TY - JOUR
T1 - Modelling and stabilization of a nonlinear hybrid system of elasticity
AU - Chentouf, Boumediène
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
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
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U2 - 10.1016/j.apm.2014.06.015
DO - 10.1016/j.apm.2014.06.015
M3 - Article
AN - SCOPUS:84922595723
SN - 0307-904X
VL - 39
SP - 621
EP - 629
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 2
ER -