Affiliations: Department of Applied Mechanics, Lublin University of
Technology, Lublin, Poland | Department of Mechanical Engineering, University of
Sheffield, Sheffield, UK
Note: [] Corresponding author: Jerzy Warminski, Department of Applied
Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin,
Poland. Fax: +48 081 538 4205; E-mail: [email protected]
Abstract: An application of the nonlinear saturation control (NSC) algorithm
for a self-excited strongly nonlinear beam structure driven by an external
force is presented in the paper. The mathematical model accounts for an
Euler-Bernoulli beam with nonlinear curvature, reduced to first mode
oscillations. It is assumed that the beam vibrates in the presence of a
harmonic excitation close to the first natural frequency of the beam, and
additionally the beam is self-excited by fluid flow, which is modelled by a
nonlinear Rayleigh term for self-excitation. The self- and externally excited
vibrations have been reduced by the application of an active, saturation-based
controller. The approximate analytical solutions for a full structure have been
found by the multiple time scales method, up to the first-order approximation.
The analytical solutions have been compared with numerical results obtained
from direct integration of the ordinary differential equations of motion.
Finally, the influence of a negative damping term and the controller's
parameters for effective vibrations suppression are presented.
