A virtual design methodology is developed to minimize the noise in enclosures when coupled to optimally designed systems of passive acoustic absorbers (Helmholtz resonators). This methodology utilizes a computationally efficient modeling technique in order to determine the modified response of a system by modal expansion of the unmodified system eigenvectors. A determination of this type (efficient model/reanalysis approach) significantly increases the design possibilities when current optimization techniques are implemented. This novel methodology is experimentally verified for a 30.5 cm by 40.6 cm by 2.5 cm 2D enclosure coupled to two optimally designed Helmholtz resonators. A 4.2 dB experimental reduction of potential energy averaged over the 300—700 Hz band was obtained.