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.
- nonlinear saturation control (NSC)
- Euler-Bernoulli beam
- vibrations suppression
- negative damping term
Warminski, J., Cartmell, M. P., Mitura, A., & Bochenski, M. (2013). Active vibration control of a nonlinear beam with self- and external excitations. Shock and Vibration, 20(6), 1033-1047. https://doi.org/10.3233/SAV-130821