Regulation of flexible structures via nonlinear coupling

Abstract

In this article, we propose an active/passive vibration controller for a cantilever beam using a sliding mass-spring-dashpot mechanism. The controller is placed at the free end of the beam, introducing Coriolis, inertia, and centripetal nonlinearities into the system, resulting in nonlinear coupling that may be used to quench the transient vibration of the beam. When the natural frequency of the slider is twice the fundamental beam frequency (2:1 internal resonance), the two systems will be coupled through nonlinearities that cause the oscillatory energy to be transferred back and forth between the beam and the slider. Control is achieved once the vibration of the beam is absorbed by the slider and dissipated through the slider damping. Numerical results show that this technique can improve the effective damping ratio of the structure by a factor of 15. This technique is particularly useful for reducing large-amplitude oscillations to levels that may be managed using conventional methods.

Due to the nonlinearities in the system, for small or zero controller damping, chaotic transient oscillations can occur depending on the amplitude of the initial disturbance of the beam.