Abstract
In the present report, two dynamic vibration absorbers attached to a damped two degree-of-freedom system are numerically optimized. The design criteria require the minimization of the maximum transmissibility from the ground motion to the absolute velocity of the first level of the structure. Applying the concept of the optimality criteria method as in the author’s previous reports, the design problem reduces to the solution of simultaneous nonlinear equations. The primal equations are derived using Vieta’s formula with the assumption that the optimal design is realized with four resonance points that have the equal transmissibility. The additional equations are derived as the determinants of Jacobian matrices that represent the optimality of the transmissibility that is included in the simultaneous equations as one of the unknowns. These formulations realize the direct numerical solution via these simultaneous nonlinear equations. Examples are provided that demonstrate the effects of this parametric optimization, in which the distribution of the mass among two DVAs is also optimized.
