Free and forced motion in an asymmetric liquid-column oscillator

M. J. Smith, J.J. Kobine, F.A. Davidson

    Research output: Contribution to journalArticle

    Abstract

    The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order ordinary differential equation that is nonlinear when the widths of the two vertical columns are unequal. It is shown that this asymmetry can be used as a tuning parameter to determine the natural frequency of free oscillations in the system, in addition to the known tuning effect of the connecting chamber height. The effects of viscous damping and periodic forcing are considered, leading to a description of probable initial and long-term resonance behaviour in a practical asymmetric device.
    Original languageEnglish
    Pages (from-to)905-922
    Number of pages18
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume464
    Issue number2092
    DOIs
    Publication statusPublished - 8 Apr 2008

    Fingerprint

    oscillators
    Liquid
    Motion
    Liquids
    liquids
    Tuning
    tuning
    Oscillation
    viscous damping
    manometers
    Periodic Forcing
    Second-order Ordinary Differential Equations
    free vibration
    Damper
    dampers
    Parameter Tuning
    Probable
    Natural Frequency
    Unequal
    Ordinary differential equations

    Keywords

    • Structural damping
    • Tuning
    • Perturbation analysis
    • Nonlinear resonance

    Cite this

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    abstract = "The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order ordinary differential equation that is nonlinear when the widths of the two vertical columns are unequal. It is shown that this asymmetry can be used as a tuning parameter to determine the natural frequency of free oscillations in the system, in addition to the known tuning effect of the connecting chamber height. The effects of viscous damping and periodic forcing are considered, leading to a description of probable initial and long-term resonance behaviour in a practical asymmetric device.",
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    Free and forced motion in an asymmetric liquid-column oscillator. / Smith, M. J.; Kobine, J.J.; Davidson, F.A.

    In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 464, No. 2092, 08.04.2008, p. 905-922.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Free and forced motion in an asymmetric liquid-column oscillator

    AU - Smith, M. J.

    AU - Kobine, J.J.

    AU - Davidson, F.A.

    PY - 2008/4/8

    Y1 - 2008/4/8

    N2 - The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order ordinary differential equation that is nonlinear when the widths of the two vertical columns are unequal. It is shown that this asymmetry can be used as a tuning parameter to determine the natural frequency of free oscillations in the system, in addition to the known tuning effect of the connecting chamber height. The effects of viscous damping and periodic forcing are considered, leading to a description of probable initial and long-term resonance behaviour in a practical asymmetric device.

    AB - The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order ordinary differential equation that is nonlinear when the widths of the two vertical columns are unequal. It is shown that this asymmetry can be used as a tuning parameter to determine the natural frequency of free oscillations in the system, in addition to the known tuning effect of the connecting chamber height. The effects of viscous damping and periodic forcing are considered, leading to a description of probable initial and long-term resonance behaviour in a practical asymmetric device.

    KW - Structural damping

    KW - Tuning

    KW - Perturbation analysis

    KW - Nonlinear resonance

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    JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

    JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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