Nonlinear dynamics of systems involving widely spaced frequencies

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dc.contributor.authorNayfeh, Samir Alien
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T21:39:24Zen
dc.date.adate2009-06-30en
dc.date.available2014-03-14T21:39:24Zen
dc.date.issued1993en
dc.date.rdate2009-06-30en
dc.date.sdate2009-06-30en
dc.description.abstractThis document focuses on the dynamics of nonlinear oscillatory systems involving widely spaced frequencies. First, experiments on the forced oscillations of a cantilever beam with a circular cross-section are presented. The beam is excited near its fifth natural frequency but sustained large-amplitude oscillations of the first mode accompanied by modulated oscillations of the fifth mode occur. Thus, energy is transferred from the fifth to the first mode of the beam, whose natural frequencies are roughly in the ratio of 60:1. Some simple two-degree-of-freedom systems are studied in an effort to explain the strong nonlinear coupling between modes with widely spaced frequencies. In these systems, the coupling is found to give rise to some novel phenomena including static displacements or sustained oscillations of the low-frequency mode in response to a high-frequency excitation. The possibility that resonances may occur between a high-frequency excitation and a single low-frequency mode is then investigated. A single-degree-of-freedom oscillator driven at a frequency much higher than its natural frequency is analyzed. It is found that, if the excitation is modulated, resonant excitation of the oscillator may occur.en
dc.description.degreeMaster of Scienceen
dc.format.extentv, 80 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06302009-040426en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06302009-040426/en
dc.identifier.urihttp://hdl.handle.net/10919/43501en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V855_1993.N394.pdfen
dc.relation.isformatofOCLC# 28513847en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V855 1993.N394en
dc.subject.lcshFrequency modulation detectorsen
dc.subject.lcshNonlinear mechanics -- Mathematical modelsen
dc.titleNonlinear dynamics of systems involving widely spaced frequenciesen
dc.typeThesisen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen
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