Acoustic radiation from a rectangular plate reinforced by springs at arbitrary locations

The vibration of a simply supported rectangular plate which is reinforced by a finite number of springs at arbitrary locations is sought as a linear combination of the flexural modes of the corresponding unloaded (or simple) plate. Although these modes cannot be directly used to decouple the dynamic equations of the motion of the reinforced plate, it is still advantageous to use them as a complete set of basis functions to represent the interested quantities such as the deflection of the plate. A linear transformation is established between the two modal spaces spanned by the modes, respectively, for the reinforced and the unloaded plates. The radiation characteristics of the spring-reinforced plate are investigated by using a near field formulation. In order to reduce computational burden, a frequency interpolation technique is employed so that numerical integration now needs to be carried out only at some key frequencies. The specific radiation resistances of the basis modes are first determined as a set of invariants from which the modal radiation efficiency of the reinforced plate can be readily extracted. The effects of cross-modal coupling between the basis modes have been considered, which is necessary for an accurate determination of the modal radiation efficiency for the reinforced plate. A qualitative procedure is also described for locating the "coincidence" frequencies where the modal radiation efficiencies of the reinforced plate tend to reach their peak values. (C) 1999 Academic Press.