A new vibration suppression technique is presented based on mode shape coupling for a two-degree-of-freedom flexible gyroscopic system. The system contains a mode which cannot be controlled using conventional methods. The technique presented in this paper involves using a simple PD control strategy to regulate vibrations in one direction. Oscillations in the other direction, which cannot be controlled directly using the actuator, are controlled indirectly by coupling the mode shapes. To effectively regulate the vibrations, the coupling between the two directions is enhanced by tuning the system to establish a commensurable relationship between the modal amplitudes. This results in a strong coupling between the two directions and the energy from the system can be quickly dissipated via the controller. Numerical simulations are used for verification of this method.
When the system parameters are varied, the stability of the response becomes an important issue. Stability is established using Lyapunov's direct method. For autonomous systems the Hamiltonian (H) is a constant of motion. A new method is presented which uses H to obtain global stability properties. One distinct advantage of this method over the existing linear techniques, used for gyroscopic systems, is that global stability properties can be easily established by plotting contours of H, and the effect of variation of the system parameters on stability can also be studied. It is also shown that, using H, zero velocity curves can be obtained which form the bounds for trajectories.