Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T02:28:13.949Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate evaluation of integrals

Published online by Cambridge University Press:  17 February 2009

Roger J. Hosking
Roger J. Hosking
Affiliation:
Department of Mathematics, Universiti Brunei Darussalam, Gadong BE1410, Brunei.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Asymptotic and numerical analysis provides essential insight into the behaviour of Fourier integral solutions for the deflexion of an infinite continuously-supported flexible plate due to moving load. Thus we can define in detail how the plate deflexion depends upon the load speed, including (a) the wave patterns generated by a load moving steadily at various supercritical speeds; and (b) the time-dependent behaviour of the deflexion due to an impulsively-started load, where the two-dimensional response tends to a steady state except at the critical speed, when it grows continuously with time (in the absence of dissipation).

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 110 - 118
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Davys, J. W., Hosking, R. J. and Sneyd, A. D., “Waves due to a steadily moving source on a floating ice plate”, J. Fluid Mech. 159 (1985) 269–287.CrossRefGoogle Scholar
[2]Kheysin, D. Ye., “Moving load on an elastic plate which floats on the surface of an ideal fluid”, Izvestiya Akademii Nauk S.S.S.R., Otd. Tekh. Nauk, Mekhanika i Mashinostroenie 1 (1963) 178–180, (in Russian).Google Scholar
[3]Kheysin, D. Ye., “Some unsteady-state problems in ice-cover dynamics”, in Studies in Ice Physics and Ice Engineering (ed. Yakovlev, G. N.), (Israel Program for Scientific Translations, 1973) 69–78.Google Scholar
[4]Lighthill, J., Waves in Fluids (Cambridge University Press, 1978).Google Scholar
[5]Milinazzo, F., Shinbrot, M. and Evans, N. W., “A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load”, J. Fluid Mech. 287 (1995) 173–197.CrossRefGoogle Scholar
[6]Nevel, D. E., “Moving loads on a floating ice sheet”, CRREL Research Report 261, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, USA, 1970.Google Scholar
[7]Nugroho, W. S., Wang, K., Hosking, R. J. and Milinazzo, F., “Time-dependent response of a floating flexible plate to an impulsively-started steadily moving load”, J. Fluid Mech. 381 (1999) 337–355.CrossRefGoogle Scholar
[8]Schulkes, R. M. S. M. and Sneyd, A. D., “Time-dependent response of a floating ice sheet to a steadily moving load”, J. Fluid Mech. 186 (1988) 25–46.CrossRefGoogle Scholar
[9]Sneyd, A. D. and Hosking, R. J., “Seepage flow through homogeneous soil into a row of drain pipes”, J. Hydrology 30 (1976) 127–146.CrossRefGoogle Scholar
[10]Squire, V. A., Hosking, R. J., Kerr, A. D. and Langhorne, P. J., Moving Loads on Ice Plates (Kluwer Academic Publishers, 1996).CrossRefGoogle Scholar
[11]Wang, K. and Hosking, R. J., “Time-dependent response of a floating flexible plate to an impulsivelystarted steadily moving uniform circular load”, Department of Mathematics and Statistics Preprint 96/7, James Cook University, Queensland, Australia, 1996.Google Scholar