Optimal dynamic vibration absorbers for general beam systems

A technique is developed to give the optimal dynamic vibration absorber parameters for the elimination of excessive vibration in sinusoidally forced Bernoulli-Euler beams. The result is presented in a general form so as to include all possible sets of ordinary boundary conditions and absorber attachment points. This is done by employing a single mode expansion for the beam in an assumed mode approach. The general equations developed are then applied to a point-forced cantilever beam with a viscously damped dynamic absorber attached at the beam midpoint. The optimal values developed for the single mode approximation are then evaluated with account taken of the first five beam modes where discrepancies are noted near the higher order beam resonances which are shifted somewhat due to the absorber.