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Title

Analytical formulation and evaluation for free vibration of naturally curved and twisted beams
Authors

A.M. Yu
C.J. Yang
G.H. Nie
Journal / Anthology

Journal of sound and vibration
Year: 2010
Volume: 329
Issue: 9
Page range: 1376-1389
Description

An analyticalstudyforfreevibrationofnaturallycurvedandtwistedbeamswith uniformcross-sectionalshapesiscarriedoutusingspatialcurvedbeamtheorybasedon theWashizu’sstaticmodel.Inthegoverningequationsofmotionofthebeams,all displacementfunctionsandthegeneralizedwarpingcoordinatearedefinedatthe centroidaxisandalsotheeffectsofrotaryinertia,transversesheardeformationsand torsion-relatedwarpingareincludedintheproposedmodel.Explicitanalytical expressionsarederivedforthevibratingmodeshapesofacurved,bending-torsional- shearingcoupledbeamunderclamped–clampedboundaryconditionwiththehelpof symboliccomputingpackage Mathematica, andaprocessofsearchingisusedto determinethenaturalfrequencies.ComparisonsofthepresentresultswiththeFEM resultsusingbeamelementsinANSYScodeshowgoodaccuracyincomputationand validityofthemodel.Further,thepresentmodelisusedforcylindricalhelicalsprings with circularcross-sectionfixedatbothends,andtheresultsindicatethatthenatural frequenciesagreewellwiththetheoreticalandexperimentalresultsavailable.
Subject

*Unclassified