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Advances in Mathematical Physics
Volume 2017, Article ID 2837603, 9 pages
https://doi.org/10.1155/2017/2837603
Research Article

Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current

1School of Mathematics and Physics, Qingdao University of Science and Technology, Songling Road, Qingdao 266061, China
2College of Electromechanical Engineering, Qingdao University of Science and Technology, Songling Road, Qingdao 266061, China

Correspondence should be addressed to Yongyan Wang; moc.361@861naygnoygnaw

Received 25 March 2017; Accepted 10 July 2017; Published 13 December 2017

Academic Editor: Ming Mei

Copyright © 2017 Ping Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM), consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.