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

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

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34 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1033-1047
Number of pages15
JournalShock and Vibration
Issue number6
Publication statusPublished - 2013


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


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