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Moving loads on ice plates of finite thickness

Published online by Cambridge University Press:  26 April 2006

J. Strathdee ,
W. H. Robinson  and
E. M. Haines
J. Strathdee
Affiliation:
Physics and Engineering Laboratory, DSIR, Lower Hutt, New Zealand
W. H. Robinson
Affiliation:
Physics and Engineering Laboratory, DSIR, Lower Hutt, New Zealand
E. M. Haines
Affiliation:
Physics and Engineering Laboratory, DSIR, Lower Hutt, New Zealand
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Abstract

The response of a floating ice plate to a moving load is given in terms of a pair of Green's functions. General expressions for these Green's functions are derived for the case of an infinite isotropic plate of uniform thickness supported on a fluid base of uniform depth. The distributions of stress and strain in the vicinity of a concentrated load receive significant contributions from waves of length comparable with the plate thickness and their description necessitates an exact description of thickness effects. Circumstances in which the classical thin-plate theory can be recovered are discussed. The steady-state response to a uniformly moving load displays a so-called ‘critical’ behaviour for load velocities in the neighbourhood of a threshold value at which radiation commences. At the critical speed the amplitude is limited by dissipative forces in the ice plate. To describe this a simple viscoelastic term is included in our model. Calculations indicate that thin-plate theory is accurate to within 5% for distances greater than twenty times the ice thickness.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 37 - 61
Copyright
© 1991 Cambridge University Press

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