Phononicmaterialswithspecificband-gapcharacteristicsatdesiredfrequencyrangesareingreatdemandforvibrationandnoiseisolation,elasticwavefilters,andacousticdevices.Theattenuationcoefficientcurvedepictsboththefrequencyrangeofbandgapandtheattenuationofelasticwave,wherethefrequencyrangescorrespondingtothenone-zeroattenuationcoefficientsarebandgaps.Therefore,theband-gapcharacteristicscanbeachievedthroughmaximizingtheattenuationcoefficientatthecorrespondingfrequencyorwithinthecorrespondingfrequencyrange.Becausetheattenuationcoefficientcurveisnotsmoothinthefrequencydomain,thegradient-basedoptimizationmethodscannotbedirectlyusedinthedesignoptimizationofphononicband-gapmaterialstoachievethemaximumattenuationwithinthedesiredfrequencyrange.Toovercomethisdifficulty,theobjectiveofmaximizingtheattenuationcoefficientistransformedintomaximizingitsCosine,andinthisway,theobjectivefunctionissmoothedandbecomesdifferentiable.Basedonthisobjectivefunction,anovelgradient-basedoptimizationapproachisproposedtoopenthebandgapataprescribedfrequencyrangeandtofurthermaximizetheattenuationefficiencyoftheelasticwaveataspecificfrequencyorwithinaprescribedfrequencyrange.Numericalresultsdemonstratetheeffectivenessoftheproposedgradient-basedoptimizationmethodforenhancingthewaveattenuationproperties.
