Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T21:21:47.786Z Has data issue: false hasContentIssue false
  • English
  • Français

An application in hydrodynamics of the Green's function of an elastic plate

Published online by Cambridge University Press:  26 February 2010

W. R. Dean
W. R. Dean
Affiliation:
University College, London.
Get access

Extract

Some examples of the bending of a plane elastic plate by transverse forces applied at isolated points are first considered. The plate is infinite and is bounded internally by a circular edge along which it is clamped; simple expressions are found for the displacement.

The analogous hydrodynamical problem is that of the steady flow of viscous incompressible liquid past a fixed circular cylinder; the equation for the stream function is in the same form as the equation for the displacement of a plate due to a distributed force of amount Z per unit area. The inertia terms in the hydrodynamical problem correspond to Z. In slow motion there is no stream function with the correct form at infinity, because in this case the inertia terms are ignored so that in the plate problem Z = 0. The effect of a transverse force system can be most simply illustrated by supposing that the forces are concentrated at isolated points; in the corresponding stream functions a simple form of allowance for inertia is therefore made, and they display some of the features of steady flow past a cylinder.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 85 - 92
Copyright
Copyright © University College London 1958

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Dean, W. R., Proc. Cambridge Phil. Soc., 50 (1954), 623–627.Google Scholar
2.Goldstein, S. (ed.) Modern developments in fluid dynamics (Oxford, 1938), 418.Google Scholar
3.Lamb, H., Hydrodynamics (6th ed., Cambridge, 1932), 614–617.Google Scholar
4.Love, A. E. H., Mathematical theory of elasticity (4th ed., Cambridge, 1934), 488–491.Google Scholar
5.Stokes, G. G., Mathematical and physical papers, vol. 3 (Cambridge, 1922), 65.Google Scholar