Vibration of simply supported rectangular and square plates to which lumped masses and dynamic vibration absorbers are attached

The forced vibration of internally damped rectangular and square plates with simply supported boundaries is described theoretically. Calculations that illustrate the frequency dependence of the force transmissibility and driving−point impedance of the plates are presented. Both central and noncentral driving forces are considered, and the reduction in plate vibration that results from the attachment of central loading masses and dynamic vibration absorbers is demonstrated. The way in which the natural frequencies of the plates are moved to progressively lower frequencies as the loading mass is increased is explained and illustrated. Conditions of optimum tuning and damping for the dynamic absorbers are described and design data are tabulated. The resilient mounting of massive vibrating items on the plates is also considered. The vibrating items are supported via four damped springs that are symmetrically, but otherwise arbitrarily, located with respect to the plate centers. Advantageous reductions in forc...