The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length

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Abstract

A passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed. Due to the time-varying length of the vertical cable the natural frequencies of the system vary slowly, and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is proposed. This model is analyzed by using a combined perturbation and numerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance, and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system is integrated numerically on a slow time scale. A model example is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. © 1997 Academic Press Limited.
Original languageEnglish
Pages (from-to)243-269
Number of pages27
JournalJournal of Sound and Vibration
Volume208
Issue number2
DOIs
Publication statusPublished - 1997

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cables
perturbation
dynamic characteristics
excitation
resonant frequencies
differential equations
damping
expansion

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title = "The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length",
abstract = "A passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed. Due to the time-varying length of the vertical cable the natural frequencies of the system vary slowly, and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is proposed. This model is analyzed by using a combined perturbation and numerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance, and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system is integrated numerically on a slow time scale. A model example is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. {\circledC} 1997 Academic Press Limited.",
author = "Stefan Kaczmarczyk",
year = "1997",
doi = "10.1006/jsvi.1997.1220",
language = "English",
volume = "208",
pages = "243--269",
journal = "Journal of Sound and Vibration",
issn = "1095-8568",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length

AU - Kaczmarczyk, Stefan

PY - 1997

Y1 - 1997

N2 - A passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed. Due to the time-varying length of the vertical cable the natural frequencies of the system vary slowly, and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is proposed. This model is analyzed by using a combined perturbation and numerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance, and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system is integrated numerically on a slow time scale. A model example is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. © 1997 Academic Press Limited.

AB - A passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed. Due to the time-varying length of the vertical cable the natural frequencies of the system vary slowly, and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is proposed. This model is analyzed by using a combined perturbation and numerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance, and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system is integrated numerically on a slow time scale. A model example is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. © 1997 Academic Press Limited.

UR - http://www.mendeley.com/research/passage-through-resonance-catenaryvertical-cable-hoisting-system-slowly-varying-length

U2 - 10.1006/jsvi.1997.1220

DO - 10.1006/jsvi.1997.1220

M3 - Article

VL - 208

SP - 243

EP - 269

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 1095-8568

IS - 2

ER -