Regularized friction and continuation: Comparison with Coulomb's law
Periodic solutions of systems with friction are difficult to investigate because of the non-smooth nature of friction laws. This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law,...
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| Veröffentlicht in: | Journal of sound and vibration 2017-02, Vol.389, p.350-363 |
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| container_title | Journal of sound and vibration |
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| creator | Vigué, Pierre Vergez, Christophe Karkar, Sami Cochelin, Bruno |
| description | Periodic solutions of systems with friction are difficult to investigate because of the non-smooth nature of friction laws. This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter). With Coulomb's law, the stick–slip solution is constructed step by step, which gives a usable existence condition. With the regularized law, the Asymptotic Numerical Method and the Harmonic Balance Method provide bifurcation diagrams with respect to the belt speed or normal force, and for several values of the regularization parameter. Formulations from the Coulomb case give the means of a comparison between regularized solutions and a standard reference. With an appropriate definition, regularized stick–slip motion exists, its amplitude increases with respect to the belt speed and its pulsation decreases with respect to the normal force. |
| doi_str_mv | 10.1016/j.jsv.2016.11.002 |
| format | Article |
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This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter). With Coulomb's law, the stick–slip solution is constructed step by step, which gives a usable existence condition. With the regularized law, the Asymptotic Numerical Method and the Harmonic Balance Method provide bifurcation diagrams with respect to the belt speed or normal force, and for several values of the regularization parameter. Formulations from the Coulomb case give the means of a comparison between regularized solutions and a standard reference. With an appropriate definition, regularized stick–slip motion exists, its amplitude increases with respect to the belt speed and its pulsation decreases with respect to the normal force.</description><identifier>ISSN: 0022-460X</identifier><identifier>EISSN: 1095-8568</identifier><identifier>DOI: 10.1016/j.jsv.2016.11.002</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Acoustics ; Asymptotic methods ; Bifurcations ; Coefficient of friction ; Comparative analysis ; Engineering research ; Formulations ; Friction ; Harmonic balance method ; Mechanics ; Nonlinear equations ; Nonlinear modes ; Numerical continuation ; Numerical methods ; Parameters ; Periodic solutions ; Physics ; Regularization ; Slip ; Stiffness ; Vibrations</subject><ispartof>Journal of sound and vibration, 2017-02, Vol.389, p.350-363</ispartof><rights>2016 Elsevier Ltd</rights><rights>Copyright Elsevier Science Ltd. 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This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter). With Coulomb's law, the stick–slip solution is constructed step by step, which gives a usable existence condition. With the regularized law, the Asymptotic Numerical Method and the Harmonic Balance Method provide bifurcation diagrams with respect to the belt speed or normal force, and for several values of the regularization parameter. Formulations from the Coulomb case give the means of a comparison between regularized solutions and a standard reference. With an appropriate definition, regularized stick–slip motion exists, its amplitude increases with respect to the belt speed and its pulsation decreases with respect to the normal force.</description><subject>Acoustics</subject><subject>Asymptotic methods</subject><subject>Bifurcations</subject><subject>Coefficient of friction</subject><subject>Comparative analysis</subject><subject>Engineering research</subject><subject>Formulations</subject><subject>Friction</subject><subject>Harmonic balance method</subject><subject>Mechanics</subject><subject>Nonlinear equations</subject><subject>Nonlinear modes</subject><subject>Numerical continuation</subject><subject>Numerical methods</subject><subject>Parameters</subject><subject>Periodic solutions</subject><subject>Physics</subject><subject>Regularization</subject><subject>Slip</subject><subject>Stiffness</subject><subject>Vibrations</subject><issn>0022-460X</issn><issn>1095-8568</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kF9LwzAUxYMoOKcfwLeCD-JD671t06X6NOafCQNBFHwLWZq4lK6ZSbuhn96Mio8-JTn5ncO9h5BzhAQBi-s6qf02ScM1QUwA0gMyQihpzGjBDskoKGmcF_B-TE68rwGgzLN8RO5e1EffCGe-VRVpZ2RnbBuJtoqkbTvT9mIv3EQzu94EyofPnelW4d03dr289FEjdqfkSIvGq7Pfc0zeHu5fZ_N48fz4NJsuYplD2sU6xwmyDIQsqBZQCiqlXuoUCqGKMkMJMqsyQDXRZa4hQxA0ZeUSy6JiE51nY3I15K5EwzfOrIX74lYYPp8u-F4DzCgUlG3TwF4M7MbZz175jte2d20Yj6dAKWWUMQwUDpR01nun9F8sAt8Xy2seiuX7YjkiDzUGz-3gUWHVrVGOe2lUK1VlnJIdr6z5x_0D2Uh_RQ</recordid><startdate>20170217</startdate><enddate>20170217</enddate><creator>Vigué, Pierre</creator><creator>Vergez, Christophe</creator><creator>Karkar, Sami</creator><creator>Cochelin, Bruno</creator><general>Elsevier Ltd</general><general>Elsevier Science Ltd</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-6480-2139</orcidid><orcidid>https://orcid.org/0000-0002-7922-6373</orcidid></search><sort><creationdate>20170217</creationdate><title>Regularized friction and continuation: Comparison with Coulomb's law</title><author>Vigué, Pierre ; Vergez, Christophe ; Karkar, Sami ; Cochelin, Bruno</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-f4171830ac65fa09a5ccfbf206ae6931c0c3d301e7f94f0310a5289b196d87f43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Acoustics</topic><topic>Asymptotic methods</topic><topic>Bifurcations</topic><topic>Coefficient of friction</topic><topic>Comparative analysis</topic><topic>Engineering research</topic><topic>Formulations</topic><topic>Friction</topic><topic>Harmonic balance method</topic><topic>Mechanics</topic><topic>Nonlinear equations</topic><topic>Nonlinear modes</topic><topic>Numerical continuation</topic><topic>Numerical methods</topic><topic>Parameters</topic><topic>Periodic solutions</topic><topic>Physics</topic><topic>Regularization</topic><topic>Slip</topic><topic>Stiffness</topic><topic>Vibrations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vigué, Pierre</creatorcontrib><creatorcontrib>Vergez, Christophe</creatorcontrib><creatorcontrib>Karkar, Sami</creatorcontrib><creatorcontrib>Cochelin, Bruno</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of sound and vibration</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vigué, Pierre</au><au>Vergez, Christophe</au><au>Karkar, Sami</au><au>Cochelin, Bruno</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regularized friction and continuation: Comparison with Coulomb's law</atitle><jtitle>Journal of sound and vibration</jtitle><date>2017-02-17</date><risdate>2017</risdate><volume>389</volume><spage>350</spage><epage>363</epage><pages>350-363</pages><issn>0022-460X</issn><eissn>1095-8568</eissn><abstract>Periodic solutions of systems with friction are difficult to investigate because of the non-smooth nature of friction laws. This paper examines periodic solutions and most notably stick–slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter). With Coulomb's law, the stick–slip solution is constructed step by step, which gives a usable existence condition. With the regularized law, the Asymptotic Numerical Method and the Harmonic Balance Method provide bifurcation diagrams with respect to the belt speed or normal force, and for several values of the regularization parameter. Formulations from the Coulomb case give the means of a comparison between regularized solutions and a standard reference. 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| ispartof | Journal of sound and vibration, 2017-02, Vol.389, p.350-363 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Acoustics Asymptotic methods Bifurcations Coefficient of friction Comparative analysis Engineering research Formulations Friction Harmonic balance method Mechanics Nonlinear equations Nonlinear modes Numerical continuation Numerical methods Parameters Periodic solutions Physics Regularization Slip Stiffness Vibrations |
| title | Regularized friction and continuation: Comparison with Coulomb's law |
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