Low-frequency sound radiation from harmonic vibrating structures such as power transformers poses a serious noise problem to nearby residents. In this paper, a passive method is outlined for attenuating the tonal noise radiation by suppressing the harmonic structural vibration. This method utilises mechanical constraints to break down uniform vibrating shapes into irregular ones and to reduce the total vibration level resulting in an attenuation of sound radiation. Both the theoretical analysis and laboratory experiments have demonstrated the effectiveness of this method in controlling the tonal noise radiation from vibrating structures. For a fixed number of constraints, the efficiency for controlling fluid-borne harmonic vibration and sound radiation is lower than that for a point excited harmonic vibration. (C) 2000 Elsevier Science Ltd. All rights reserved.