Radiation

tim oint nsv ion d. T deduce the associated fields in the physical space. This transform necessitates truncation of the wave-mation 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 e flank d by t hip no nd thro some kilo-Hertz); and (c) the model has to provide the spatial dis-tribution – with phase dependency – of the pressure at hydropho-ne positions in order to study the effects of Sonar treatments like beamforming. In the past, the dynamic response and the sound radiation from periodically stiffened structures have been analyzed by different authors. They developed different methods to predict the behav-[6]. The propagation constant curves were obtained for each cir-cumferential order. By using a modal approach, Laulagnet and Guyader [7] analyzed the characteristic of the sound radiated by a finite ring-stiffened cylindrical shell submerged in a fluid. The difficulty to estimate numerically the modal radiation impedances restricts this method to low frequencies. More recently, Yan et al. [8,9] applied the space-Harmonic approach to predict the sound radiation from a submerged periodic ring-stiffened shell. By using Bloch’s or Floquet’s theorem, the response of the periodic structure to harmonic excitations has been obtained by expanding the re-sponse in terms of a series of space harmonics (see [10] for a ful