Vibration of Circular Plates with Edge-Beams

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Abstract
Extensive research in the general area of circular plate vibration has been conducted by numerous researchers, and a compilation of results in the general subject of the vibration of plates has been published by Leissa. The majority of the research has considered the idealized problem in which the plate is characterized by simply supported or clamped boundary conditions. In actuality, plate structures rarely posses simply supported or clamped edges but instead are subjected to conditions somewhat between these two extreme cases. When conditions on the boundary of a plate are changed from those approximating a simple support to a clamped one, small deflections and a more favorable distribution of stress usually result. It is very difficult to actually clamp the edges to take advantage of this fact in design, but a similar stiffening effect can be achieved by providing the plate with an edge-beam, as is shown in this note. By analyzing the coupled problem of the vibrating plate and edge-beam structure simultaneously, an exact solution to the problem is obtained.

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