Transient Response of Circular, Elastic Plates to Point Loads

Abstract

When a dynamic point load is applied laterally to a plate, the deflection gradually spreads over time until the entire plate surface is affected. The determination of early stages of response presents substantial mathematical difficulties. The normal mode superposition is made awkward by the fact that the number of modal components necessary to get a reasonably accurate answer increases as the time of interest becomes smaller. This brief presents a different approach, based on a flexural wave concept, which solves the problem by formulating compact expressions. At the same time, the approach illustrates the basic mechanism of spreading deflections. A shear correction is introduced for the early phase of motion. The quantification is also of some interest in explaining certain aspects of mass impact against a plate.