The present study addresses the possibility of using resonator-like cavities for noise attenuation of an acoustic enclosure covered by a double-wall structure with shallow gap. Different from the conventional design of using Helmholtz resonators, a set of coupled equation describing resonator-like cavity is integrated into the vibro-acoustic model, under which the modes in a broad frequency range will be controlled. Based on the tuned weighting coefficient and the acoustic potential energy, an objective function is developed to optimize parameters (number and location) of resonator-like cavities. The effect of shallow gap on the first two dominant modes of the coupled system and energy transmission is investigated. Simulation results indicate the effectiveness of the proposed method for noise attenuation, which might be of direct benefit to engineering applications.