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Volume 13, Issue 3
Nonlinear Hydroelastic Waves Traveling in a Plate in Terms of Plotnikov-Toland's Model

Ping Wang & Dongqiang Lu

Adv. Appl. Math. Mech., 13 (2021), pp. 724-734.

Published online: 2020-12

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  • Abstract

Analytical study on nonlinear hydroelastic waves beneath a very large floating structure or a thin ice sheet floating on deep water is presented. Adopting the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis to describe the floating sheet, we use the potential flow theory with the dynamic boundary condition expressing a balance among the hydrodynamic, surface tension, inertial, and elastic forces. For the case of incident progressive waves, the influences of different physical parameters on the hydroelastic waves are discussed with the aid of the homotopy analysis method. We compare the hydroelastic wave deflections based on nonlinear Plotnikov and Toland's model with those obtained by the corresponding linear Euler-Bernoulli model. It is found that the behaviors of both models are almost the same for small amplitudes, while the nonlinear plate deflections increase greatly at large amplitudes. Further, the graphical comparisons are presented to show the behavior of the angular frequency versus wave amplitudes.

  • Keywords

Nonlinear hydroelastic waves, incident progressive waves, special Cosserat theory of hyperelastic shells, homotopy analysis method.

  • AMS Subject Headings

74J30, 76B07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-724, author = {Wang , Ping and Lu , Dongqiang}, title = {Nonlinear Hydroelastic Waves Traveling in a Plate in Terms of Plotnikov-Toland's Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {3}, pages = {724--734}, abstract = {

Analytical study on nonlinear hydroelastic waves beneath a very large floating structure or a thin ice sheet floating on deep water is presented. Adopting the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis to describe the floating sheet, we use the potential flow theory with the dynamic boundary condition expressing a balance among the hydrodynamic, surface tension, inertial, and elastic forces. For the case of incident progressive waves, the influences of different physical parameters on the hydroelastic waves are discussed with the aid of the homotopy analysis method. We compare the hydroelastic wave deflections based on nonlinear Plotnikov and Toland's model with those obtained by the corresponding linear Euler-Bernoulli model. It is found that the behaviors of both models are almost the same for small amplitudes, while the nonlinear plate deflections increase greatly at large amplitudes. Further, the graphical comparisons are presented to show the behavior of the angular frequency versus wave amplitudes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0307}, url = {http://global-sci.org/intro/article_detail/aamm/18504.html} }
TY - JOUR T1 - Nonlinear Hydroelastic Waves Traveling in a Plate in Terms of Plotnikov-Toland's Model AU - Wang , Ping AU - Lu , Dongqiang JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 724 EP - 734 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0307 UR - https://global-sci.org/intro/article_detail/aamm/18504.html KW - Nonlinear hydroelastic waves, incident progressive waves, special Cosserat theory of hyperelastic shells, homotopy analysis method. AB -

Analytical study on nonlinear hydroelastic waves beneath a very large floating structure or a thin ice sheet floating on deep water is presented. Adopting the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis to describe the floating sheet, we use the potential flow theory with the dynamic boundary condition expressing a balance among the hydrodynamic, surface tension, inertial, and elastic forces. For the case of incident progressive waves, the influences of different physical parameters on the hydroelastic waves are discussed with the aid of the homotopy analysis method. We compare the hydroelastic wave deflections based on nonlinear Plotnikov and Toland's model with those obtained by the corresponding linear Euler-Bernoulli model. It is found that the behaviors of both models are almost the same for small amplitudes, while the nonlinear plate deflections increase greatly at large amplitudes. Further, the graphical comparisons are presented to show the behavior of the angular frequency versus wave amplitudes.

Ping Wang & Dongqiang Lu. (1970). Nonlinear Hydroelastic Waves Traveling in a Plate in Terms of Plotnikov-Toland's Model. Advances in Applied Mathematics and Mechanics. 13 (3). 724-734. doi:10.4208/aamm.OA-2019-0307
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