Non-negative intensity formulations for stochastically excited finite structures

Non-negative intensity (NNI) has been previously proposed for identifying the surface areas of a vibrating structure that most significantly contributes to the sound power. Formulations of finite radiating structures under a deterministic load using the boundary element method and infinite radiating structures excited by a stochastic excitation have been developed in the literature. However, these formulations cannot permit the calculation of the NNI of a finite structure excited by a stochastic excitation, which has engineering applications for structures exposed to flow-induced vibrations or machinery noise, typically represented by a turbulent boundary layer excitation or diffuse acoustic field. To fill this gap, two formulations are proposed: one that is an analytical approach based on the wavenumber space formulation and another that is useful for numerical approaches using the realizations of deterministic wall pressure fields. Numerical results for both baffled and unbaffled finite panels under a turbulent boundary layer excitation are presented and compared against a relevant previous investigation.