{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/101255"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/101255","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Nonlinear forced response of circular cylindrical shells","abstract":"A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of circular cylindrical shells in the presence of internal (autoparametric) resonances. If ω<sub>f</sub> and a<sub>f</sub> denote the frequency and amplitude of a flexural mode and ω<sub>b</sub> and a<sub>b</sub> denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ω<sub>b</sub> ≈ 2w<sub>f</sub> if the shell is excited by a harmonic load having a frequency Ω near ω<sub>b</sub>. As the amplitude f of the excitation increases from zero, a<sub>b</sub> increases linearly whereas a<sub>f</sub> remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ω<sub>b</sub> -2w<sub>f</sub>. Beyond this threshold, a<sub>b</sub> remains constant (i.e., the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude).","abstract_html":"A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of circular cylindrical shells in the presence of internal (autoparametric) resonances. If ω&lt;sub&gt;f&lt;/sub&gt; and a&lt;sub&gt;f&lt;/sub&gt; denote the frequency and amplitude of a flexural mode and ω&lt;sub&gt;b&lt;/sub&gt; and a&lt;sub&gt;b&lt;/sub&gt; denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ω&lt;sub&gt;b&lt;/sub&gt; ≈ 2w&lt;sub&gt;f&lt;/sub&gt; if the shell is excited by a harmonic load having a frequency Ω near ω&lt;sub&gt;b&lt;/sub&gt;. As the amplitude f of the excitation increases from zero, a&lt;sub&gt;b&lt;/sub&gt; increases linearly whereas a&lt;sub&gt;f&lt;/sub&gt; remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ω&lt;sub&gt;b&lt;/sub&gt; -2w&lt;sub&gt;f&lt;/sub&gt;. Beyond this threshold, a&lt;sub&gt;b&lt;/sub&gt; remains constant (i.e., the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude).","abstract_has_math":false,"creators":["Raouf, Raouf A."],"institution":"Virginia Polytechnic Institute and State University","degree_name":"M.S.","degree_level":"masters","degree_discipline":"Engineering Science and Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1985,"date_issued":"1985","date_published":"1985","updated_at":"2026-07-22T22:19:26Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/101255","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Raouf, Raouf A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-12-14T16:35:03Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-12-14T16:35:03Z"]},{"key":"dc:date.issued","label":"Date","values":["1985"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"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 Science and Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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:language.iso","label":"Language (ISO)","values":["en"]},{"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/10919/101255"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of circular cylindrical shells in the presence of internal (autoparametric) resonances. If ω<sub>f</sub> and a<sub>f</sub> denote the frequency and amplitude of a flexural mode and ω<sub>b</sub> and a<sub>b</sub> denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ω<sub>b</sub> ≈ 2w<sub>f</sub> if the shell is excited by a harmonic load having a frequency Ω near ω<sub>b</sub>. As the amplitude f of the excitation increases from zero, a<sub>b</sub> increases linearly whereas a<sub>f</sub> remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ω<sub>b</sub> -2w<sub>f</sub>. Beyond this threshold, a<sub>b</sub> remains constant (i.e., the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.S."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Nonlinear forced response of circular cylindrical shells"]}]}],"canonical_facts":{"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Raouf, Raouf A."],"dc:date.accessioned":["2020-12-14T16:35:03Z"],"dc:date.available":["2020-12-14T16:35:03Z"],"dc:date.issued":["1985"],"dc:description.abstract":["A combination of the Galerkin procedure and the method of multiple scales is used to analyze the nonlinear forced response of circular cylindrical shells in the presence of internal (autoparametric) resonances. If ω<sub>f</sub> and a<sub>f</sub> denote the frequency and amplitude of a flexural mode and ω<sub>b</sub> and a<sub>b</sub> denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ω<sub>b</sub> ≈ 2w<sub>f</sub> if the shell is excited by a harmonic load having a frequency Ω near ω<sub>b</sub>. As the amplitude f of the excitation increases from zero, a<sub>b</sub> increases linearly whereas a<sub>f</sub> remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ω<sub>b</sub> -2w<sub>f</sub>. Beyond this threshold, a<sub>b</sub> remains constant (i.e., the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude)."],"dc:description.degree":["M.S."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/101255"],"dc:language.iso":["en"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Nonlinear forced response of circular cylindrical shells"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Engineering Science and Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:26Z"}