{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/87530"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/87530","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Modeling and Analysis of a Moving Conductive String in a Magnetic Field","abstract":"A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled.","abstract_html":"A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled.","abstract_has_math":false,"creators":["Hasanyan, Jalil Davresh"],"institution":"Virginia Tech","degree_name":"MS","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Zietsman, Lizette"],"committee_members":["Burns, John A.","Embree, Mark P."],"year":2019,"date_issued":"2019-02-07","date_published":"2019-02-07","updated_at":"2026-07-22T22:19:53Z","subjects":["Current-carrying string","stability","Modeling","magnetic field","resonance vibrations"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:18887"],"render_values":[{"text":"vt_gsexam:18887","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/87530","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Zietsman, Lizette"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Burns, John A.","Embree, Mark P."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Hasanyan, Jalil Davresh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-02-08T09:00:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-02-08T09:00:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2019-02-07"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]},{"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":["Current-carrying string","stability","Modeling","magnetic field","resonance vibrations"]}]},{"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":["vt_gsexam:18887"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/87530"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["The modeling and analysis of elastic conductors has applications in areas ranging from manufacturing to particle physics. In this study, we model the motion of a conductive string being pulled (between two rings) while a magnetic field is applied in the lateral direction. This system’s stability is categorized through certain parameters such as the applied magnetic field, speed of pulling, and current flowing through the string. The equilibrium states are also analyzed. When the string has a periodic current, approximate solutions (string shape/orientation) are computed. In this case, we find domains of parameters that give rise to chaos. Wave speeds of traveling wave solutions are also found for certain cases."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["MS"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Modeling and Analysis of a Moving Conductive String in a Magnetic Field"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Zietsman, Lizette"],"dc:contributor.committeemember":["Burns, John A.","Embree, Mark P."],"dc:contributor.department":["Mathematics"],"dc:creator":["Hasanyan, Jalil Davresh"],"dc:date.accessioned":["2019-02-08T09:00:30Z"],"dc:date.available":["2019-02-08T09:00:30Z"],"dc:date.issued":["2019-02-07"],"dc:description.abstract":["A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled."],"dc:description.abstractgeneral":["The modeling and analysis of elastic conductors has applications in areas ranging from manufacturing to particle physics. In this study, we model the motion of a conductive string being pulled (between two rings) while a magnetic field is applied in the lateral direction. This system’s stability is categorized through certain parameters such as the applied magnetic field, speed of pulling, and current flowing through the string. The equilibrium states are also analyzed. When the string has a periodic current, approximate solutions (string shape/orientation) are computed. In this case, we find domains of parameters that give rise to chaos. Wave speeds of traveling wave solutions are also found for certain cases."],"dc:description.degree":["MS"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:18887"],"dc:identifier.uri":["http://hdl.handle.net/10919/87530"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Current-carrying string","stability","Modeling","magnetic field","resonance vibrations"],"dc:title":["Modeling and Analysis of a Moving Conductive String in a Magnetic Field"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["MS"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:53Z"}