### 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 n^{th}-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 n^{th}-mode principal parametric instability regions. Example results highlight important conclusions concerning the response of automotive belt drives.

Original language | English (US) |
---|---|

Pages (from-to) | 31-37 |

Number of pages | 7 |

Journal | American Society of Mechanical Engineers, Applied Mechanics Division, AMD |

Volume | 192 |

State | Published - Dec 1 1994 |

Event | Proceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA Duration: Nov 6 1994 → Nov 11 1994 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering

### Cite this

*American Society of Mechanical Engineers, Applied Mechanics Division, AMD*,

*192*, 31-37.

}

*American Society of Mechanical Engineers, Applied Mechanics Division, AMD*, vol. 192, pp. 31-37.

**Stability and limit cycles of parametrically excited, axially moving strings.** / Mockensturm, Eric M.; Perkins, Noel C.; Ulsoy, A. Galip.

Research output: Contribution to journal › Conference 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.

UR - http://www.scopus.com/inward/record.url?scp=0028752424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028752424&partnerID=8YFLogxK

M3 - Conference article

VL - 192

SP - 31

EP - 37

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

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

SN - 0160-8835

ER -