Intermodal resonance of vibrating suspended cables

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Abstract

The weakly nonlinear free vibrations of a single suspended cable, or a coupled system of suspended cables, may be classified as gravity modes (no tension variations to leading order) and elasto-gravity modes (tension and vertical displacement equally important). It was found earlier [12] that the gravity mode (probably the most common type of vibration of relatively inelastic spans) does not exist for particular values of the problem parameter. The reason is that for these parameter values the 1st and 2nd harmonic are in resonance. The true nature of this resonance has now been established and analysed in detail by an application of the Lindstedt-Poincaré technique. The leading order 1st and 2nd harmonic can only exist together with each other. As a result, the tension, albeit of 2nd harmonic, does not vanish at leading order and the mode is not anymore truly dominated by gravity alone. The analysis is worked out here in detail for a single span. It is conjectured that designing the suspended cable with parameter values right at this resonance will delay or hinder the occurrence of galloping.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages13
Publication statusPublished - 2010

Publication series

NameCASA-report
Volume1004
ISSN (Print)0926-4507

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cables
gravitation
harmonics
free vibration
occurrences
vibration

Cite this

Rienstra, S. W. (2010). Intermodal resonance of vibrating suspended cables. (CASA-report; Vol. 1004). Eindhoven: Technische Universiteit Eindhoven.
Rienstra, S.W. / Intermodal resonance of vibrating suspended cables. Eindhoven : Technische Universiteit Eindhoven, 2010. 13 p. (CASA-report).
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abstract = "The weakly nonlinear free vibrations of a single suspended cable, or a coupled system of suspended cables, may be classified as gravity modes (no tension variations to leading order) and elasto-gravity modes (tension and vertical displacement equally important). It was found earlier [12] that the gravity mode (probably the most common type of vibration of relatively inelastic spans) does not exist for particular values of the problem parameter. The reason is that for these parameter values the 1st and 2nd harmonic are in resonance. The true nature of this resonance has now been established and analysed in detail by an application of the Lindstedt-Poincar{\'e} technique. The leading order 1st and 2nd harmonic can only exist together with each other. As a result, the tension, albeit of 2nd harmonic, does not vanish at leading order and the mode is not anymore truly dominated by gravity alone. The analysis is worked out here in detail for a single span. It is conjectured that designing the suspended cable with parameter values right at this resonance will delay or hinder the occurrence of galloping.",
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Rienstra, SW 2010, Intermodal resonance of vibrating suspended cables. CASA-report, vol. 1004, Technische Universiteit Eindhoven, Eindhoven.

Intermodal resonance of vibrating suspended cables. / Rienstra, S.W.

Eindhoven : Technische Universiteit Eindhoven, 2010. 13 p. (CASA-report; Vol. 1004).

Research output: Book/ReportReportAcademic

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T1 - Intermodal resonance of vibrating suspended cables

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N2 - The weakly nonlinear free vibrations of a single suspended cable, or a coupled system of suspended cables, may be classified as gravity modes (no tension variations to leading order) and elasto-gravity modes (tension and vertical displacement equally important). It was found earlier [12] that the gravity mode (probably the most common type of vibration of relatively inelastic spans) does not exist for particular values of the problem parameter. The reason is that for these parameter values the 1st and 2nd harmonic are in resonance. The true nature of this resonance has now been established and analysed in detail by an application of the Lindstedt-Poincaré technique. The leading order 1st and 2nd harmonic can only exist together with each other. As a result, the tension, albeit of 2nd harmonic, does not vanish at leading order and the mode is not anymore truly dominated by gravity alone. The analysis is worked out here in detail for a single span. It is conjectured that designing the suspended cable with parameter values right at this resonance will delay or hinder the occurrence of galloping.

AB - The weakly nonlinear free vibrations of a single suspended cable, or a coupled system of suspended cables, may be classified as gravity modes (no tension variations to leading order) and elasto-gravity modes (tension and vertical displacement equally important). It was found earlier [12] that the gravity mode (probably the most common type of vibration of relatively inelastic spans) does not exist for particular values of the problem parameter. The reason is that for these parameter values the 1st and 2nd harmonic are in resonance. The true nature of this resonance has now been established and analysed in detail by an application of the Lindstedt-Poincaré technique. The leading order 1st and 2nd harmonic can only exist together with each other. As a result, the tension, albeit of 2nd harmonic, does not vanish at leading order and the mode is not anymore truly dominated by gravity alone. The analysis is worked out here in detail for a single span. It is conjectured that designing the suspended cable with parameter values right at this resonance will delay or hinder the occurrence of galloping.

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Rienstra SW. Intermodal resonance of vibrating suspended cables. Eindhoven: Technische Universiteit Eindhoven, 2010. 13 p. (CASA-report).