Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 2, Pages 103-110

Flexible plate and foundation modelling

R. J. Hosking

Department of Mathematics, Universiti Brunei Darussalam, BRUNEI BE1410, Gadong, China

Copyright © 2000 R. J. Hosking. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the most common mathematical model for a moving load on a continuously- supported flexible plate, the plate is assumed thin and elastic. An exception is the inclusion of viscoelasticity in the theory for the response of a floating ice plate, where the deflexion at the critical load speed corresponding to the minimum phase speed of hybrid flexural-gravity waves consequently approaches a steady state. This is in contrast to the elastic theory, where the response is predicted to grow continuously at this critical load speed. In the theory for a floating ice plate, the dominant pressure due to the underlying water is inertial, introduced via a velocity potential and the Bernoulli equation (assuming non-cavitation at the plate-water interface). On the other hand, the classical Winkler representation used in early railway engineering analysis corresponds to retaining a term which is generally negligible in the ice plate context. Critical load speeds are consequently predicted to be much higher, at wavelengths correspondingly much lower, for commonly accepted railway engineering parameters. Other models might be considered.