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

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  • Ping Wang
  • Yongyan Wang
  • Chuanqi Su
  • Yanzhao Yang

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.

Suggested Citation

  • Ping Wang & Yongyan Wang & Chuanqi Su & Yanzhao Yang, 2017. "Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:2837603
    DOI: 10.1155/2017/2837603
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    References listed on IDEAS

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    1. Shijun Liao, 2012. "Homotopy Analysis Method in Nonlinear Differential Equations," Springer Books, Springer, number 978-3-642-25132-0, March.
    2. Wang, P. & Lu, D.Q., 2016. "Nonlinear hydroelastic waves traveling in a thin elastic plate floating on a two-layer fluid," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 700-710.
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