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Plotnikov--Toland板模型中水弹性孤立波的迎撞

巴迪M.M., 卢东强

巴迪M.M., 卢东强. Plotnikov--Toland板模型中水弹性孤立波的迎撞[J]. 力学学报, 2018, 50(6): 1406-1417. DOI: 10.6052/0459-1879-18-287
引用本文: 巴迪M.M., 卢东强. Plotnikov--Toland板模型中水弹性孤立波的迎撞[J]. 力学学报, 2018, 50(6): 1406-1417. DOI: 10.6052/0459-1879-18-287
Bhatti M. M., Lu Dongqiang. HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1406-1417. DOI: 10.6052/0459-1879-18-287
Citation: Bhatti M. M., Lu Dongqiang. HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1406-1417. DOI: 10.6052/0459-1879-18-287
巴迪M.M., 卢东强. Plotnikov--Toland板模型中水弹性孤立波的迎撞[J]. 力学学报, 2018, 50(6): 1406-1417. CSTR: 32045.14.0459-1879-18-287
引用本文: 巴迪M.M., 卢东强. Plotnikov--Toland板模型中水弹性孤立波的迎撞[J]. 力学学报, 2018, 50(6): 1406-1417. CSTR: 32045.14.0459-1879-18-287
Bhatti M. M., Lu Dongqiang. HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1406-1417. CSTR: 32045.14.0459-1879-18-287
Citation: Bhatti M. M., Lu Dongqiang. HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1406-1417. CSTR: 32045.14.0459-1879-18-287

Plotnikov--Toland板模型中水弹性孤立波的迎撞

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;

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

  • 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.
    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.
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  • 期刊类型引用(3)

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    2. 浦俊,卢东强. 三层流体中斜入射波作用下半无限板的水弹性响应. 力学学报. 2019(06): 1614-1629 . 本站查看
    3. M.M.Bhatti,D.Q.Lu. Head-on collision between two hydroelastic solitary waves with Plotnikov-Toland's plate model. Theoretical & Applied Mechanics Letters. 2018(06): 384-392 . 必应学术

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出版历程
  • 收稿日期:  2018-07-26
  • 刊出日期:  2018-11-17

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