The selection of the design parameters of passive vibration absorbers attached to a long cantilevered beam is studied. This study was motivated by the need for conducting p arametric analysis of dynamics and control for spaceshuttle-attached l ong beams. An optimization scheme using a quadratic cost f unction is introduced yiedding the optimal sizing of the tip vibration absorber. Analytical s olutions for an optimal absorber are presented for the case of one beam vibrational mode coupled with the absorber dynamics, and results are extended to cover the m ultiple mode case. An algorithm is developed to make an initial estimate of optimal tuning parameters which m inimize the quadratic error cost function. Examples are given to illustrate the design concept.
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Jer-Nan Juang (1984) studied this question.