Subcritical parametric response of an axially accelerating beam

Ghayesh, Mergen H.; Païdoussis, Michael P.; Amabili, Marco

doi:10.1016/j.tws.2012.06.012

In thispaper,theplanarnonlineardynamicsofanaxiallyacceleratingbeaminthesubcriticalspeed regime isexaminedtheoretically,viatwodifferentnumericaltechniques,employingalargeenough numberofmodesinordertoinvestigatemodalinteractions.Theequationofmotionisdiscretizedvia the Galerkinmethodwhichresultsinasetofcouplednonlinearordinarydifferentialequations (NODEs)withtime-dependentcoefficients.ThesetofNODEsissolvedbymeansofthepseudo- arclengthcontinuationtechniqueandsomeoftheresultsaretestedandverifiedviadirecttime integrationoftheNODEs.Theanalysesincludethesystemtunedtoathree-to-oneinternalresonance, as wellasforthecasewhereitisnot.Resultsareillustratedthroughfrequency–responsediagrams, time traces,phase–planeportraits,andfastFouriertransforms(FFTs).

Subcritical parametric response of an axially accelerating beam / Mergen H., Ghayesh; Michael P., Païdoussis; Amabili, Marco. - In: THIN-WALLED STRUCTURES. - ISSN 0263-8231. - 60:(2012), pp. 185-193. [10.1016/j.tws.2012.06.012]