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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.
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Abstract

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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