### Abstract

The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

Original language | Undefined/Unknown |
---|---|

Pages (from-to) | 971-986 |

Number of pages | 16 |

Journal | Journal of Theoretical and Applied Mechanics |

Volume | 49 |

Issue number | 4 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Liapunov second method
- Limit cycles
- Stick-slip oscillations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Theoretical and Applied Mechanics*,

*49*(4), 971-986.

**Analityczna metoda określania amplitudy drgań ciernych (typu stick-slip).** / Abdo, Jamil; Abouelsoud, Ahmed A.

Research output: Contribution to journal › Article

*Journal of Theoretical and Applied Mechanics*, vol. 49, no. 4, pp. 971-986.

}

TY - JOUR

T1 - Analityczna metoda określania amplitudy drgań ciernych (typu stick-slip)

AU - Abdo, Jamil

AU - Abouelsoud, Ahmed A.

PY - 2011

Y1 - 2011

N2 - The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

AB - The objective of the present work is to evaluate alternative approximate techniques to determine the amplitudes of the limit cycles that evolve from stick-slip vibrations based on a mass-on-moving-belt model. The control of self-excited systems is a very interesting problem because of friction-induced self sustained oscillations which result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using the Liapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition, an estimate of the amplitude of the velocity of the limit cycle of stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are indistinguishable.

KW - Liapunov second method

KW - Limit cycles

KW - Stick-slip oscillations

UR - http://www.scopus.com/inward/record.url?scp=84860134994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860134994&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 971

EP - 986

JO - Journal of Theoretical and Applied Mechanics

JF - Journal of Theoretical and Applied Mechanics

SN - 1429-2955

IS - 4

ER -