{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32616"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32616","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials","abstract":"Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package.","abstract_html":"Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package.","abstract_has_math":false,"creators":["Kim, Yong Y."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace and Ocean Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Kapania, Rakesh K."],"committee_members":["Johnson, Eric R.","Nikolaidis, Efstratios"],"year":2000,"date_issued":"2000-05-01","date_published":"2000-05-01","updated_at":"2026-07-22T22:19:18Z","subjects":["Rotating blade","Orthogonal polynomials","Rayleigh-Ritzm method","Natural frequency","Felxural-torsional coupled vibration"],"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-05122000-14040026"],"render_values":[{"text":"etd-05122000-14040026","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32616","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Kapania, Rakesh K."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Johnson, Eric R.","Nikolaidis, Efstratios"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Kim, Yong Y."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:36:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:36:24Z","2001-05-16"]},{"key":"dc:date.issued","label":"Date","values":["2000-05-01"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace and Ocean Engineering"]},{"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":["Rotating blade","Orthogonal polynomials","Rayleigh-Ritzm method","Natural frequency","Felxural-torsional coupled vibration"]}]},{"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-05122000-14040026"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32616"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Kapania, Rakesh K."],"dc:contributor.committeemember":["Johnson, Eric R.","Nikolaidis, Efstratios"],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Kim, Yong Y."],"dc:date.accessioned":["2014-03-14T20:36:24Z"],"dc:date.available":["2014-03-14T20:36:24Z","2001-05-16"],"dc:date.issued":["2000-05-01"],"dc:description.abstract":["Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of flexural-torsional coupled vibration analysis using basic beam theories. In obtaining natural frequencies, orthogonal polynomials used in the Rayleigh-Ritz method are studied as an efficient way of getting results. The study is also performed for both non-rotating and rotating beams. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the eigenfunctions of a pinned-free uniform beam, and the special trigonometric functions used in conjunction with Hermite cubics. Studied cases are non-rotating and rotating Timoshenko beams, bending-torsion coupled beam with free-free boundary conditions, a cantilever beam, and a rotating cantilever beam. The obtained natural frequencies and mode shapes are compared to those available in various references and results for coupled flexural-torsional vibrations are compared to both previously available references and with those obtained using NASTRAN finite element package."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-05122000-14040026"],"dc:identifier.uri":["http://hdl.handle.net/10919/32616"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Rotating blade","Orthogonal polynomials","Rayleigh-Ritzm method","Natural frequency","Felxural-torsional coupled vibration"],"dc:title":["Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials"],"dc:type":["Thesis"],"thesis:degree_discipline":["Aerospace and Ocean Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:18Z"}