The effect of cracks on the dynamic behavior of bars and shafts

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dc.contributor.authorCollins, Kevin Ralphen
dc.contributor.committeechairPlaut, Raymond H.en
dc.contributor.committeememberRojiani, Kamal B.en
dc.contributor.committeememberHolzer, Siegfried M.en
dc.contributor.departmentCivil Engineeringen
dc.date.accessioned2014-03-14T21:42:02Zen
dc.date.adate2012-08-01en
dc.date.available2014-03-14T21:42:02Zen
dc.date.issued1989-03-29en
dc.date.rdate2012-08-01en
dc.date.sdate2012-08-01en
dc.description.abstractNondestructive methods of detecting cracks in structural components and machinery are important, both in preventing failures and in establishing maintenance procedures. This thesis considers how the vibration behavior of cracked members can be modelled mathematically and how these mathematical models may lead to advancements in crack detection procedures. Two separate cases are considered: the longitudinal vibration of a cracked bar and the coupled vibrations of a cracked rotating shaft. In the longitudinal vibration study, the equation of motion is developed for a cantilevered bar with a symmetric surface crack. Next, Galerkin's Method is used to obtain one- and two-term approximate solutions. Both forced and free vibrations of the bar are analyzed. Graphical results showing the relationships between displacement and crack size, crack position, and forcing frequency are presented and discussed. Spectral analysis is used to compare uncracked and cracked bar behavior. Finally, a sensitivity analysis of the forced vibration case is conducted to observe how the forcing frequency affects the rate of change of steady-state response at the onset of cracking. In the second part of the thesis, a similar analysis is conducted for a cracked, simply-supported Timoshenko shaft rotating at a constant angular speed. The equations of motion derived by Wauer (b) are used as the basis of the study. Again, Galerkin's Method is applied to obtain approximate solutions. Time histories and spectra are used to observe how changes in various parameters influence the vibration behavior. The effects of mass eccentricity and gravity are studied. Finally, the effect of a periodic axial impact load is considered.en
dc.description.degreeMaster of Scienceen
dc.format.extentx, 118 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-08012012-040538en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08012012-040538/en
dc.identifier.urihttp://hdl.handle.net/10919/44112en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V855_1989.C668.pdfen
dc.relation.isformatofOCLC# 21188451en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V855 1989.C668en
dc.subject.lcshRotational motion -- Mathematical modelsen
dc.titleThe effect of cracks on the dynamic behavior of bars and shaftsen
dc.typeThesisen
dc.type.dcmitypeTexten
thesis.degree.disciplineCivil Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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