-dimensional phononic crystal plates with three different material combinations were studied.The energy band structure and the band edge modes are analyzed,and the effect of material parameters on the band gaps of one-dimensional phononic crystal plates was studied.(2)A one-dimensional tungsten-aluminum phononic crystal plate model is established.The band gap characteristics of one-dimensional phononic crystal plates are studied.Using the finite element method and changing the parameters such as filling rates,a/h values,symmetrical coating thickness,size of the diffuser or the embedded air column of the substrate,etc.the band gaps of Lamb waves in phononic crystal plates were analyzed to study the influence of different parameter on the band gap center frequency and band gap width.(3)An optimization model of one-dimensional phononic crystal plates is built,two optimization schemes about mirror symmetry and non-mirror symmetry in primitive cells are designed.And the filling rate of the phononic crystal plate and the relative bandgap width of the three lowest band gaps are optimized based on the genetic algorithm.The relative bandgap width of the three lowest band gaps are increased.(4)The relative bandgap width and topological configuration of one-dimensional phononic crystal plates at different filling rates are optimized,the band structure diagram of the topological structure of the primitive cells at different filling rates are analyzed,and the band gap characteristics and the band gap boundary modes before and after optimization are compared and analyzed.