Vibration suppression in a flexible gyroscopic system using modal coupling strategies

Several recent studies have shown that vibrations in a two-degree-of-freedom system can be suppressed by using modal coupling based control techniques. This involves making the first two natural frequencies commensurable ( e.g , in a ratio of 1:1 or 1:2) to establish a state of Internal Resonance (IR). When the system exhibits IR, vibrations in the two directions are strongly coupled resulting in a beat phenomenon. Upon introducing damping in one direction, oscillations in both directions can be quickly suppressed. In this paper we consider vibration suppression of a flexible two-degree-of-freedom gyroscopic system using 1:1 and 1:2 IR. The possibility of using 1:1 and 1:2 IR to enhance the coupling in the system is established analytically using the perturbation method of multiple scales. The results of IR based control strategy are compared with a new method, which is based on tuning the system parameters to make the mode shapes identical. Results indicate that this new technique is more efficient and easy to implement than IR based control strategies. Another advantage of this method is that there is no restriction on the frequencies as in the case of IR. Finally, a control torque is obtained which on application automatically tunes the system parameters to establish modal coupling.