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Technical Briefs

Transient Response of Circular, Elastic Plates to Point Loads

[+] Author and Article Information
Gregory Szuladziński

 Analytical Service Pty. Ltd., Killara/Sydney 2071, Australiaggg@bigpond.net.au

At the time of this writing this fact does not appear to be widely known.

For nondispersive waves, like the one spreading along an axial bar, calculating displacements as if they were caused by a static load applied to a deformed portion of the structural member gives exact results. (It can be better visualized using a shear beam concept, as presented by Szuladzinski (7).) For dispersive cases, like here, acting in the same manner is merely an approximation.

J. Comput. Nonlinear Dynam 4(3), 034502 (May 20, 2009) (4 pages) doi:10.1115/1.3124782 History: Received August 21, 2007; Revised October 21, 2008; Published May 20, 2009

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.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

End-loaded axial bar

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Figure 2

Flex waves resulting from application of a step load: (a) edge loading and (b) center loaded, infinite-radius plate

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Figure 3

The same deflected patterns as in Fig. 2 applied to finite-radius plates: (a) annular plate with edge loading and (b) clamped plate loaded at center

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Figure 4

Edge-loaded plate, deflection study (u is from FEA simulation)

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Figure 5

Center-loaded plate, deflection study (u is from FEA simulation)

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