On the sampling criterion for structural radiation in fluid

When experimentally investigating the sound radiating from vibrating structures the surface is discretised into elemental areas also referred to as patches in which the surface vibrations are considered uniform. In many cases the structural Nyquist criterion imposes very small patch sizes which turn the experimental analysis into an overwhelmingly elaborate and error-prone task. The possibility to use a coarse sampling scheme for the surface velocity can greatly enhance the practical feasibility of such experimental investigations. Here the special case of a simply supported baffled plate excited by a broadband point force is considered. It is shown that accurate approximations of the radiated power may be obtained well beyond the frequency limit imposed by the structural Nyquist sampling criterion, provided the complex-valued vibration field is averaged over each patch. This is due to the fact that the structural wave components with wavenumbers greater than the acoustic wavenumber tend to be averaged out, owing to the mutual canceling of areas which vibrate out-of-phase within each patch, leaving only those components that contribute significantly to the radiated sound. It turns out, however, that this canceling process is not complete and that an error is introduced by the spatial aliasing. An analytical expression is derived allowing one to quantify this error and to optimise the patch size given a desired accuracy level and frequency range for the assessment of the radiated power. The proposed sampling criterion not only allows one to significantly reduce the measurement efforts when the radiation of vibro-acoustic systems are experimentally investigated but can also be applied to reduce the size of numerical models for weakly coupled structural-acoustic systems.