Active vibration control of a nonlinear beam with self- and external excitations

J. Warminski, M.P. Cartmell, A. Mitura, M. Bochenski

Research output: Contribution to journalArticle

20 Citations (Scopus)

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.
LanguageEnglish
Pages1033-1047
Number of pages15
JournalShock and Vibration
Volume20
Issue number6
DOIs
Publication statusPublished - 2013

Fingerprint

Vibration control
vibration
saturation
Controllers
Ordinary differential equations
Vibrations (mechanical)
damping
excitation
curvature
Equations of motion
fluid flow
Flow of fluids
Natural frequencies
controllers
Damping
oscillation
Mathematical models
self excitation
timescale
Euler-Bernoulli beams

Keywords

  • nonlinear saturation control (NSC)
  • Euler-Bernoulli beam
  • vibrations suppression
  • negative damping term

Cite this

Warminski, J. ; Cartmell, M.P. ; Mitura, A. ; Bochenski, M. / Active vibration control of a nonlinear beam with self- and external excitations. In: Shock and Vibration. 2013 ; Vol. 20, No. 6. pp. 1033-1047.
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Active vibration control of a nonlinear beam with self- and external excitations. / Warminski, J.; Cartmell, M.P.; Mitura, A.; Bochenski, M.

In: Shock and Vibration, Vol. 20, No. 6, 2013, p. 1033-1047.

Research output: Contribution to journalArticle

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T1 - Active vibration control of a nonlinear beam with self- and external excitations

AU - Warminski, J.

AU - Cartmell, M.P.

AU - Mitura, A.

AU - Bochenski, M.

PY - 2013

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AB - 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.

KW - nonlinear saturation control (NSC)

KW - Euler-Bernoulli beam

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KW - negative damping term

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