Wavenumber space and physical space responses of a periodically ribbed plate to a point drive: A discrete approach

An efficient technique to estimate the vibration of and sound radiation from a stiffened fluid-loaded plate excited by a mechanical point force is presented. The process is based on the formulation in the wavenumber domain of the transversal displacement of the plate and of the acoustic pressure in the fluid domain. Analytical expressions can be easily obtained for these fields in the case of an infinite plate with stiffeners uniformly spaced. The approach consists then on using the discrete Fourier Transform to deduce the associated fields in the physical space. This transform necessitates truncation of the wavenumber domain and sampling of these wavenumber fields with adequate criterions to avoid loss of information and aliasing. These criterions are discussed in this paper concerning displacement point results on the plate and pressure point results in a part of the fluid domain “close to” the plate. This technique requires relatively small computing time and provides an efficient tool to analyse the vibro-acoustic behaviour of the stiffened plate, both, in the physical and the wavenumber spaces. A comparison between a case discussed in the literature and some examples are presented to illustrate the validity and interests of this approach.