T frequency response optimization methods for vibrating structures are developed for appending absorbers to the system. The methods are suitable for discrete models with a large number of degrees of freedom and are applied to obtain optimal broadband response. Reanalysis and modal synthesis techniques are used in the structural dynamic analysis phase of the design algorithm and optimization is carried out by a feasible directions approach. These optimal design algorithms have been applied to a 39 degree-of-freedom helicopter model with discrete conventional absorbers and beam absorbers.