简介：Thebandgap,animportantcharacteristicoftheperiodicstructure,isdispersionrelated,whichcanbedesignedbytailoringthelayoutofmaterialswithintheperiodicmicrostructures.Atypicalexampleofaperiodicstructureisphononiccrystals(PnCs),whicharetraditionallyfabricatedfromtwo-phasematerials.Herein,weinvestigatethetopologiesofperiodicthree-phasePnCs.Themicrostructuresofthethree-phasePnCsareoptimizedusingatwo-stagegeneticalgorithm,andthreecasestudiesareproposedtoobtainthefollowing:(1)themaximumrelativebandgapwidth,(2)themaximumabsolutebandgapwidth,and(3)themax-imumbandgapataspecifiedfrequency.Moreimportantly,thethree-phasematerialprovidessignificantadvantagescomparedtothetypicaltwo-phasematerials,suchasalow-frequencybandgap.Thisresearchisexpectedtocontributehighlytovibrationandnoiseisolation,elasticwavefilters,andacousticdevices.