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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]. Copyright 1993, 1999 Academic Press

In this paper, an unconventional technique to control the vibrations of a cantilevered flexible beam, based on a non-linear dynamics phenomenon known as internal resonance, is proposed. The controller consists of a DC motor, itself a part of a simple regulated feedback system, with a rigid beam/tip mass configuration attached to the motor shaft. The addition of the controller to the tip of the flexible beam introduces quadratic, dynamic non-linearities into an otherwise linear system. Under the proper circumstances, these non-linearities can be used to generate a coupling effect between the modes of vibration of the system. An internally resonant state exists if the equations of motion are characterized by frequency-amplitude interactions and the first two natural frequencies of the linear portion of the non-linear equations of motion are commensurable or nearly commensurable. Once a resonance condition is established, a transfer of energy transpires between the modes of vibration. Thus, due to modal coupling, energy is, in effect, transferred from the flexible beam to the secondary beam, where it is dissipated through velocity feedback of the motor. Theoretical analysis predicts that the planar oscillations of a cantilevered beam displaced at its tip a distance equal to 18 percent of its length can be reduced to a relatively small amplitude in approximately four cycles. This controller has proven to be most effective in controlling large amplitude, low frequency oscillations which are typical for large flexible structures. Copyright 1993, 1999 Academic Press