Near-periodicity in acoustically excited stiffened plates and its influence on vibration, radiation and sound insulation

Due to variabilities in the material, the geometrical configuration, or the manufacturing properties, a structure that is designed to be spatially periodic cannot be exactly periodic. The presence of small irregularities in a nearly periodic structure may influence the propagation of the vibration field, the field being localised. A number of papers have addressed such localisation phenomena. This paper will instead focus on the mean vibration field and its influence on sound radiation and sound insulation in a plate stiffened by supports or beams. The approach is to seek a formal solution with the aid of spatial transform technique (similar to the perfect periodic case) and then apply the expected value operator to the solution. Two assumptions must then be introduced: I) The reaction forces are statistically independent of a phase-term that is due to the irregularity, and II) the mean field is periodic. The approach is presented in general terms, the specific configuration (a stiffened plate) being presented as an example. Numerical results are presented and discussed, and it can be seen that the small irregularities cause an increase in stiffness and damping (when material damping is present).