Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances
Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequenci...
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| Autor*in: |
Monteil, Mélodie [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 75(2013), 1-2 vom: 28. Sept., Seite 175-200 |
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| Übergeordnetes Werk: |
volume:75 ; year:2013 ; number:1-2 ; day:28 ; month:09 ; pages:175-200 |
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| DOI / URN: |
10.1007/s11071-013-1057-7 |
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OLC2051100446 |
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| 245 | 1 | 0 | |a Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances |
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| 520 | |a Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. | ||
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| 650 | 4 | |a Nonlinear oscillations | |
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| 700 | 1 | |a Touzé, Cyril |4 aut | |
| 700 | 1 | |a Thomas, Olivier |4 aut | |
| 700 | 1 | |a Benacchio, Simon |4 aut | |
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10.1007/s11071-013-1057-7 doi (DE-627)OLC2051100446 (DE-He213)s11071-013-1057-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Monteil, Mélodie verfasserin aut Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. Internal resonance Nonlinear oscillations Multiple scales Touzé, Cyril aut Thomas, Olivier aut Benacchio, Simon aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 75(2013), 1-2 vom: 28. Sept., Seite 175-200 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:75 year:2013 number:1-2 day:28 month:09 pages:175-200 https://doi.org/10.1007/s11071-013-1057-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 75 2013 1-2 28 09 175-200 |
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10.1007/s11071-013-1057-7 doi (DE-627)OLC2051100446 (DE-He213)s11071-013-1057-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Monteil, Mélodie verfasserin aut Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. Internal resonance Nonlinear oscillations Multiple scales Touzé, Cyril aut Thomas, Olivier aut Benacchio, Simon aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 75(2013), 1-2 vom: 28. Sept., Seite 175-200 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:75 year:2013 number:1-2 day:28 month:09 pages:175-200 https://doi.org/10.1007/s11071-013-1057-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 75 2013 1-2 28 09 175-200 |
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10.1007/s11071-013-1057-7 doi (DE-627)OLC2051100446 (DE-He213)s11071-013-1057-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Monteil, Mélodie verfasserin aut Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. Internal resonance Nonlinear oscillations Multiple scales Touzé, Cyril aut Thomas, Olivier aut Benacchio, Simon aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 75(2013), 1-2 vom: 28. Sept., Seite 175-200 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:75 year:2013 number:1-2 day:28 month:09 pages:175-200 https://doi.org/10.1007/s11071-013-1057-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 75 2013 1-2 28 09 175-200 |
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10.1007/s11071-013-1057-7 doi (DE-627)OLC2051100446 (DE-He213)s11071-013-1057-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Monteil, Mélodie verfasserin aut Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. Internal resonance Nonlinear oscillations Multiple scales Touzé, Cyril aut Thomas, Olivier aut Benacchio, Simon aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 75(2013), 1-2 vom: 28. Sept., Seite 175-200 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:75 year:2013 number:1-2 day:28 month:09 pages:175-200 https://doi.org/10.1007/s11071-013-1057-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 75 2013 1-2 28 09 175-200 |
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10.1007/s11071-013-1057-7 doi (DE-627)OLC2051100446 (DE-He213)s11071-013-1057-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Monteil, Mélodie verfasserin aut Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. Internal resonance Nonlinear oscillations Multiple scales Touzé, Cyril aut Thomas, Olivier aut Benacchio, Simon aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 75(2013), 1-2 vom: 28. Sept., Seite 175-200 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:75 year:2013 number:1-2 day:28 month:09 pages:175-200 https://doi.org/10.1007/s11071-013-1057-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 75 2013 1-2 28 09 175-200 |
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Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances |
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Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. © Springer Science+Business Media Dordrecht 2013 |
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Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. © Springer Science+Business Media Dordrecht 2013 |
| abstract_unstemmed |
Abstract This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies. The first model considers three modes with eigenfrequencies ω1, ω2, and ω3 such that ω3≃2ω2≃4ω1, thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads ω3≃ω2≃2ω1. Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits. © Springer Science+Business Media Dordrecht 2013 |
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| title_short |
Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances |
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https://doi.org/10.1007/s11071-013-1057-7 |
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Touzé, Cyril Thomas, Olivier Benacchio, Simon |
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Touzé, Cyril Thomas, Olivier Benacchio, Simon |
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