### 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 |
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Pages (from-to) | 621-629 |

Number of pages | 9 |

Journal | Applied Mathematical Modelling |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

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### 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