### Abstract

In this article, we briefly present a model which consists of a non-homogeneous flexible beam clamped at its left end to a rigid disk and free at the right end, where another rigid body is attached. We assume that the disk rotates with a non-uniform angular velocity while the beam is supposed to rotate with the disk in another plane perpendicular to that of the disk. Thereafter, we propose a wide class of feedback laws depending on the assumptions made on the physical parameters. In each case, we show that whenever the angular velocity is not exceeding a certain upper bound, the beam vibrations decay exponentially to zero and the disk rotates with a desired angular velocity.

Original language | English |
---|---|

Pages (from-to) | 621-629 |

Number of pages | 9 |

Journal | Applied Mathematical Modelling |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Exponential stability
- Non-homogeneous beam
- Nonlinear hybrid system
- Rotating flexible structure
- Torque and boundary controls

### ASJC Scopus subject areas

- Applied Mathematics
- Modelling and Simulation

### Cite this

*Applied Mathematical Modelling*,

*39*(2), 621-629. https://doi.org/10.1016/j.apm.2014.06.015

**Modelling and stabilization of a nonlinear hybrid system of elasticity.** / Chentouf, Boumediène.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 39, no. 2, pp. 621-629. https://doi.org/10.1016/j.apm.2014.06.015

}

TY - JOUR

T1 - Modelling and stabilization of a nonlinear hybrid system of elasticity

AU - Chentouf, Boumediène

PY - 2015

Y1 - 2015

N2 - In this article, we briefly present a model which consists of a non-homogeneous flexible beam clamped at its left end to a rigid disk and free at the right end, where another rigid body is attached. We assume that the disk rotates with a non-uniform angular velocity while the beam is supposed to rotate with the disk in another plane perpendicular to that of the disk. Thereafter, we propose a wide class of feedback laws depending on the assumptions made on the physical parameters. In each case, we show that whenever the angular velocity is not exceeding a certain upper bound, the beam vibrations decay exponentially to zero and the disk rotates with a desired angular velocity.

AB - In this article, we briefly present a model which consists of a non-homogeneous flexible beam clamped at its left end to a rigid disk and free at the right end, where another rigid body is attached. We assume that the disk rotates with a non-uniform angular velocity while the beam is supposed to rotate with the disk in another plane perpendicular to that of the disk. Thereafter, we propose a wide class of feedback laws depending on the assumptions made on the physical parameters. In each case, we show that whenever the angular velocity is not exceeding a certain upper bound, the beam vibrations decay exponentially to zero and the disk rotates with a desired angular velocity.

KW - Exponential stability

KW - Non-homogeneous beam

KW - Nonlinear hybrid system

KW - Rotating flexible structure

KW - Torque and boundary controls

UR - http://www.scopus.com/inward/record.url?scp=84922595723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922595723&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2014.06.015

DO - 10.1016/j.apm.2014.06.015

M3 - Article

VL - 39

SP - 621

EP - 629

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 2

ER -