{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/26145"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/26145","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dynamic instabilities in a system with geometrically nonlinear damping and stiffness","abstract":"The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system are realized due to geometric effects. It is shown that the effects of nonlinear damping are far from being purely parasitic and introduce new dynamics when compared to the corresponding systems with linear damping. The dynamics is analyzed by performing a slow/fast decomposition leading to slow flows, which, in turn, are used to study transient instability caused by a bifurcation to 1:3 resonance capture. In addition, a new dynamical phenomenon of continuous resonance scattering is observed that is both persistent and prevalent for the case of the nonlinearly damped system. For certain moderate excitations the transient dynamics ‘tracks’ a manifold of impulsive orbits, in effect transitioning between multiple resonance captures over definitive frequency and energy ranges. Eventual bifurcation to 1:3 resonance capture generates the dynamic instability, which is manifested as a sudden high amplitude burst of the response of the light attachment. Such instabilities that result in strong energy transfer indicate potential for various applications of nonlinear damping such as in vibration suppression and energy harvesting.","abstract_html":"The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system are realized due to geometric effects. It is shown that the effects of nonlinear damping are far from being purely parasitic and introduce new dynamics when compared to the corresponding systems with linear damping. The dynamics is analyzed by performing a slow/fast decomposition leading to slow flows, which, in turn, are used to study transient instability caused by a bifurcation to 1:3 resonance capture. In addition, a new dynamical phenomenon of continuous resonance scattering is observed that is both persistent and prevalent for the case of the nonlinearly damped system. For certain moderate excitations the transient dynamics ‘tracks’ a manifold of impulsive orbits, in effect transitioning between multiple resonance captures over definitive frequency and energy ranges. Eventual bifurcation to 1:3 resonance capture generates the dynamic instability, which is manifested as a sudden high amplitude burst of the response of the light attachment. Such instabilities that result in strong energy transfer indicate potential for various applications of nonlinear damping such as in vibration suppression and energy harvesting.","abstract_has_math":false,"creators":["Andersen, David K."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Vakakis, Alexander F.","Bergman, Lawrence A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-25T22:16:11Z","date_published":"2011-08-25T22:16:11Z","updated_at":"2026-07-22T22:25:26Z","subjects":["Continuous Resonance Scattering","Nonlinear Energy Sink","Targeted Energy Transfer"],"languages":["en"],"rights":["Copyright 2011 David K. Andersen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/26145","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Vakakis, Alexander F.","Bergman, Lawrence A."]},{"key":"dc:creator","label":"Author","values":["Andersen, David K."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-08-25T22:16:11Z","2011-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Continuous Resonance Scattering","Nonlinear Energy Sink","Targeted Energy Transfer"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2011 David K. Andersen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/26145"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system are realized due to geometric effects. It is shown that the effects of nonlinear damping are far from being purely parasitic and introduce new dynamics when compared to the corresponding systems with linear damping. The dynamics is analyzed by performing a slow/fast decomposition leading to slow flows, which, in turn, are used to study transient instability caused by a bifurcation to 1:3 resonance capture. In addition, a new dynamical phenomenon of continuous resonance scattering is observed that is both persistent and prevalent for the case of the nonlinearly damped system. For certain moderate excitations the transient dynamics ‘tracks’ a manifold of impulsive orbits, in effect transitioning between multiple resonance captures over definitive frequency and energy ranges. Eventual bifurcation to 1:3 resonance capture generates the dynamic instability, which is manifested as a sudden high amplitude burst of the response of the light attachment. Such instabilities that result in strong energy transfer indicate potential for various applications of nonlinear damping such as in vibration suppression and energy harvesting.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-07-09T18:08:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Andersen_David.pdf: 2793239 bytes, checksum: 401b2129ac1cef771b469c9a466e995f (MD5)","Made available in DSpace on 2011-08-25T22:16:11Z (GMT). No. of bitstreams: 2 Andersen_David.pdf: 2793239 bytes, checksum: 401b2129ac1cef771b469c9a466e995f (MD5) license.txt: 4064 bytes, checksum: 7909b160b1aab46da53b7ae7b62ee4fc (MD5)"]},{"key":"dc:title","label":"Title","values":["Dynamic instabilities in a system with geometrically nonlinear damping and stiffness"]}]}],"canonical_facts":{"dc:contributor":["Vakakis, Alexander F.","Bergman, Lawrence A."],"dc:creator":["Andersen, David K."],"dc:date":["2011-08-25T22:16:11Z","2011-08"],"dc:description":["The dynamics of a system of coupled oscillators possessing strongly nonlinear stiffness and damping is examined. The system consists of a linear oscillator coupled to a strongly nonlinear, light attachment, where the nonlinear terms of the system are realized due to geometric effects. It is shown that the effects of nonlinear damping are far from being purely parasitic and introduce new dynamics when compared to the corresponding systems with linear damping. The dynamics is analyzed by performing a slow/fast decomposition leading to slow flows, which, in turn, are used to study transient instability caused by a bifurcation to 1:3 resonance capture. In addition, a new dynamical phenomenon of continuous resonance scattering is observed that is both persistent and prevalent for the case of the nonlinearly damped system. For certain moderate excitations the transient dynamics ‘tracks’ a manifold of impulsive orbits, in effect transitioning between multiple resonance captures over definitive frequency and energy ranges. Eventual bifurcation to 1:3 resonance capture generates the dynamic instability, which is manifested as a sudden high amplitude burst of the response of the light attachment. Such instabilities that result in strong energy transfer indicate potential for various applications of nonlinear damping such as in vibration suppression and energy harvesting.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-07-09T18:08:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Andersen_David.pdf: 2793239 bytes, checksum: 401b2129ac1cef771b469c9a466e995f (MD5)","Made available in DSpace on 2011-08-25T22:16:11Z (GMT). No. of bitstreams: 2 Andersen_David.pdf: 2793239 bytes, checksum: 401b2129ac1cef771b469c9a466e995f (MD5) license.txt: 4064 bytes, checksum: 7909b160b1aab46da53b7ae7b62ee4fc (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/26145"],"dc:language":["en"],"dc:rights":["Copyright 2011 David K. Andersen"],"dc:subject":["Continuous Resonance Scattering","Nonlinear Energy Sink","Targeted Energy Transfer"],"dc:title":["Dynamic instabilities in a system with geometrically nonlinear damping and stiffness"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:26Z"}