Tutorial on wavenumber transforms of structural vibration fields

While most new vibro-acousticians quickly understand time-frequency Fourier transforms, learning the similar concept of space-wavenumber transforms is more difficult. Two features of spatial Fourier transforms complicate the learning process: spatial transforms are over two dimensions (time is one dimensional) and negative wavenumber terms are important (negative frequencies are ignored in time-frequency transforms). In this tutorial, we try to demystify spatial Fourier transforms using examples of flat rectangular panel vibration fields which include positive and negative two dimensional wavenumber terms. We also demonstrate the well-known wavenumber filtering approach to eliminate subsonic components of a vibration field, thereby revealing the supersonic radiating vibration field. Finally, we show how wavenumber filtering of measured vibration fields may be used to determine structure-borne transmission coefficients between two panels bolted along a common edge.