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Viscoelastic response of a floating ice plate to a steadily moving load

Published online by Cambridge University Press:  21 April 2006

R. J. Hosking
Affiliation:
Mathematics Department, University of Waikato, Hamilton, New Zealand New address: Department of Mathematics, James Cook University, Townsville Q4811, Australia.
A. D. Sneyd
Affiliation:
Mathematics Department, University of Waikato, Hamilton, New Zealand
D. W. Waugh
Affiliation:
Mathematics Department, University of Waikato, Hamilton, New Zealand

Abstract

Viscoelastic theory is used to describe the response of a floating ice sheet to a moving vehicle. We adopt a two-parameter memory function to describe the behaviour of the ice, subjected to a steadily moving line or point load. The viscoelastic dissipation produces an asymmetric quasi-static response at subcritical speed, renders a finite response at the critical speed, and damps the shorter leading waves rather more severely than the longer trailing waves at supercritical speed. We extend earlier asymptotic theory to consider the anisotropic damping of the flexural waves. There is enhanced agreement between theory and experiment.

Type
Research Article
Copyright
© 1988 Cambridge University Press

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References

Bates, H. F. & Shapiro, L. H. 1981a Plane waves in a viscoelastic floating ice sheet. J. Geophys. Res. 86(C5), 4263–4723.Google Scholar
Bates, H. F. & Shapiro, L. H. 1981b Stress amplification under a moving load on floating ice. J. Geophys. Res. 86(C7), 6638–6642.Google Scholar
Beltaos, S. 1981 Field studies on the response of floating ice sheets to moving loads. Can. J. Civ. Engng 8, 18.Google Scholar
Boltzmann, L. 1874 Zur theorie der elastischen nachwirkung. Sitzber. Akad. Wiss. Wien, Math.-Naturw. 70, 275306.Google Scholar
Coleman, B. D. & Noll, W. 1961 Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239249.Google Scholar
Davys, J. W., Hosking, R. J. & Sneyd, A. D. 1985 Waves due to a steadily moving source on a floating ice plate. J. Fluid Mech. 158, 269287.Google Scholar
Eyre, D. 1977 The flexural motion of a floating ice sheet induced by moving vehicles. J. Glaciol. 19, 555570.Google Scholar
Graffi, D. 1982 Mathematical models and waves in linear viscoelasticity. In Wave Propagation in Viscoelastic Media (ed. F. Mainardi), pp. 1–27. Pitman.
Greenhill, A. G. 1887 Wavemotion in hydrodynamics. Am. J. Maths 9, 62112.Google Scholar
Hosking, R. J. & Sneyd, A. D. 1986 Waves due to vehicles on floating ice sheets. In Proc. Ninth Australasian Fluid Mech. Conf., Auckland, pp. 51–54.
Kerr, A. D. 1981 Continuously supported beams and plates subjected to moving loads – a survey. Solid Mech. Arch. 6, 401449.Google Scholar
Kerr, A. D. 1983 The critical velocities of a load moving on a floating ice plate that is subjected to in-plane forces. Cold Regions Sci. Tech. 6, 267274.Google Scholar
Kheisin, D. Ye. 1963 Moving load on an elastic plate which floats on the surface of an ideal fluid (in Russian). Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk Mekh. Mashinostr. 1, 178180.Google Scholar
Schulkes, R. M. S. M., Hosking, R. J. & Sneyd, A. D. 1987 Waves due to a steadily moving source on a floating ice plate. Part 2. J. Fluid Mech. 180, 297318.Google Scholar
Schulkes, R. M. S. M. & Sneyd, A. D. 1988 Time-dependent response of a floating ice sheet to a steadily moving load. J. Fluid Mech. 186, 2546.Google Scholar
Sneyd, A. D. 1987 Effect of dissipation on waves due to a steadily moving source. University of Waikato Res. Rep. 152.Google Scholar
Squire, V. A. & Allan, A. J. 1980 Propagation of flexural gravity waves in sea ice. In Sea Ice Processes and Models (ed. R. S. Pritchard), pp. 327–338. University of Washington Press, Seattle and London.
Squire, V. A., Langhorne, P. J., Robinson, W. H. & Heine, A. J. 1986 KIWI 131 - an Antarctic field experiment to study strains and acoustic emission generated by loads moving over sea ice. Report for the Royal Society of London.
Squire, V. A., Robinson, W. H., Haskell, T. G. & Moore, S. G. 1985 Dynamic strain response of lake and sea ice to moving loads. Cold Regions Sci. Tech. 11, 123139.Google Scholar
Tabata, T. 1958 Studies on viscoelastic properties of sea ice. In Arctic Sea Ice. US National Academy of Sciences & National Research Council (Washington, DC), publication 598, pp. 139–147.
Takizawa, T. 1985 Deflection of a floating sea ice sheet induced by a moving load. Cold Regions Sci. Tech. 11, 171180.Google Scholar
Takizawa, T. 1986 Response of a floating sea ice sheet to a moving vehicle. In Proc. Fifth International Offshore Mechanics and Arctic Engineering Symposium, Tokyo; vol. 4, pp. 614–621.
Titchmarsh, E. C. 1939 The Theory of Functions. Oxford University Press.
Wilson, J. T. 1958 Moving loads on floating ice sheets. Project 2432. University of Michigan Research Institute.