Appropriate cost functions for minimizing the radiated sound power of a simply supported baffled plate

In this paper, the sound power of a simply supported baffled point force excited plate is compared to the kinetic energy of the plate. At this point, it is important to make a distinction between the near- and far-field sound radiation. Therefore, the concept of near-field independent radiation modes is presented, obtained as the eigenvectors of the radiation reactance matrix and the reactive sound power is considered as a cost function to minimize the near field radiation of the plate. Following the same approach, the active sound power is defined as the cost function to minimize the far field radiation of the plate and for completeness also the corresponding independent radiation modes are presented. Since plate vibrations result in radiation of sound, the kinetic energy of the plate is the most straightforward choice for the cost function but, in general, minimizing the vibration response does not mean that also the radiation characteristics are optimally reduced. Therefore, the cost functions describing the active and reactive sound power are compared to the kinetic energy. It is well known that the coincidence frequency determines which cost function should be used but maybe less obvious is that the modal density also plays a role. To be more specific, if the plate resonances are well below the coincidence frequency, the kinetic energy of the plate is approximately proportional to the reactive sound power. In contrast, if the plate resonances are near/above the coincidence frequency, the kinetic energy is approximately proportional to the active sound power. In addition, the near field is negligible when compared to the far field in this case. Hence, the kinetic energy can be used as the cost function to minimize both the near and the far field sound radiation.