{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36721"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36721","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams","abstract":"There is a need for reliable methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of these concepts and procedures, we compare the outcomes of these two approaches (the Galerkin discretization and the direct application of a reduction method to the original governing equations) with experimental results. The nonlinear planar vibrations of a buckled beam around its first buckling mode shape are investigated. Frequency-response curves characterizing single-mode responses of the beam under a primary resonance are generated using both approaches and contrasted with experimentally obtained frequency-response curves. It is shown that discretization leads to erroneous quantitative as well as qualitative results in certain ranges of the buckling level, whereas the direct approach predicts the correct dynamics of the system.","abstract_html":"There is a need for reliable methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of these concepts and procedures, we compare the outcomes of these two approaches (the Galerkin discretization and the direct application of a reduction method to the original governing equations) with experimental results. The nonlinear planar vibrations of a buckled beam around its first buckling mode shape are investigated. Frequency-response curves characterizing single-mode responses of the beam under a primary resonance are generated using both approaches and contrasted with experimentally obtained frequency-response curves. It is shown that discretization leads to erroneous quantitative as well as qualitative results in certain ranges of the buckling level, whereas the direct approach predicts the correct dynamics of the system.","abstract_has_math":false,"creators":["Lacarbonara, Walter"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Science and Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Nayfeh, Ali H."],"committee_members":["Ragab, Saad A.","Batra, Romesh C."],"year":1997,"date_issued":"1997-02-27","date_published":"1997-02-27","updated_at":"2026-07-22T22:19:59Z","subjects":["direct approach","galerkin discretization","post-buckling","internal resonances","nonlinear normal modes"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-441520272974850"],"render_values":[{"text":"etd-441520272974850","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36721","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 H."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ragab, Saad A.","Batra, Romesh C."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Lacarbonara, Walter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:51:35Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:51:35Z","1997-02-27"]},{"key":"dc:date.issued","label":"Date","values":["1997-02-27"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Science and Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["direct approach","galerkin discretization","post-buckling","internal resonances","nonlinear normal modes"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-441520272974850"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36721"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There is a need for reliable methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of these concepts and procedures, we compare the outcomes of these two approaches (the Galerkin discretization and the direct application of a reduction method to the original governing equations) with experimental results. The nonlinear planar vibrations of a buckled beam around its first buckling mode shape are investigated. Frequency-response curves characterizing single-mode responses of the beam under a primary resonance are generated using both approaches and contrasted with experimentally obtained frequency-response curves. It is shown that discretization leads to erroneous quantitative as well as qualitative results in certain ranges of the buckling level, whereas the direct approach predicts the correct dynamics of the system."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Nayfeh, Ali H."],"dc:contributor.committeemember":["Ragab, Saad A.","Batra, Romesh C."],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Lacarbonara, Walter"],"dc:date.accessioned":["2014-03-14T20:51:35Z"],"dc:date.available":["2014-03-14T20:51:35Z","1997-02-27"],"dc:date.issued":["1997-02-27"],"dc:description.abstract":["There is a need for reliable methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures yield reliable approximate solutions. Starting from these results and extending some of these concepts and procedures, we compare the outcomes of these two approaches (the Galerkin discretization and the direct application of a reduction method to the original governing equations) with experimental results. The nonlinear planar vibrations of a buckled beam around its first buckling mode shape are investigated. Frequency-response curves characterizing single-mode responses of the beam under a primary resonance are generated using both approaches and contrasted with experimentally obtained frequency-response curves. It is shown that discretization leads to erroneous quantitative as well as qualitative results in certain ranges of the buckling level, whereas the direct approach predicts the correct dynamics of the system."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-441520272974850"],"dc:identifier.uri":["http://hdl.handle.net/10919/36721"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["direct approach","galerkin discretization","post-buckling","internal resonances","nonlinear normal modes"],"dc:title":["A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering Science and Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:59Z"}