{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/76012"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/76012","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Transient vibrations of a cantilever beam rotating at a constant angular acceleration","abstract":"A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected. These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer. Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation. The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis. Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained.","abstract_html":"A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected. These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer. Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation. The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis. Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained.","abstract_has_math":false,"creators":["Ermold, Leonard Frederick"],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1963,"date_issued":"1963","date_published":"1963","updated_at":"2026-07-22T22:18:41Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/76012","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Ermold, Leonard Frederick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-03-09T21:35:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-09T21:35:13Z"]},{"key":"dc:date.issued","label":"Date","values":["1963"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"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":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"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.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/76012"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected. These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer. Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation. The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis. Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Transient vibrations of a cantilever beam rotating at a constant angular acceleration"]}]}],"canonical_facts":{"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Ermold, Leonard Frederick"],"dc:date.accessioned":["2017-03-09T21:35:13Z"],"dc:date.available":["2017-03-09T21:35:13Z"],"dc:date.issued":["1963"],"dc:description.abstract":["A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected. These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer. Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation. The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis. Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/76012"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Transient vibrations of a cantilever beam rotating at a constant angular acceleration"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Engineering Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:18:41Z"}