Nonlinear planar vibrations of a cable with a linear damper
This paper minutely studies the effects of the damper on nonlinear behaviors of a cable–damper system. By modeling the damper as a combination of a viscous damper and a linear spring, the primary resonance and subharmonic resonance (1/2 order and 1/3 order) of the cable are explored. The equation of...
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| Veröffentlicht in: | Acta mechanica 2022-04, Vol.233 (4), p.1393-1412 |
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| container_title | Acta mechanica |
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| creator | Su, Xiaoyang Kang, Houjun Guo, Tieding Zhu, Weidong |
| description | This paper minutely studies the effects of the damper on nonlinear behaviors of a cable–damper system. By modeling the damper as a combination of a viscous damper and a linear spring, the primary resonance and subharmonic resonance (1/2 order and 1/3 order) of the cable are explored. The equation of motion of the cable is treated by using Galerkin’s method, and the ordinary differential equation (ODE) is obtained subsequently. To solve the ODE, the method of multiple timescales is applied, and the modulation equations corresponding to different types of resonance are derived. Then, the frequency–/force–response curves are acquired by utilizing Newton–Raphson method and pseudo-arclength algorithm, so as to explore the vibration suppression effect from a nonlinear point of view. Meanwhile, the time histories, phase portraits and Poincaré sections are also provided to discuss the influences of the damping and spring stiffness on the nonlinear characteristics of the cable. The results show that the damper has a significant effect on nonlinear resonances of the cable, and the increase in damping (spring stiffness) makes the dual characteristic gradually convert to the softening (hardening) characteristic. |
| doi_str_mv | 10.1007/s00707-022-03171-0 |
| format | Article |
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By modeling the damper as a combination of a viscous damper and a linear spring, the primary resonance and subharmonic resonance (1/2 order and 1/3 order) of the cable are explored. The equation of motion of the cable is treated by using Galerkin’s method, and the ordinary differential equation (ODE) is obtained subsequently. To solve the ODE, the method of multiple timescales is applied, and the modulation equations corresponding to different types of resonance are derived. Then, the frequency–/force–response curves are acquired by utilizing Newton–Raphson method and pseudo-arclength algorithm, so as to explore the vibration suppression effect from a nonlinear point of view. Meanwhile, the time histories, phase portraits and Poincaré sections are also provided to discuss the influences of the damping and spring stiffness on the nonlinear characteristics of the cable. The results show that the damper has a significant effect on nonlinear resonances of the cable, and the increase in damping (spring stiffness) makes the dual characteristic gradually convert to the softening (hardening) characteristic.</description><identifier>ISSN: 0001-5970</identifier><identifier>EISSN: 1619-6937</identifier><identifier>DOI: 10.1007/s00707-022-03171-0</identifier><language>eng</language><publisher>Vienna: Springer Vienna</publisher><subject>Algorithms ; Analysis ; Classical and Continuum Physics ; Control ; Differential equations ; Dynamical Systems ; Engineering ; Engineering Fluid Dynamics ; Engineering Thermodynamics ; Equations of motion ; Heat and Mass Transfer ; Newton-Raphson method ; Ordinary differential equations ; Original Paper ; Resonance ; Solid Mechanics ; Stiffness ; Television programs ; Theoretical and Applied Mechanics ; Vibration ; Vibration control ; Viscous damping</subject><ispartof>Acta mechanica, 2022-04, Vol.233 (4), p.1393-1412</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022</rights><rights>COPYRIGHT 2022 Springer</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-b4ac944e7bc61f42e6ce3c08d2e1d4e34f09425e65ac94418e0bcbb8a245ad493</citedby><cites>FETCH-LOGICAL-c358t-b4ac944e7bc61f42e6ce3c08d2e1d4e34f09425e65ac94418e0bcbb8a245ad493</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00707-022-03171-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00707-022-03171-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27928,27929,41492,42561,51323</link.rule.ids></links><search><creatorcontrib>Su, Xiaoyang</creatorcontrib><creatorcontrib>Kang, Houjun</creatorcontrib><creatorcontrib>Guo, Tieding</creatorcontrib><creatorcontrib>Zhu, Weidong</creatorcontrib><title>Nonlinear planar vibrations of a cable with a linear damper</title><title>Acta mechanica</title><addtitle>Acta Mech</addtitle><description>This paper minutely studies the effects of the damper on nonlinear behaviors of a cable–damper system. By modeling the damper as a combination of a viscous damper and a linear spring, the primary resonance and subharmonic resonance (1/2 order and 1/3 order) of the cable are explored. The equation of motion of the cable is treated by using Galerkin’s method, and the ordinary differential equation (ODE) is obtained subsequently. To solve the ODE, the method of multiple timescales is applied, and the modulation equations corresponding to different types of resonance are derived. Then, the frequency–/force–response curves are acquired by utilizing Newton–Raphson method and pseudo-arclength algorithm, so as to explore the vibration suppression effect from a nonlinear point of view. Meanwhile, the time histories, phase portraits and Poincaré sections are also provided to discuss the influences of the damping and spring stiffness on the nonlinear characteristics of the cable. The results show that the damper has a significant effect on nonlinear resonances of the cable, and the increase in damping (spring stiffness) makes the dual characteristic gradually convert to the softening (hardening) characteristic.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>Classical and Continuum Physics</subject><subject>Control</subject><subject>Differential equations</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Engineering Fluid Dynamics</subject><subject>Engineering Thermodynamics</subject><subject>Equations of motion</subject><subject>Heat and Mass Transfer</subject><subject>Newton-Raphson method</subject><subject>Ordinary differential equations</subject><subject>Original Paper</subject><subject>Resonance</subject><subject>Solid Mechanics</subject><subject>Stiffness</subject><subject>Television programs</subject><subject>Theoretical and Applied Mechanics</subject><subject>Vibration</subject><subject>Vibration control</subject><subject>Viscous damping</subject><issn>0001-5970</issn><issn>1619-6937</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kE1LxDAQhoMouK7-AU8Fz9HJR5sWT8viFyx60XNI0-mapZvWpKv4743bBW8yMMMMzzszvIRcMrhmAOompgSKAucUBFOMwhGZsYJVtKiEOiYzAGA0rxSckrMYN6njSrIZuX3ufec8mpANnfGpfLo6mNH1PmZ9m5nMmrrD7MuN76k5oI3ZDhjOyUlruogXhzonb_d3r8tHunp5eFouVtSKvBxpLY2tpERV24K1kmNhUVgoG46skShkC5XkORb5nmMlQm3rujRc5qaRlZiTq2nvEPqPHcZRb_pd8Omk5kUuJCugYom6nqi16VA73_ZjMDZFg1tne4-tS_OFAiYEL6s8CfgksKGPMWCrh-C2JnxrBvrXVT25qpOreu9qynMiJlFMsF9j-PvlH9UPXjV4wg</recordid><startdate>20220401</startdate><enddate>20220401</enddate><creator>Su, Xiaoyang</creator><creator>Kang, Houjun</creator><creator>Guo, Tieding</creator><creator>Zhu, Weidong</creator><general>Springer Vienna</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L6V</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>20220401</creationdate><title>Nonlinear planar vibrations of a cable with a linear damper</title><author>Su, Xiaoyang ; Kang, Houjun ; Guo, Tieding ; Zhu, Weidong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-b4ac944e7bc61f42e6ce3c08d2e1d4e34f09425e65ac94418e0bcbb8a245ad493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Analysis</topic><topic>Classical and Continuum Physics</topic><topic>Control</topic><topic>Differential equations</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Engineering Fluid Dynamics</topic><topic>Engineering Thermodynamics</topic><topic>Equations of motion</topic><topic>Heat and Mass Transfer</topic><topic>Newton-Raphson method</topic><topic>Ordinary differential equations</topic><topic>Original Paper</topic><topic>Resonance</topic><topic>Solid Mechanics</topic><topic>Stiffness</topic><topic>Television programs</topic><topic>Theoretical and Applied Mechanics</topic><topic>Vibration</topic><topic>Vibration control</topic><topic>Viscous damping</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Su, Xiaoyang</creatorcontrib><creatorcontrib>Kang, Houjun</creatorcontrib><creatorcontrib>Guo, Tieding</creatorcontrib><creatorcontrib>Zhu, Weidong</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Acta mechanica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Su, Xiaoyang</au><au>Kang, Houjun</au><au>Guo, Tieding</au><au>Zhu, Weidong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlinear planar vibrations of a cable with a linear damper</atitle><jtitle>Acta mechanica</jtitle><stitle>Acta Mech</stitle><date>2022-04-01</date><risdate>2022</risdate><volume>233</volume><issue>4</issue><spage>1393</spage><epage>1412</epage><pages>1393-1412</pages><issn>0001-5970</issn><eissn>1619-6937</eissn><abstract>This paper minutely studies the effects of the damper on nonlinear behaviors of a cable–damper system. By modeling the damper as a combination of a viscous damper and a linear spring, the primary resonance and subharmonic resonance (1/2 order and 1/3 order) of the cable are explored. The equation of motion of the cable is treated by using Galerkin’s method, and the ordinary differential equation (ODE) is obtained subsequently. To solve the ODE, the method of multiple timescales is applied, and the modulation equations corresponding to different types of resonance are derived. Then, the frequency–/force–response curves are acquired by utilizing Newton–Raphson method and pseudo-arclength algorithm, so as to explore the vibration suppression effect from a nonlinear point of view. Meanwhile, the time histories, phase portraits and Poincaré sections are also provided to discuss the influences of the damping and spring stiffness on the nonlinear characteristics of the cable. The results show that the damper has a significant effect on nonlinear resonances of the cable, and the increase in damping (spring stiffness) makes the dual characteristic gradually convert to the softening (hardening) characteristic.</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00707-022-03171-0</doi><tpages>20</tpages></addata></record> |
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| subjects | Algorithms Analysis Classical and Continuum Physics Control Differential equations Dynamical Systems Engineering Engineering Fluid Dynamics Engineering Thermodynamics Equations of motion Heat and Mass Transfer Newton-Raphson method Ordinary differential equations Original Paper Resonance Solid Mechanics Stiffness Television programs Theoretical and Applied Mechanics Vibration Vibration control Viscous damping |
| title | Nonlinear planar vibrations of a cable with a linear damper |
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