Sound radiation from a vibrating plate with uncertainty

Sound radiation into open space from a vibrating structure has been investigated since Rayleigh. On the other hand the sound power transferring into neighboring reverberant subsystems has also been rigorously studied using statistical energy analysis, particularly for the high frequency range. Falling between the two well-known problems, pressure and intensity fields from the sound radiation have not yet been widely studied using statistical methods. In this paper, the sound radiation from a vibrating thin plate having uncertain dynamic properties is investigated. Estimates are developed for the reverberant vibration field in the uncertain plate subjected to a point-excitation, and for the ensemble average of pressure from the direct field and from the reverberant field, leading to an estimate of the average sound intensity. The power radiated from the plate and the radiation efficiency is also derived. Monte Carlo simulations are conducted with an ensemble of plates with randomly-distributed point masses, and the simulation results compare well with the estimates.