Plotnikov--Toland板模型中水弹性孤立波的迎撞

巴迪M.M.; 卢东强

doi:10.6052/0459-1879-18-287

Plotnikov--Toland板模型中水弹性孤立波的迎撞

doi: 10.6052/0459-1879-18-287

巴迪M.M.,
卢东强^2), ,

上海大学上海市应用数学和力学研究所, 上海 200072
上海市能源工程力学重点实验室, 上海 200072

基金项目: 1) 国家自然科学基金资助项目(11472166).

详细信息

作者简介:
null

2) 卢东强, 研究员, 主要研究方向水波动力学. E-mail: dqlu@shu.edu.cn

通讯作者:
卢东强

中图分类号: TV131.2;
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- 文章访问数: 945
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- 被引次数: 0
出版历程
- 收稿日期: 2018-07-27
- 刊出日期: 2018-11-18

HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL

Bhatti M. M.,
Lu Dongqiang^{2)
, ,}

Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Yanchang Road,Shanghai 200072, China
Shanghai Key Laboratory of Mechanics in Energy Engineering,Yanchang Road, Shanghai 200072, China

摘要

摘要: 通过奇异摄动方法研究了在薄冰层覆盖的不可压缩理想流体表面上传播的两个水弹性孤立波之间的迎面碰撞.借助特殊的 Cosserat 超弹性壳理论以及Kirchhoff--Love 板理论,冰层由 Plotnikov--Toland板模型描述.流体运动采用浅水假设和Boussinesq 近似. 应用Poincaré--Lighthill--Kuo 方法进行坐标变形,进而渐近求解控制方程及边界条件, 给出了三阶解的显式表达. 可以观察到碰撞后的孤立波不会改变它们的形状和振幅. 波浪轮廓在碰撞之前是对称的, 而在碰撞之后变成不对称的并且在波传播方向上向后倾斜. 弹性板和流体表面张力减小了波幅. 图示比较了本文与已有结果可知线性板模型可作为本文的一个特例.
- 迎面碰撞 /
- 水弹性孤立波 /
- 冰层 /
- PLK 方法
Abstract: Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov--Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff--Love plate theory. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations along with the boundary conditions are solved asymptotically with the aid of the Poincaré--Lighthill--Kuo method, and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. The graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.
- head-on collision /
- hydroelastic solitary waves /
- ice sheet /
- PLK method

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参考文献(1)

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