TY - JOUR

T1 - Modelling and stabilization of a nonlinear hybrid system of elasticity

AU - Chentouf, Boumediène

N1 - Funding Information:
The author is grateful to the anonymous referee for the valuable suggestions and comments which have led to an improved version of this paper. Also, the author acknowledges the support of Sultan Qaboos University.
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

VL - 39

SP - 621

EP - 629

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 2

ER -