We present a solution for the interaction of normally incident linear waves with a submerged elastic plate of semi-infinite extent, where the water has finite depth. While the problem has been solved previously by the eigenfunction-matching method, the present study shows that this problem is also amenable to the more analytical, and extremely efficient, Wiener–Hopf (WH) and residue calculus (RC) methods. We also show that the WH and RC solutions are actually equivalent for problems of this type, a result which applies to many other problems in linear wave theory. (e.g., the much-studied floating elastic plate scattering problem, or acoustic wave propagation in a duct where one wall has an abrupt change in properties.) We present numerical results and a detailed convergence study, and discuss as well the scattering by a submerged rigid dock, particularly the radiation condition beneath the dock.
Elastic plates Hydroelasticity Linear water waves Residue calculus Wiener–Hopf
This is a preview of subscription content, log in to check access.
Cheong H-F, Shankar NJ, Nallayarasu S (1996) Analysis of submerged platform breakwater by eigenfunction expansion method. Ocean Eng 23(8): 649–666CrossRefGoogle Scholar
Wang K-H, Shen Q (1999) Wave motion over a group of submerged horizontal plates. Int J Eng Sci 37: 703–715CrossRefGoogle Scholar
Williams TD (2005) Reflections on ice: the scattering of flexural-gravity waves by irregularitiies in Arctic and Antarctic ice sheets. Ph.D. thesis, University of Otago, Dunedin, New ZealandGoogle Scholar
Williams TD, Porter R (2009) The effect of submergence on the scattering by the interface between two semi-infinite sheets. J Fluids Struct 25: 777–793CrossRefGoogle Scholar
McIver M, Linton C (2005) Waveguides, Chap. 6. In: Wright MCM (ed) Lecture notes on the mathematics of acoustics. Imperial College Press, London, pp 125–144Google Scholar