Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam
The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equatio...
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| Autor*in: |
Luongo, Angelo [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: © The Author(s) 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematics and mechanics of solids - Thousand Oaks [u.a.] : Sage, 1996, 22(2017), 6, Seite 1347-1365 |
|---|---|
| Übergeordnetes Werk: |
volume:22 ; year:2017 ; number:6 ; pages:1347-1365 |
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10.1177/1081286516632381 |
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| 520 | |a The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. | ||
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10.1177/1081286516632381 doi PQ20171125 (DE-627)OLC1995537470 (DE-599)GBVOLC1995537470 (PRQ)sage_journals_10_1177_10812865166323810 (KEY)0569248220170000022000601347nonlinearhystereticdampingeffectsonthepostcritical DE-627 ger DE-627 rakwb eng 510 620 DE-600 Luongo, Angelo verfasserin aut Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. Nutzungsrecht: © The Author(s) 2016 D’Annibale, Francesco oth Enthalten in Mathematics and mechanics of solids Thousand Oaks [u.a.] : Sage, 1996 22(2017), 6, Seite 1347-1365 (DE-627)215140451 (DE-600)1333991-6 (DE-576)060902477 1081-2865 nnns volume:22 year:2017 number:6 pages:1347-1365 http://dx.doi.org/10.1177/1081286516632381 Volltext http://journals.sagepub.com/doi/full/10.1177/1081286516632381 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 22 2017 6 1347-1365 |
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10.1177/1081286516632381 doi PQ20171125 (DE-627)OLC1995537470 (DE-599)GBVOLC1995537470 (PRQ)sage_journals_10_1177_10812865166323810 (KEY)0569248220170000022000601347nonlinearhystereticdampingeffectsonthepostcritical DE-627 ger DE-627 rakwb eng 510 620 DE-600 Luongo, Angelo verfasserin aut Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. Nutzungsrecht: © The Author(s) 2016 D’Annibale, Francesco oth Enthalten in Mathematics and mechanics of solids Thousand Oaks [u.a.] : Sage, 1996 22(2017), 6, Seite 1347-1365 (DE-627)215140451 (DE-600)1333991-6 (DE-576)060902477 1081-2865 nnns volume:22 year:2017 number:6 pages:1347-1365 http://dx.doi.org/10.1177/1081286516632381 Volltext http://journals.sagepub.com/doi/full/10.1177/1081286516632381 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 22 2017 6 1347-1365 |
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10.1177/1081286516632381 doi PQ20171125 (DE-627)OLC1995537470 (DE-599)GBVOLC1995537470 (PRQ)sage_journals_10_1177_10812865166323810 (KEY)0569248220170000022000601347nonlinearhystereticdampingeffectsonthepostcritical DE-627 ger DE-627 rakwb eng 510 620 DE-600 Luongo, Angelo verfasserin aut Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. Nutzungsrecht: © The Author(s) 2016 D’Annibale, Francesco oth Enthalten in Mathematics and mechanics of solids Thousand Oaks [u.a.] : Sage, 1996 22(2017), 6, Seite 1347-1365 (DE-627)215140451 (DE-600)1333991-6 (DE-576)060902477 1081-2865 nnns volume:22 year:2017 number:6 pages:1347-1365 http://dx.doi.org/10.1177/1081286516632381 Volltext http://journals.sagepub.com/doi/full/10.1177/1081286516632381 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 22 2017 6 1347-1365 |
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10.1177/1081286516632381 doi PQ20171125 (DE-627)OLC1995537470 (DE-599)GBVOLC1995537470 (PRQ)sage_journals_10_1177_10812865166323810 (KEY)0569248220170000022000601347nonlinearhystereticdampingeffectsonthepostcritical DE-627 ger DE-627 rakwb eng 510 620 DE-600 Luongo, Angelo verfasserin aut Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. Nutzungsrecht: © The Author(s) 2016 D’Annibale, Francesco oth Enthalten in Mathematics and mechanics of solids Thousand Oaks [u.a.] : Sage, 1996 22(2017), 6, Seite 1347-1365 (DE-627)215140451 (DE-600)1333991-6 (DE-576)060902477 1081-2865 nnns volume:22 year:2017 number:6 pages:1347-1365 http://dx.doi.org/10.1177/1081286516632381 Volltext http://journals.sagepub.com/doi/full/10.1177/1081286516632381 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 22 2017 6 1347-1365 |
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10.1177/1081286516632381 doi PQ20171125 (DE-627)OLC1995537470 (DE-599)GBVOLC1995537470 (PRQ)sage_journals_10_1177_10812865166323810 (KEY)0569248220170000022000601347nonlinearhystereticdampingeffectsonthepostcritical DE-627 ger DE-627 rakwb eng 510 620 DE-600 Luongo, Angelo verfasserin aut Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. Nutzungsrecht: © The Author(s) 2016 D’Annibale, Francesco oth Enthalten in Mathematics and mechanics of solids Thousand Oaks [u.a.] : Sage, 1996 22(2017), 6, Seite 1347-1365 (DE-627)215140451 (DE-600)1333991-6 (DE-576)060902477 1081-2865 nnns volume:22 year:2017 number:6 pages:1347-1365 http://dx.doi.org/10.1177/1081286516632381 Volltext http://journals.sagepub.com/doi/full/10.1177/1081286516632381 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 22 2017 6 1347-1365 |
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Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam |
| abstract |
The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. |
| abstractGer |
The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. |
| abstract_unstemmed |
The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients. |
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| title_short |
Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam |
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http://dx.doi.org/10.1177/1081286516632381 http://journals.sagepub.com/doi/full/10.1177/1081286516632381 |
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| author2 |
D’Annibale, Francesco |
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D’Annibale, Francesco |
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215140451 |
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| doi_str |
10.1177/1081286516632381 |
| up_date |
2024-07-03T22:06:27.119Z |
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1803597263268741120 |
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The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation θ of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. 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