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.
Highlights
A floating elastic plate may be an appropriate physical model for a very large floating structure (VLFS) in the ocean or an ice sheet in the polar region due to its huge horizontal dimension compared with its vertical thickness
Wang and Lu (2013) [5] investigated the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate in deep water by the homotopy analysis method (HAM), which is completely independent of any small physical parameter [6]
Using the HAM in a similar way, the two-layer fluid was considered by Wang and Lu (2016) [7] to study the effects of the stratification of the fluid on the nonlinear hydroelastic waves traveling in an infinite elastic plate
Summary
A floating elastic plate may be an appropriate physical model for a very large floating structure (VLFS) in the ocean or an ice sheet in the polar region due to its huge horizontal dimension compared with its vertical thickness. Forbes (1986) [1] studied preliminarily the nonlinear periodic waves beneath an elastic ice sheet in infinite water depths by the perturbation technology. Wang and Lu (2013) [5] investigated the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate in deep water by the homotopy analysis method (HAM), which is completely independent of any small physical parameter [6]. Mohanty et al (2014) [11] studied a combined effect of current and compressive force on time-dependent flexural gravity wave motion in both the cases of single and two-layer fluids and obtained the asymptotic results for Green’s function and the deflection of ice sheet using the method of stationary phase. Convergent analytical series solutions are deduced for the nonlinear hydroelastic response
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