Closed-loop mode localization for vibration control in flexible structures

The purpose of this paper is to investigate the effect of closed-loop mode localization on the absolute vibration amplitudes in a flexible structure. The techniques used in this paper to produce localized mode shapes permit the calculation of the analytic solution of the controlled system. The advantage to this approach is that, unlike mode shape analysis, the development of the analytic solution permits the investigation of the absolute magnitudes of system vibrations. Displacements in controlled mode-localized structures may therefore be examined and compared to uncontrolled open-loop displacements in the same structure. Further, this paper outlines conditions that insure the containment of vibrational energy, showing through a multi-degree-of-freedom example that it is possible to use mode localization techniques to isolate system vibration.