Matrix Wiener-Hopf approximation for a partially clamped plate

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. © The author 2008. Published by Oxford University Press; all rights reserved.