Calculation Method Of Band Structure Of Phononic Crystal Base On COMSOL

"Phononic crystal" was proposed firstly in the 1990s,which is a type of artificial functional composite composed of_two or more materials with different mass densities and elastic properties,arranged in geometric periodicity.The propagation characteristics of elastic waves in periodic structures have always been one of the research focus.As a new type of artificial functional material,due to the highly designability and rich acoustic characteristics,phononic crystal has a widely application prospect.The bandgap characteristic of phononic crystal is one of its most important features,which means that the elastic wave within the frequency range of bandgap can not propagate through it.Thus phononic crystal has potential applications in noise and vibration control,etc.The band structures are able to characterize the band features of periodic composite structure directly,through which the elastic wave propagating in phononic crystal can be shown.Thus the calculation of band structures is one of the important studies for phononic crystal.In addition,for the needs of practical application,the frequency ranges of the elastic waves which can propagate in phononic crystal are able to be designed through changing the structure or component materials of the phononic crystal.Therefore,it is also important to study the influence factors of band structures for phononic crystal,and which can guide the optimization and design of phononic crystal.In this thesis,all work is based on the finite element method,and the commercial software—Comsol Multiphysics is taken to model the two-dimensional phononic crystal and calculate the band structures of that.Firstly,we take the two-dimensional phononic crystal composed of gold cylinder scatterers embedded in epoxy matrix for example.The band structures are calculated with considering the plane mixed harmonic wave modes and the purely transverse harmonic wave mode propagating in the gold/epoxy phononic crystal,respectively.In comparison with the results of other numerical methods,it could be found that the finite element method can not only yield accurate results which are in good agreement with those of other methods,but also is memory-saving as well as time-saving,and with good convergence.Besides,the band structures of the two-dimensional phononic crystals composed of solid scatterers in fluid matrix and hole scatterers in solid matrix are calculated and analyzed,respectively.In order to study the influence factors of the band gap frequency range for two-dimensional phononic crystal,the two-dimensional gold/epoxy phononic crystal is still taken to investigate the influence of the lattice geometrical topology structure,the shape of scatterer,the filling fraction,and the material parameters on the low frequency bandgap.It is found that the lattice geometry of phonon crystal not only influence the width of the first low frequency bandgap,but also the upper and lower edges and center frequency.The filling fraction of phononic crystals has also a significant influence on the width of the first bandgap.In addition,change of the mass density and elastic modulus of the materials can also alter the low frequency band gap of the phononic crystal.At present,the plate structures with periodicity are widely applied in engineering.By using the finite element software-Comsol Multiphysics,the band structure of some two-dimensional phononic crystal plates are calculated,at the same time,the factors affecting the bandgap of the phononic crystal are analyzed.It is found that two-dimensional phononic crystal plates with two-sided protrusions have wide range of low frequency bandgap by comparing and analyzing of single convex and double-sided convex phononic crystal plates in the cylindrical,square,conical,spherical aspect..It can be found that phononic crystals are highly designed and adjustable.Therefore the research work can provide theoretical basis for the correspond application of phononic crystals in engineering.