{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/43402"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/43402","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Nonlinear oscillations under multifrequency parametric excitation","abstract":"A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λs + λt ~2Ï q, is examined. Second, the influence of an internal resonance, Ï q~3Ï r, on the previous case is studied. Finally, the effect of the internal resonance wr~3wq on the resonance λs + λt ~2Ï q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λs + λt.","abstract_html":"A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub>, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w<sub>r</sub><u>~</u>3w<sub>q</sub> on the resonance λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub> is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ<sub>s</sub> + λ<sub>t</sub>.","abstract_has_math":false,"creators":["Gentry, Jeanette J."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Mook, Dean T.","Plaut, Raymond H."],"committee_members":["Nayfeh, Ali H."],"year":1988,"date_issued":"1988-11-05","date_published":"1988-11-05","updated_at":"2026-07-24T05:56:05Z","subjects":[],"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-06222010-020244"],"render_values":[{"text":"etd-06222010-020244","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/43402","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Mook, Dean T.","Plaut, Raymond H."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Nayfeh, Ali H."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Gentry, Jeanette J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:39:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:39:00Z","2010-06-22"]},{"key":"dc:date.issued","label":"Date","values":["1988-11-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"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 and State University"]}]},{"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-06222010-020244"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/43402"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λs + λt ~2Ï q, is examined. Second, the influence of an internal resonance, Ï q~3Ï r, on the previous case is studied. Finally, the effect of the internal resonance wr~3wq on the resonance λs + λt ~2Ï q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λs + λt."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Nonlinear oscillations under multifrequency parametric excitation"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Mook, Dean T.","Plaut, Raymond H."],"dc:contributor.committeemember":["Nayfeh, Ali H."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Gentry, Jeanette J."],"dc:date.accessioned":["2014-03-14T21:39:00Z"],"dc:date.available":["2014-03-14T21:39:00Z","2010-06-22"],"dc:date.issued":["1988-11-05"],"dc:description.abstract":["A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λs + λt ~2Ï q, is examined. Second, the influence of an internal resonance, Ï q~3Ï r, on the previous case is studied. Finally, the effect of the internal resonance wr~3wq on the resonance λs + λt ~2Ï q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λs + λt."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-06222010-020244"],"dc:identifier.uri":["http://hdl.handle.net/10919/43402"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Nonlinear oscillations under multifrequency parametric excitation"],"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 and State University"]},"updated_at":"2026-07-24T05:56:05Z"}