Vibration Control Of A Flexible Beam Using A Rotational Internal Resonance Controller, Part II: Experiment

Abstract

This paper demonstrates the effectiveness of a unique vibration control technique which utilizes a non-linear vibration phenomenon at 2:1 internal resonance to attenuate the vibrations of a cantilever beam. The controller is attached to the tip of the beam and consists of a second link and a DC motor (with position and velocity feedback), introducing quadratic non-linearities to the system. An internally resonant system will exhibit modal interaction, which produces a response having a beat pattern. Therefore, energy can be transferred from a lightly damped mode to a heavily damped mode and then dissipated. The high level of damping is a result of velocity feedback. Internal resonance is attained by adjusting the position feedback gain such that the natural frequencies of the linear portions of the equations of motion of the system are in the ratio of 2:1.Experimental results indicate that planar oscillations of the beam, which is displaced at its tip a distance equal to 22 percent of its length, can be reduced to a relatively small amplitude in approximately three cycles. The experimental results, along with the validation of the mathematical model, are presented in this paper. Details of the theoretical analysis of the controller are discussed in the companion paper, Part I [1].