On the physical meaning of subsonic wavenumber truncation as applied to source identification on vibrating structures

Wavenumber methods have been used to identify the supersonic portions of a vibrating structure that radiate to the farfield. To estimate the supersonic wave energy of a vibrating structure, the discrete Fourier transform can be used to determine the wavenumber spectrum which is then truncated above the acoustic wavenumber. The purely supersonic wavenumber spectrum can now be transformed back into the spatial domain to determine the vibration pattern associated only with the supersonic waves. Often, a cut-off coefficient associated with the acoustic wavenumber of the spatial radiation filter is used to reduce error. Equivalent spatial convolutions have also been formulated to obtain supersonic components of a vibrating pattern. This paper discusses the physical meaning of wavenumber truncation and its accuracy in identifying the surface areas of a vibrating structure that radiate sound. It is shown that truncating subsonic components of the vibration pattern will create non-physical vibration patterns which lie outside of the physical boundaries of the structure. Thus, subsonic wavenumber truncation methods may not be a reliable method for determining the radiated portions of a vibration pattern.