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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 10, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2008 61(2):241-265; doi:10.1093/qjmam/hbn004
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Q. Jl Mech. Appl. Math, Vol. 61. No. 2 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Matrix Wiener–Hopf approximation for a partially clamped plate

I. David Abrahams

( School of Mathematics, University of Manchester, Manchester M13 9PL )

Anthony M. J. Davis and Stefan G. Llewellyn Smith{dagger}

( Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA )

{dagger} < sgls{at}ucsd.edu>

Received 17 August 2007. Revise 14 January 2008.
  Abstract

This article examines the classic problem of deflection of a thin elastic plate subjected to static or dynamic normal loading. The plate is infinite in extent in one coordinate direction and finite in the other. On one infinite edge, the plate is clamped, and on the other the plate has mixed boundary conditions, clamped on a semi-infinite part of the edge and free on the remaining half. The boundary-value problem is reduced to a Wiener–Hopf equation, but it is of matrix form belonging to a class for which no exact solution technique is known. An explicit approximate solution, in general accurate to any specified degree, is obtained by a recent method which employs Padé approximants. Numerical results are presented for the plate deflection, and these exhibit convergence to the exact solution as the order of the approximant is increased.


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