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 |
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