Description:
In this paper, a rather unconventional active/passive vibration suppression technique for a cantilever beam based on simple principles in nonlinear vibrations is proposed. The controller is a sliding mass-spring-dashpot mechanism placed at the free end of the beam, introducing Coriolis, inertia, and centripetal nonlinearities into the system. These nonlinear terms may be used to eliminate the transient vibration of the beam when the natural frequency of the slider is twice the fundamental beam frequency (internal resonance). Once at 2:1 internal resonance, the oscillation energy is transferred from the beam to the slider and dissipated for sufficiently high slider damping. Numerical results show that this technique may be used to increase the effective damping ratio of the structure from 0.5% to ∼6%. The controller is particularly successful in reducing large amplitudes of oscillation to levels that may be handled by conventional methods. For lower or zero controller damping, subharmonic and chaotic transient oscillations occur depending on the amplitude of the initial disturbance of the beam. Physical experiments are currenlly underway to verify the numerical and theoretical results.