Nearfield acoustic radiation modes and minimization of sound power in enclosed spaces

Acoustic radiation modes are powerful tools in acoustic studies because they contribute independently to the sound power in an acoustic field. In farfield conditions, they can be obtained by solving an eigenvalue problem relating to the real part of the acoustic power, since only this propagates over longer distances. However, this is not sufficient in nearfield conditions, where the reactive part of the sound power is non-negligible, as for instance in room acoustics for low frequencies. The present contribution aims to examine how Nearfield Acoustic Radiation Modes (NFARMs) behave in enclosed spaces, as opposed to free-field conditions where radiation modes have already been widely investigated. It will be demonstrated that the reactive NFARMs exhibit greater sound radiation efficiency than the active ones. Subsequently, information regarding these NFARMs will be used in an optimal control approach to minimize the sound power radiated by one vibrating surface in a rectangular room. The goal is to minimize performance indexes relating to total sound power and reactive sound power. This will be compared with usual approaches to structural vibration mitigation, such as acceleration and velocity feedback, in terms not only of reducing surface vibration, but also of their effects on sound radiation. The study shows that acceleration and velocity feedback, as well as minimization of total sound power are effective in reducing structural vibration and sound propagation. However, minimizing reactive sound power provides means of directly controlling sound propagation by intervening only with the vibrating surface.