Active control of sound transmission into an enclosure using structural modal filters

This paper deals with active control of sound transmission through a flexible structure into an enclosed space. The control system consists of sensors and actuators used to measure and control the vibration of a flexible structure for reducing sound transmission. However, since the structural modes mutually contribute to the acoustic potential energy in the enclosure, evaluating the contribution of each structural mode independently is not straightforward. Hence, it is not clear which structural modes should be measured and controlled. In this paper, a formulation for expressing the contribution from each structural mode to the acoustic potential energy via interaction between structural modes is developed. Though the formulation is not a closed form, it enables one to evaluate the contribution of each structural mode independently. Once the highly contributive structural modes are identified, these structural modes can be measured and controlled independently without spillover to other structural modes by using structural modal filters. It is found that the proposed control method can effectively reduce the acoustic potential energy and can avoid an increase in the vibration of the flexible structure. The theory is developed for an arbitrarily-shaped enclosure. A numerical simulation for a rectangular enclosure is also conducted to verify the theory.