{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/6833"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/6833","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Nonlinear Behaviors Analysis and Nonlinear Characteristics Diagnosing of Mechanical Vibration Systems","abstract":"Comprehensive understanding and effective diagnosis of nonlinear behaviors are important in dynamical analyses of mechanical systems and may provide crucial guidance to the design and control of mechanical systems. In this research, the nonlinear behavior and stability of an elastic suspended cable under combined parametric and external excitations are studied first. Such cable is commonly used in suspended bridges. The governing equations of the cable with geometric nonlinearity are developed with considerations of the first in-plane and out-of-plane mode vibrations. The solutions of the nonlinear system are derived as per the perturbation method of higher accuracy. The nonlinear stability of the cable system is investigated in the research with focus on the influence of different system parameters on the stability. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. With application of the Periodicity-Ratio (P-R) method, the effects of different external excitations on the nonlinear vibrations of the cable are examined. With a periodic-nonperiodic-chaotic region diagram developed on the basis of the P-R method, the nonlinear behavior of the cable can be quantified and graphically identified corresponding to a large range of external excitation. In addition, to diagnose nonlinear behavior more accurately and efficiently, a proposed method combining the P-R method and Lyapunov exponent method is established in this research. The Lyapunov exponent method is probably the most widely used method in diagnosing nonlinear behaviors of dynamic systems. However, in comparing with the P-R method, Lyapunov approach is rather tedious in diagnosing the nonlinear characteristics of a dynamic system. And also, Lyapunov exponent method may yield incorrect results for many cases. On the other hand, the P-R method describes the periodicity of a nonlinear system with a single value index and reveals the fact that there are actually infinite types of nonlinear behaviors in between periodic and chaotic cases. However, with the P-R method, it is difficult to directly distinguish between chaotic and quasiperiodic responses of a nonlinear system. With combination of the two methods, as shown in the research, nonlinear behaviors can be diagnosed much more accurately and efficiently. To demonstrate the advantages of the method proposed, the method combing the P-R and Lyapunov exponent methods is applied to analyze a dynamic system governed by Duffing’s equation. Comparisons of the P-R and Lyapunov exponent methods are also conducted. The proposed method shows higher efficiency and reliability in comparing with either the Lyapunov exponent method or the P-R method.","abstract_html":"Comprehensive understanding and effective diagnosis of nonlinear behaviors are important in dynamical analyses of mechanical systems and may provide crucial guidance to the design and control of mechanical systems. In this research, the nonlinear behavior and stability of an elastic suspended cable under combined parametric and external excitations are studied first. Such cable is commonly used in suspended bridges. The governing equations of the cable with geometric nonlinearity are developed with considerations of the first in-plane and out-of-plane mode vibrations. The solutions of the nonlinear system are derived as per the perturbation method of higher accuracy. The nonlinear stability of the cable system is investigated in the research with focus on the influence of different system parameters on the stability. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. With application of the Periodicity-Ratio (P-R) method, the effects of different external excitations on the nonlinear vibrations of the cable are examined. With a periodic-nonperiodic-chaotic region diagram developed on the basis of the P-R method, the nonlinear behavior of the cable can be quantified and graphically identified corresponding to a large range of external excitation. In addition, to diagnose nonlinear behavior more accurately and efficiently, a proposed method combining the P-R method and Lyapunov exponent method is established in this research. The Lyapunov exponent method is probably the most widely used method in diagnosing nonlinear behaviors of dynamic systems. However, in comparing with the P-R method, Lyapunov approach is rather tedious in diagnosing the nonlinear characteristics of a dynamic system. And also, Lyapunov exponent method may yield incorrect results for many cases. On the other hand, the P-R method describes the periodicity of a nonlinear system with a single value index and reveals the fact that there are actually infinite types of nonlinear behaviors in between periodic and chaotic cases. However, with the P-R method, it is difficult to directly distinguish between chaotic and quasiperiodic responses of a nonlinear system. With combination of the two methods, as shown in the research, nonlinear behaviors can be diagnosed much more accurately and efficiently. To demonstrate the advantages of the method proposed, the method combing the P-R and Lyapunov exponent methods is applied to analyze a dynamic system governed by Duffing’s equation. Comparisons of the P-R and Lyapunov exponent methods are also conducted. The proposed method shows higher efficiency and reliability in comparing with either the Lyapunov exponent method or the P-R method.","abstract_has_math":false,"creators":["Xia, Dandan"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Applied Science (MASc)","degree_level":"Master's","degree_discipline":"Engineering - Industrial Systems","degree_department":null,"school":null,"contributors":[],"advisors":["Dai, Liming"],"committee_chairs":[],"committee_members":["Mehrandezh, Mehran","Ismail, Mohamed"],"year":2016,"date_issued":"2016-02","date_published":"2016-02","updated_at":"2026-07-24T04:03:32Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4111"],"render_values":[{"text":"https://doi.org/10.82465/4111","href":"https://doi.org/10.82465/4111","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/6833","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dai, Liming"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Mehrandezh, Mehran","Ismail, Mohamed"]},{"key":"dc:creator","label":"Author","values":["Xia, Dandan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-07-27T19:34:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-07-27T19:34:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-02"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering - Industrial Systems"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Applied Science (MASc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4111"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/6833"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Industrial Systems Engineering, University of Regina. x , 92 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["Comprehensive understanding and effective diagnosis of nonlinear behaviors are important in dynamical analyses of mechanical systems and may provide crucial guidance to the design and control of mechanical systems. In this research, the nonlinear behavior and stability of an elastic suspended cable under combined parametric and external excitations are studied first. Such cable is commonly used in suspended bridges. The governing equations of the cable with geometric nonlinearity are developed with considerations of the first in-plane and out-of-plane mode vibrations. The solutions of the nonlinear system are derived as per the perturbation method of higher accuracy. The nonlinear stability of the cable system is investigated in the research with focus on the influence of different system parameters on the stability. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. With application of the Periodicity-Ratio (P-R) method, the effects of different external excitations on the nonlinear vibrations of the cable are examined. With a periodic-nonperiodic-chaotic region diagram developed on the basis of the P-R method, the nonlinear behavior of the cable can be quantified and graphically identified corresponding to a large range of external excitation. In addition, to diagnose nonlinear behavior more accurately and efficiently, a proposed method combining the P-R method and Lyapunov exponent method is established in this research. The Lyapunov exponent method is probably the most widely used method in diagnosing nonlinear behaviors of dynamic systems. However, in comparing with the P-R method, Lyapunov approach is rather tedious in diagnosing the nonlinear characteristics of a dynamic system. And also, Lyapunov exponent method may yield incorrect results for many cases. On the other hand, the P-R method describes the periodicity of a nonlinear system with a single value index and reveals the fact that there are actually infinite types of nonlinear behaviors in between periodic and chaotic cases. However, with the P-R method, it is difficult to directly distinguish between chaotic and quasiperiodic responses of a nonlinear system. With combination of the two methods, as shown in the research, nonlinear behaviors can be diagnosed much more accurately and efficiently. To demonstrate the advantages of the method proposed, the method combing the P-R and Lyapunov exponent methods is applied to analyze a dynamic system governed by Duffing’s equation. Comparisons of the P-R and Lyapunov exponent methods are also conducted. The proposed method shows higher efficiency and reliability in comparing with either the Lyapunov exponent method or the P-R method."]},{"key":"dc:title","label":"Title","values":["Nonlinear Behaviors Analysis and Nonlinear Characteristics Diagnosing of Mechanical Vibration Systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dai, Liming"],"dc:contributor.committeemember":["Mehrandezh, Mehran","Ismail, Mohamed"],"dc:creator":["Xia, Dandan"],"dc:date.accessioned":["2016-07-27T19:34:19Z"],"dc:date.available":["2016-07-27T19:34:19Z"],"dc:date.issued":["2016-02"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in Industrial Systems Engineering, University of Regina. x , 92 p."],"dc:description.abstract":["Comprehensive understanding and effective diagnosis of nonlinear behaviors are important in dynamical analyses of mechanical systems and may provide crucial guidance to the design and control of mechanical systems. In this research, the nonlinear behavior and stability of an elastic suspended cable under combined parametric and external excitations are studied first. Such cable is commonly used in suspended bridges. The governing equations of the cable with geometric nonlinearity are developed with considerations of the first in-plane and out-of-plane mode vibrations. The solutions of the nonlinear system are derived as per the perturbation method of higher accuracy. The nonlinear stability of the cable system is investigated in the research with focus on the influence of different system parameters on the stability. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. With application of the Periodicity-Ratio (P-R) method, the effects of different external excitations on the nonlinear vibrations of the cable are examined. With a periodic-nonperiodic-chaotic region diagram developed on the basis of the P-R method, the nonlinear behavior of the cable can be quantified and graphically identified corresponding to a large range of external excitation. In addition, to diagnose nonlinear behavior more accurately and efficiently, a proposed method combining the P-R method and Lyapunov exponent method is established in this research. The Lyapunov exponent method is probably the most widely used method in diagnosing nonlinear behaviors of dynamic systems. However, in comparing with the P-R method, Lyapunov approach is rather tedious in diagnosing the nonlinear characteristics of a dynamic system. And also, Lyapunov exponent method may yield incorrect results for many cases. On the other hand, the P-R method describes the periodicity of a nonlinear system with a single value index and reveals the fact that there are actually infinite types of nonlinear behaviors in between periodic and chaotic cases. However, with the P-R method, it is difficult to directly distinguish between chaotic and quasiperiodic responses of a nonlinear system. With combination of the two methods, as shown in the research, nonlinear behaviors can be diagnosed much more accurately and efficiently. To demonstrate the advantages of the method proposed, the method combing the P-R and Lyapunov exponent methods is applied to analyze a dynamic system governed by Duffing’s equation. Comparisons of the P-R and Lyapunov exponent methods are also conducted. The proposed method shows higher efficiency and reliability in comparing with either the Lyapunov exponent method or the P-R method."],"dc:identifier.doi":["https://doi.org/10.82465/4111"],"dc:identifier.uri":["https://hdl.handle.net/10294/6833"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Nonlinear Behaviors Analysis and Nonlinear Characteristics Diagnosing of Mechanical Vibration Systems"],"dc:type":["master thesis"],"thesis:degree_discipline":["Engineering - Industrial Systems"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Applied Science (MASc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:32Z"}