Passive vibration control of the SCOLE beam system

We investigate the optimization of multiple tuned mass dampers (TMDs) to reduce vibrations of flexible structures described by partial differential equations, using the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) beam system with multiple dominant modes as an illustrative application. We use multiple groups of TMDs with each group being placed at the antinode of the mode shape of a dominant mode of the SCOLE beam. We consider both the harmonic and random excitations, for which we employ frequency-limited H ∞ and H 2 optimizations respectively to determine the parameters of the TMDs. Our optimization scheme takes into account the trade-off between effectiveness and robustness of the multiple TMDs to suppress the multiple dominant modes of the SCOLE beam. Simulation studies show that our scheme achieves substantial improvements over the traditional methods in terms of both effectiveness and robustness and that with equal total mass, TMD systems with each group having multiple TMDs are more effective and more robust than the ones with each group having a single TMD.

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