A new tunable vibration absorber, Delayed Resonator (DR), is considered on a flexible beam. The point of absorber attachment (PAA) on the beam is shown to be quieted (i.e., an artificial node is introduced at this point). This is achieved if the excitation forcing is simple harmonic. The DR absorber is tuned to this frequency and this tuning can track a relatively fast varying excitation frequency. There is, however, a short-fall of DR absorber: as they eliminate the vibration completely at the tuning frequency they introduce some vulnerable side frequencies. This scenario suggests a trade-off: less perfection in suppressing the tuning frequency, with reduced vulnerability at the side frequencies. In order to resolve this trade-off an optimization procedure is suggested which forms the main contribution of this text. The dynamics of the beam, exciter, and absorber setting is studied in modal coordinates. This constrained optimization problem is solved utilizing direct update method, one of the constraints being the stability assurance of the proposed active system. Example simulations are presented to show the benefits of this trade-off.
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