摘要
Someofthemostinterestingrefractionpropertiesofphononiccrystalsarerevealedbyexaminingtheanti-planeshearwavesindoublyperiodicelasticcompositeswithunitcellscontainingrectangularand/orellipticalmultiinclusions.Thecorrespondingbandstructure,groupvelocity,andenergy–fluvectorarecalculatedusingapowerfulmixedvariationalmethodthataccuratelyandefficientlyieldsallthefielquantitiesovermultiplefrequencypass-bands.Thebackgroundmatrixandtheinclusionscanbeanisotropic,eachhavingdistinctelasticmoduliandmassdensities.Equifrequencycontoursandenergy–fluvectorsarereadilycalculatedasfunctionsofthewave-vectorcomponents.Bysuperimposingtheenergy–fluvectorsonequifrequencycontoursintheplaneofthewave-vectorcomponents,andsupplementingthiswithathree-dimensionalgraphofthecorrespondingfrequencysurface,awealthofinformationisextractedessentiallyataglance.Thiswayitisshownthatacompositewithevenasimplesquareunitcellcontainingacentralcircularinclusioncandisplaynegativeorpositiveenergyandphasevelocityrefractions,orsimplyperformsaharmonicvibration(standingwave),dependingonthefrequencyandthewave-vector.Moreover,thatthesamecompositewheninterfacedwithasuitablehomogeneoussolidcandisplay:(1)negativerefractionwithnegativephasevelocityrefraction;(2)negativerefractionwithpositivephasevelocityrefraction;(3)positiverefractionwithnegativephasevelocityrefraction;(4)positiverefractionwithpositivephasevelocityrefraction;oreven(5)completereflectiowithnoenergytransmission,dependingonthefrequency,anddirectionandthewavelengthoftheplane-wavethatisincidentfromthehomogeneoussolidtotheinterface.Forellipticalandrectangularinclusiongeometries,analyticalexpressionsaregivenforthekeycalculationquantities.Expressionsfordisplacement,velocity,linearmomentum,strain,andstresscomponents,aswellastheenergy–fluandgroupveloc
出版日期
2015年04月14日（中国期刊网平台首次上网日期，不代表论文的发表时间）
