On damping effects in Timoshenko beams

In thispaper,thedynamicresponseofaTimoshenkobeamwithdistributedinternalviscousdamping (DIVD) isanalyzedwiththeaimtoascertaintheirrelativeeffectsonthewholerangeofbeam slenderness. Withrespecttosomepreviousandquiterecentworks,somefurtherandfundamental generalizationsarethereforeintroduced.First,thedecouplingofshearandbendingdampingmechan- isms, withorwithoutthepresenceoftheexternalclassicalviscouscontribution.Thissplittingallowsthe outlining oftherelevantinfluences onthedynamicresponseassociatedtoanysingulardamping mechanism andtheevaluationofthemodalcriticaldamping.Asasecondcontemporarystep,anexplicit dependency issetupontheshearslendernessofthebeammodel,allowingtostudythedependenceof each singledampingmechanismupontherelevantkinematicmodel,spanningfromtrulyBernoulli's behaviortomainlyShearcontrolledresponses.Accordingtotheselecteddampingmodel,thedynamic behaviorautomaticallyselectsthecharacteristicsofkinematicalresponse(relativelevelsofshearand bending contributions)dependingoftheminimizationofthetotalinternalenergy(i.e.elasticenergyand dissipation). Inthefoldsofthisstudy,theproblemofoptimalpiece-wiseconstantdistributionofDIVDis finally alsoaddressed, firstly showingthatispossibleto find non-trivialandinterestingsolutions.