Abstract
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 bottom-mounted cylinders in waves. In their paper (J Fluid Mech 339 (1997) 309–329) 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 Sect. 6 of this paper the ideas described by Maniar and Newman are returned to and it is shown 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 that are employed. Thus extensive use has been made of classical mathematical methods including integral-transform techniques, complex-function theory and the use of special functions in a manner which reflects that used by Professor Newman in many of his important papers on ship hydrodynamics and related fields.
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References
Eatock Taylor R (ed) (2003) The third international conference on hydroelasticity in marine technology. Oxford, UK
Maniar HD, Newman JN (1997) Wave diffraction by a long array of cylinders. J Fluid Mech 339:309–329
Callan M, Linton CM, Evans DV (1991) Trapped modes in two-dimensional waveguides. J Fluid Mech 229:51–64
Evans DV, Porter R (1997) Trapped modes about multiple cylinders in a channel. J Fluid Mech 339:331–356
Evans DV, Porter R (1997) Near-trapping of water waves by circular arrays of vertical cylinders. Appl Ocean Res 19:83–89
Ziman JM (1972) Principles of the theory of solids. Cambridge University Press, Cambridge
Evans DV (1981) Power from water waves. Ann Rev Fluid Mech 13:157–187
Evans DV, Meylan MH (2005) Scattering of flexural waves by a pinned thin, elastic sheet floating on water. In: The 20th international workshop on water waves and floating bodies, Longyearbyen, Svalbard.
Norris AN, Vermula C (1995) Scattering of flexural waves on thin plates. J Sound Vib 181(1):115–125
Newman JN (1977) Marine hydrodynamics. M.I.T. Press
Hills NL, Karp SN (1965) Semi-infinite diffraction gratings – I. Comm Pure Appl Maths 18:203–233
Porter R (2002) Trapping of water waves by pairs of submerged cylinders. Proc R Soc London A 458:607–624
Wilcox CH (1984) Scattering theory for diffraction gratings, Applied mathematical sciences, vol 46, Springer
McIver P (2005) Are there trapped modes in the water-wave problem for a freely-floating structure? In: The 20th international workshop on water waves and floating bodies. Longyearbyen, Svalbard
Fox C, Chung H (1998) Green’s function for forcing of a thin floating plate. Number 408, Department of Mathematics Research Reports Series, University of Auckland
Evans DV, Porter R (2003) Wave scattering by narrow cracks in ice sheets floating on water of finite depth. J Fluid Mech 484:143–165
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Evans, D.V., Porter, R. Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water. J Eng Math 58, 317–337 (2007). https://doi.org/10.1007/s10665-006-9128-0
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DOI: https://doi.org/10.1007/s10665-006-9128-0