Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations
Abstrakt
In thispaperwedevelopmodelswithinathermodynamicstandpointthatareverysimilarinformtothe classical MaxwellandOldroyd-Bmodelsbutdifferfromtheminoneimportantaspect,themannerin which theyunloadinstantaneouslyfromthedeformedconfiguration. Aslongastheresponseisnot instantaneous, themodelsthatarederivedcannotbedifferentiatedfromtheMaxwellandOldroyd-B models, respectively.Themodelscanbeviewedwithinthecontextofmaterialswhosenatural configuration evolves,theevolutionbeingdeterminedbythemaximizationoftherateofentropy production ofthematerial.However,theunderpinningstodevelopthemodelarequitedifferentfroman earlier developmentbyRajagopalandSrinivasa [8] in thatwhilethetotalresponseoftheviscoelastic fluid satisfies theconstraintofanincompressiblematerial,theenergystoragemechanismassociated with theelasticresponseisallowedtobethatforacompressibleelasticsolidandthedissipative mechanism associatedwiththeviscousresponseallowedtobethatforacompressible fluid, thetotal deformation howeverbeingisochoric.Theanalysiscallsforacarefulevaluationof firmly heldcustomsin viscoelasticity whereinitisassumedthatitispossibletosubjectamaterialtoapurelyinstantaneous elastic responsewithoutanydissipationwhatsoever.Finally,whilethemodeldevelopedbyRajagopal and Srinivasa [8] arises fromthelinearizationofthenon-linearelasticresponsethattheychoseand leads toamodelwhereintheinstantaneouselasticresponseisisochoric,herewedevelopthemodel within thecontextofadifferentnon-linearelasticresponsethatneednotbelinearizedbutthe instantaneous elasticresponsenotnecessarilybeingisochoric.