ANALYTICAL STUDY OF A SYSTEM WITH A MECHANICAL FILTER

In the authorsʹ earlier work, a concept called a mechanical filter was introduced and investigated for suppressing non-linear, planar crane–load oscillations on floating platforms. To implement this concept, the pivot point about which the load oscillations occur was constrained to follow a circular track. In the current effort, the geometry of the planar mechanical filter is generalized, and the corresponding non-linear dynamical system is derived and presented. On the basis of a Lyapunov function, analytical results are obtained to aid the choice of the filter geometry and the control law. For weak harmonic disturbances, the method of multiple scales is used to study non-linear oscillations of the system with a circular filter. The results of the perturbation analysis demonstrate the occurrence of cyclic-fold bifurcations in the system with the passive filter and suppression of crane–load oscillations in the system with the active filter. The analytical results are found to be in agreement with the associated numerical results. For large magnitude harmonic and aperiodic disturbances, numerical results demonstrate the effectiveness of the active filter in suppressing “large” crane–load oscillations. Tailoring of the response suppression bandwidth by using the active filter is also discussed.