Stability and limit cycles of parametrically excited, axially moving strings

Eric M. Mockensturm, Noel C. Perkins, A. Galip Ulsoy

    Research output: Contribution to journalConference article

    Abstract

    Tension fluctuations are the dominant source of excitation in automotive belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impact belt life. This paper evaluates an efficient discrete model of a parametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin discretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existence and stability of limit cycles near parametric instability regions. In particular, simple expressions are found for the stability boundaries of the general nth-mode principal parametric instability regions and the first summation and difference parametric instability regions. Subsequent evaluation of the weakly non-linear equation of motion leads to an analytical expression for the amplitudes (and stability) of non-trivial limit cycles that exist around the nth-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.

    Original languageEnglish (US)
    Pages (from-to)31-37
    Number of pages7
    JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
    Volume192
    StatePublished - Dec 1 1994
    EventProceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA
    Duration: Nov 6 1994Nov 11 1994

    Fingerprint

    Belt drives
    Nonlinear equations
    Eigenvalues and eigenfunctions
    Equations of motion

    All Science Journal Classification (ASJC) codes

    • Mechanical Engineering

    Cite this

    @article{f25594dbbed24f5b9c83be6d6697849d,
    title = "Stability and limit cycles of parametrically excited, axially moving strings",
    abstract = "Tension fluctuations are the dominant source of excitation in automotive belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impact belt life. This paper evaluates an efficient discrete model of a parametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin discretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existence and stability of limit cycles near parametric instability regions. In particular, simple expressions are found for the stability boundaries of the general nth-mode principal parametric instability regions and the first summation and difference parametric instability regions. Subsequent evaluation of the weakly non-linear equation of motion leads to an analytical expression for the amplitudes (and stability) of non-trivial limit cycles that exist around the nth-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.",
    author = "Mockensturm, {Eric M.} and Perkins, {Noel C.} and Ulsoy, {A. Galip}",
    year = "1994",
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    language = "English (US)",
    volume = "192",
    pages = "31--37",
    journal = "American Society of Mechanical Engineers, Applied Mechanics Division, AMD",
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    Stability and limit cycles of parametrically excited, axially moving strings. / Mockensturm, Eric M.; Perkins, Noel C.; Ulsoy, A. Galip.

    In: American Society of Mechanical Engineers, Applied Mechanics Division, AMD, Vol. 192, 01.12.1994, p. 31-37.

    Research output: Contribution to journalConference article

    TY - JOUR

    T1 - Stability and limit cycles of parametrically excited, axially moving strings

    AU - Mockensturm, Eric M.

    AU - Perkins, Noel C.

    AU - Ulsoy, A. Galip

    PY - 1994/12/1

    Y1 - 1994/12/1

    N2 - Tension fluctuations are the dominant source of excitation in automotive belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impact belt life. This paper evaluates an efficient discrete model of a parametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin discretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existence and stability of limit cycles near parametric instability regions. In particular, simple expressions are found for the stability boundaries of the general nth-mode principal parametric instability regions and the first summation and difference parametric instability regions. Subsequent evaluation of the weakly non-linear equation of motion leads to an analytical expression for the amplitudes (and stability) of non-trivial limit cycles that exist around the nth-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.

    AB - Tension fluctuations are the dominant source of excitation in automotive belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impact belt life. This paper evaluates an efficient discrete model of a parametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin discretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existence and stability of limit cycles near parametric instability regions. In particular, simple expressions are found for the stability boundaries of the general nth-mode principal parametric instability regions and the first summation and difference parametric instability regions. Subsequent evaluation of the weakly non-linear equation of motion leads to an analytical expression for the amplitudes (and stability) of non-trivial limit cycles that exist around the nth-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.

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    JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

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