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

Xin Chen, Boumediene Chentouf, Jun Min Wang

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)1243-1261
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume423
Issue number2
DOIs
Publication statusPublished - 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

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