Nonlinear flexural-flexural-torsional dynamics of metallic and composite beams

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dc.contributor.authorPai, Perng-Jin F.en
dc.contributor.committeechairNayfeh, Alien
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T21:15:46Zen
dc.date.adate2007-07-11en
dc.date.available2014-03-14T21:15:46Zen
dc.date.issued1990-04-01en
dc.date.rdate2007-07-11en
dc.date.sdate2007-07-11en
dc.description.abstractA combination of Newton's second law, a transformation using three consecutive Euler angles, and Taylor expansions is used to develop three nonlinear integro-differential equations describing the flexural-flexural-torsional vibration of metallic and composite beams. The twisting curvature is used to define a physical twisting variable which makes the equations of motion unique and independent of the rotation sequence of the Euler angles. A numerical-perturbation approach is used to analyze the response of metallic and composite beams to parametric and external excitations. First, the linear eigenfunctions and natural frequencies are calculated using a combination of the state-space concept and the fundamental-matrix method. Then, the method of multiple scales is used to construct a set of nonlinear autonomous first-order ordinary-differential equations describing the slow-time modulation of the amplitudes and phases of the interacting modes in the presence of one-to-one and/or two-to-one internal resonances. The inversion symmetry, D, symmetry, and 0(2) symmetry of the system are studied using the modulation equations. The solutions of the modulation equations may be fixed points, limit cycles, or chaotic solutions.en
dc.description.degreePh. D.en
dc.format.extentviii, 300 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-07112007-092845en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07112007-092845/en
dc.identifier.urihttp://hdl.handle.net/10919/38755en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1990.P35.pdfen
dc.relation.isformatofOCLC# 22246198en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1990.P35en
dc.subject.lcshComposite construction -- Researchen
dc.titleNonlinear flexural-flexural-torsional dynamics of metallic and composite beamsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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