Journal of Engineering Mathematics
, Volume 58, Issue 1, pp 317337
First online:
Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water
 D. V. EvansAffiliated withSchool of Mathematics, University of Bristol
 , R. PorterAffiliated withSchool of Mathematics, University of Bristol Email author
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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 (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 trappedmode 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 integraltransform techniques, complexfunction 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.
Keywords
Flexural waves Kirchhoff plate theory Periodic arrays Trapping Title
 Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water
 Journal

Journal of Engineering Mathematics
Volume 58, Issue 14 , pp 317337
 Cover Date
 200708
 DOI
 10.1007/s1066500691280
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Flexural waves
 Kirchhoff plate theory
 Periodic arrays
 Trapping
 Industry Sectors
 Authors

 D. V. Evans ^{(1)}
 R. Porter ^{(1)}
 Author Affiliations

 1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK