Penetration of flexural waves through a periodically constrained thin
elastic plate floating on water.
D.V. Evans & R. Porter, J. Engng Maths (submitted)
The subject of this paper, the scattering of flexural waves by constrained
elastic plates floating on water is relatively new and not an area that
Professor Newman has worked in, as far as the authors are aware. However,
in two respects there are connections to his own work. The first is
the reference to his work with H. Maniar on the exciting forces on
the elements of a long line of fixed vertical bottommounted cylinders
in waves. In their paper (Maniar & Newman [1]) they pointed out
the remarkable connection between the large forces on cylinders near
the centre of the array at frequencies close to certain trapped mode
frequencies, which had been discovered earlier, and showed that there
was another type of previously unknown trapped mode, which gave rise to
large forces. In section 6 of this paper we return to the ideas described
by Maniar & Newman [1] and show how the phenomenon of large forces
is related to trapped, or standing Rayleigh-Bloch waves, in the present
context of elastic waves. But there is a more general way in which the
paper relates to Professor Newman and that is in the flavour and style
of the mathematics we have employed. Thus we have made extensive use of
classical mathematical methods including integral transform techniques,
complex function theory and the use of special functions in a manner
which we trust reflects that used by Professor Newman in many of his
important papers on ship hydrodynamics and related fields.
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