Active control of the sound radiated by a vibrating body using only a layer of simple sources

Previous research in the area of active noise control has shown that the sound radiation from a vibrating body can be completely controlled using layers of simple and dipole sources located on a surface which completely surrounds the vibrating body. In this paper, the source layer is assumed to consist of simple sources only. If complete control of the sound radiation can be achieved with simple sources only, the implementation of the control strategy will be considerably simplified because simple sources can be approximated with conventional loudspeakers. It is shown that complete control can be achieved when the simple source layer is just outside the boundary surface of the vibrating body (assuming that the fluid coupling between the vibrating body and the surrounding fluid is negligible). When the simple source layer is not near the surface of the vibrating body, the control strategy fails at the resonance frequencies of the volume of fluid between the surface of the vibrating body and the layer of simple sources. It is also shown that in the limit as the source surface approaches the surface of the vibrating body, the control source amplitudes can be written directly in terms of the normal surface velocity of the vibrating body. An example is given to demonstrate the accuracy of the analytical development.