Nonlinear Hydroelastic Interaction among a Floating Elastic Plate, Water Waves, and Exponential Shear Currents

Author:

Wang Ping1ORCID,Wang Yongyan2ORCID,Huo Xintai1

Affiliation:

1. School of Mathematics and Physics, Qingdao University of Science and Technology, Songling Road, Qingdao 266061, China

2. College of Electromechanical Engineering, Qingdao University of Science and Technology, Songling Road, Qingdao 266061, China

Abstract

Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil-Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current.

Funder

Qingdao Postdoctoral Applied Research Project

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

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