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Poincar′e–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.
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 Poincal^-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.
作者
巴迪M.M.
卢东强
浦俊(译)
Bhatti M.M.;Lu Dongqiang(Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Universit;Yanchang Road,Shanghai 200072,China）（Shanghai Key Laboratory of Mechanics in Energy Engineering,Yanchang Road,Shanghai 200072,China)
出处
《力学学报》
EI
CSCD
北大核心
2018年第6期1406-1417,共12页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(11472166)
关键词
迎面碰撞
水弹性孤立波
冰层
PLK方法
head-on collision
hydroelastic solitary waves
ice sheet
PLK method
