### Abstract

In this paper, we consider a rotating system of elasticity. It consists of a disk, a flexible beam and a tip mass. The beam is assumed to be non-homogeneous (space depending of physical parameters). Moreover, the flexible beam is clamped at one end to the center of the disk, whereas a tip mass is attached to its other end. The disk rotates freely around its axis with a time-dependent angular velocity and the motion of the beam-mass is confined to a plane perpendicular to the disk. The system is shown to be exponentially stable under the action of: i) a torque control applied on the disk; ii) a force control and moment control or only a force control. Furthermore, the Riesz basis property is proved for the system in the case of uniform angular velocity.

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

Pages (from-to) | 1243-1261 |

Number of pages | 19 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 423 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- Exponential stability
- Force and moment control
- Non-homogeneous beam
- Riesz basis
- Rotating disk-beam-mass
- Torque control

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*423*(2), 1243-1261. https://doi.org/10.1016/j.jmaa.2014.10.040

**Exponential stability of a non-homogeneous rotating disk-beam-mass system.** / Chen, Xin; Chentouf, Boumediene; Wang, Jun Min.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 423, no. 2, pp. 1243-1261. https://doi.org/10.1016/j.jmaa.2014.10.040

}

TY - JOUR

T1 - Exponential stability of a non-homogeneous rotating disk-beam-mass system

AU - Chen, Xin

AU - Chentouf, Boumediene

AU - Wang, Jun Min

PY - 2015

Y1 - 2015

N2 - In this paper, we consider a rotating system of elasticity. It consists of a disk, a flexible beam and a tip mass. The beam is assumed to be non-homogeneous (space depending of physical parameters). Moreover, the flexible beam is clamped at one end to the center of the disk, whereas a tip mass is attached to its other end. The disk rotates freely around its axis with a time-dependent angular velocity and the motion of the beam-mass is confined to a plane perpendicular to the disk. The system is shown to be exponentially stable under the action of: i) a torque control applied on the disk; ii) a force control and moment control or only a force control. Furthermore, the Riesz basis property is proved for the system in the case of uniform angular velocity.

AB - In this paper, we consider a rotating system of elasticity. It consists of a disk, a flexible beam and a tip mass. The beam is assumed to be non-homogeneous (space depending of physical parameters). Moreover, the flexible beam is clamped at one end to the center of the disk, whereas a tip mass is attached to its other end. The disk rotates freely around its axis with a time-dependent angular velocity and the motion of the beam-mass is confined to a plane perpendicular to the disk. The system is shown to be exponentially stable under the action of: i) a torque control applied on the disk; ii) a force control and moment control or only a force control. Furthermore, the Riesz basis property is proved for the system in the case of uniform angular velocity.

KW - Exponential stability

KW - Force and moment control

KW - Non-homogeneous beam

KW - Riesz basis

KW - Rotating disk-beam-mass

KW - Torque control

UR - http://www.scopus.com/inward/record.url?scp=84922538337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922538337&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.10.040

DO - 10.1016/j.jmaa.2014.10.040

M3 - Article

VL - 423

SP - 1243

EP - 1261

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -