{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/40463"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/40463","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Nonlinear vibration of beam and multibeam systems","abstract":"In this dissertation, an experimental and theoretical investigation into the nonlinear vibration of beam and beam-like structures with rectangular cross sections is presented. Two structures, a cantilever beam subject to a harmonic external excitation and a portal frame subject to a harmonic base motion, are the objects of study. For the cantilever beam, we present experimental results regarding multimode behavior. The beam was tested in both a vertical and horizontal configuration. Our experiments show that. for a forcing frequency near the fourth natural frequency of the beam, a low-frequency mode can be activated through a nonlinear mechanism. The nonlinear mechanism responsible for the transfer of energy to a low-frequency mode of the beam in the horizontal configuration was a subcombination internal resonance. However, for the same beam in the vertical configuration, both a subcombination internal resonance and a nonresonant modal interaction were observed to transfer energy to a low-frequency mode. The subcombination internal resonance consisted of contributions from the directly excited fourth mode, the fifth mode, and the low-frequency second mode. The response due to the nonresonant modal interaction consisted of contributions from the directly excited fourth mode and the indirectly excited low-frequency first mode. Both of these interactions are the result of a system with a dominant cubic nonlinearity. The single-mode response of the cantilever beam in the horizontal configuration was the subject of study. A comparison between the theoretically and experimentally obtained frequency-response curves revealed a discrepancy for an assumed ideal clamp. The model was brought into agreement by incorporating a quadratic damping term modeling the effect of air damping and a nonlinear rotational spring to model the flexibility of the clamp. The portal frame is a structure with a dominant quadratic nonlinearity. Experimental results are presented for the cases of a single combination resonance and multiple combination resonances. For the multiple combination resonances, excitation of a single mode was found to eventually activate contributions from six other modes, most of them possessing lower frequencies. The amplitudes of these lower-frequency modes were at times larger than that of the directly excited mode. The final topic is parameter identification for nonlinear systems. A scheme of experiments is designed that in conjunction with a multiple scales analysis can accurately estimate the nonlinear coefficients of a single-degree-of-freedom model. Parameters for a portal frame were ascertained by activating a subharmonic resonance of order one-half.","abstract_html":"In this dissertation, an experimental and theoretical investigation into the nonlinear vibration of beam and beam-like structures with rectangular cross sections is presented. Two structures, a cantilever beam subject to a harmonic external excitation and a portal frame subject to a harmonic base motion, are the objects of study. For the cantilever beam, we present experimental results regarding multimode behavior. The beam was tested in both a vertical and horizontal configuration. Our experiments show that. for a forcing frequency near the fourth natural frequency of the beam, a low-frequency mode can be activated through a nonlinear mechanism. The nonlinear mechanism responsible for the transfer of energy to a low-frequency mode of the beam in the horizontal configuration was a subcombination internal resonance. However, for the same beam in the vertical configuration, both a subcombination internal resonance and a nonresonant modal interaction were observed to transfer energy to a low-frequency mode. The subcombination internal resonance consisted of contributions from the directly excited fourth mode, the fifth mode, and the low-frequency second mode. The response due to the nonresonant modal interaction consisted of contributions from the directly excited fourth mode and the indirectly excited low-frequency first mode. Both of these interactions are the result of a system with a dominant cubic nonlinearity. The single-mode response of the cantilever beam in the horizontal configuration was the subject of study. A comparison between the theoretically and experimentally obtained frequency-response curves revealed a discrepancy for an assumed ideal clamp. The model was brought into agreement by incorporating a quadratic damping term modeling the effect of air damping and a nonlinear rotational spring to model the flexibility of the clamp. The portal frame is a structure with a dominant quadratic nonlinearity. Experimental results are presented for the cases of a single combination resonance and multiple combination resonances. For the multiple combination resonances, excitation of a single mode was found to eventually activate contributions from six other modes, most of them possessing lower frequencies. The amplitudes of these lower-frequency modes were at times larger than that of the directly excited mode. The final topic is parameter identification for nonlinear systems. A scheme of experiments is designed that in conjunction with a multiple scales analysis can accurately estimate the nonlinear coefficients of a single-degree-of-freedom model. Parameters for a portal frame were ascertained by activating a subharmonic resonance of order one-half.","abstract_has_math":false,"creators":["Tabaddor, Mahmood M."],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Nayfeh, Ali"],"committee_members":["Griffin, Odis H.","Kapania, Rakesh K.","Librescu, Liviu","Mook, Dean T."],"year":1996,"date_issued":"1996","date_published":"1996","updated_at":"2026-07-22T22:19:51Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12222005-090649"],"render_values":[{"text":"etd-12222005-090649","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/40463","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Nayfeh, Ali"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Griffin, Odis H.","Kapania, Rakesh K.","Librescu, Liviu","Mook, Dean T."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Tabaddor, Mahmood M."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:23:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:23:38Z","2005-12-22"]},{"key":"dc:date.issued","label":"Date","values":["1996"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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Two structures, a cantilever beam subject to a harmonic external excitation and a portal frame subject to a harmonic base motion, are the objects of study. For the cantilever beam, we present experimental results regarding multimode behavior. The beam was tested in both a vertical and horizontal configuration. Our experiments show that. for a forcing frequency near the fourth natural frequency of the beam, a low-frequency mode can be activated through a nonlinear mechanism. The nonlinear mechanism responsible for the transfer of energy to a low-frequency mode of the beam in the horizontal configuration was a subcombination internal resonance. However, for the same beam in the vertical configuration, both a subcombination internal resonance and a nonresonant modal interaction were observed to transfer energy to a low-frequency mode. The subcombination internal resonance consisted of contributions from the directly excited fourth mode, the fifth mode, and the low-frequency second mode. The response due to the nonresonant modal interaction consisted of contributions from the directly excited fourth mode and the indirectly excited low-frequency first mode. Both of these interactions are the result of a system with a dominant cubic nonlinearity. The single-mode response of the cantilever beam in the horizontal configuration was the subject of study. A comparison between the theoretically and experimentally obtained frequency-response curves revealed a discrepancy for an assumed ideal clamp. The model was brought into agreement by incorporating a quadratic damping term modeling the effect of air damping and a nonlinear rotational spring to model the flexibility of the clamp. The portal frame is a structure with a dominant quadratic nonlinearity. Experimental results are presented for the cases of a single combination resonance and multiple combination resonances. For the multiple combination resonances, excitation of a single mode was found to eventually activate contributions from six other modes, most of them possessing lower frequencies. The amplitudes of these lower-frequency modes were at times larger than that of the directly excited mode. The final topic is parameter identification for nonlinear systems. A scheme of experiments is designed that in conjunction with a multiple scales analysis can accurately estimate the nonlinear coefficients of a single-degree-of-freedom model. Parameters for a portal frame were ascertained by activating a subharmonic resonance of order one-half."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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Two structures, a cantilever beam subject to a harmonic external excitation and a portal frame subject to a harmonic base motion, are the objects of study. For the cantilever beam, we present experimental results regarding multimode behavior. The beam was tested in both a vertical and horizontal configuration. Our experiments show that. for a forcing frequency near the fourth natural frequency of the beam, a low-frequency mode can be activated through a nonlinear mechanism. The nonlinear mechanism responsible for the transfer of energy to a low-frequency mode of the beam in the horizontal configuration was a subcombination internal resonance. However, for the same beam in the vertical configuration, both a subcombination internal resonance and a nonresonant modal interaction were observed to transfer energy to a low-frequency mode. The subcombination internal resonance consisted of contributions from the directly excited fourth mode, the fifth mode, and the low-frequency second mode. The response due to the nonresonant modal interaction consisted of contributions from the directly excited fourth mode and the indirectly excited low-frequency first mode. Both of these interactions are the result of a system with a dominant cubic nonlinearity. The single-mode response of the cantilever beam in the horizontal configuration was the subject of study. A comparison between the theoretically and experimentally obtained frequency-response curves revealed a discrepancy for an assumed ideal clamp. The model was brought into agreement by incorporating a quadratic damping term modeling the effect of air damping and a nonlinear rotational spring to model the flexibility of the clamp. The portal frame is a structure with a dominant quadratic nonlinearity. Experimental results are presented for the cases of a single combination resonance and multiple combination resonances. For the multiple combination resonances, excitation of a single mode was found to eventually activate contributions from six other modes, most of them possessing lower frequencies. The amplitudes of these lower-frequency modes were at times larger than that of the directly excited mode. The final topic is parameter identification for nonlinear systems. A scheme of experiments is designed that in conjunction with a multiple scales analysis can accurately estimate the nonlinear coefficients of a single-degree-of-freedom model. Parameters for a portal frame were ascertained by activating a subharmonic resonance of order one-half."],"dc:description.degree":["Ph. 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