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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

Plotnikov--Toland板模型中水弹性孤立波的迎撞

doi: 10.6052/0459-1879-18-287
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.

     

  • [1] Gardner CS, Greene JM, Kruskal MD, et al.Method for solving the Korteweg-de Vries equation. Physical Review Letters, 1967, 19: 1095-1097
    [2] Kuo YH.On the flow of an incompressible viscous fluid past a flat plate at moderate Reynolds number. Journal of Mathematics and Physics, 1953, 32: 81-101
    [3] Kuo YH.Viscous flow along a flat plate moving at high supersonic speeds. Journal of the Aeronautical Sciences, 1956, 23(1): 125-136
    [4] Tsien HS.The Poincaré--Lighthill--Kuo method. Advances in Applied Mechanics, 1956, 4: 281-349
    [5] Van Dyke M.Perturbation Methods in Fluid Mechanics. Stanford: The Parabolic Press, 1975
    [6] Maxworthy T.Experiments on collisions between solitary waves. Journal of Fluid Mechanics, 1976, 76: 177-186
    [7] Dai SQ.Solitary waves at the interface of a two-layer fluid. Applied Mathematics and Mechanics, 1982, 3(6): 777-788
    [8] Mirie RM, Su CH.Internal solitary waves and their head-on collision. Part 1. Journal of Fluid Mechanics, 1984, 147: 213-231
    [9] Dai HH, Dai SQ, Huo Y.Head-on collision between two solitary waves in a compressible Mooney-Rivlin elastic rod. Wave Motion, 2000, 32(2): 93-111
    [10] Cohen H, Dai HH.Nonlinear axisymmetric waves in compressible hyperelastic rods: long finite amplitude waves. Acta Mechanica, 1993, 100(3-4): 223-239
    [11] Ozden AE, Demiray H.On head-on collision between two solitary waves in shallow water: the use of the extended PLK method. Nonlinear Dynamics, 2015, 82(1-2): 73-84
    [12] Hsieh CM, Hwang RR, Hsu JRC, et al.Numerical modeling of flow evolution for an internal solitary wave propagating over a submerged ridge. Wave Motion, 2015, 55: 48-72
    [13] Agafontsev D, Dias F, Kuznetsov E.Deep-water internal solitary waves near critical density ratio. Physica D : Nonlinear Phenomena, 2007, 225(2): 153-168
    [14] Chen XJ, Wu YS, Cui WC, et al.Review of hydroelasticity theories for global response of marine structures. Ocean Engineering, 2006, 33(3): 439-457
    [15] EatockTaylor R. Hydroelastic analysis of plates and some approximations. Journal of Engineering Mathematics, 2007, 58(1-4): 267-278
    [16] Xia D, Ertekin R, Kim J.Fluid-structure interaction between a two-dimensional mat-type VLFS and solitary waves by the Green-Naghdi theory. Journal of Fluids and Structures, 2008, 24(4): 527-540
    [17] Guyenne P, P$\check{a}$r$\check{a}$u EI. Forced and unforced flexural-gravity solitary waves. Procedia IUTAM, 2014, 11: 44-57
    [18] Blyth MG, P$\check{a}$r$\check{a}$u EI, Vanden-Broeck JM. Hydroelastic waves on fluid sheets. Journal of Fluid Mechanics, 2011, 689: 541-551
    [19] Korobkin A, Khabakhpasheva T.Regular wave impact onto an elastic plate. Journal of Engineering Mathematics, 2006, 55(1-4): 127-150
    [20] Davys J, Hosking R, Sneyd AD.Waves due to a steadily moving source on a floating ice plate. Journal of Fluid Mechanics, 1985, 158: 269-287
    [21] Sahoo T, Yip TL, Chwang AT.Scattering of surface waves by a semi-infinite floating elastic plate. Physics of Fluids, 2001, 13(11): 3215-3222
    [22] P$\check{a}$r$\check{a}$u EI, Vanden-Broeck JM. Three-dimensional waves beneath an ice sheet due to a steadily moving pressure. Philosophical Transactions of the Royal Society A-mathematical Physical and Engineering Sciences, 2011, 369(1947): 2973-2988
    [23] Plotnikov PI, Toland JF.Modelling nonlinear hydroelastic waves. Philosophical Transactions of the Royal Society A-mathematical Physical and Engineering Sciences, 2011, 369(1947): 2942-2956
    [24] Milewski PA, Vanden-Broeck JM, Wang Z.Hydroelastic solitary waves in deep water. Journal of Fluid Mechanics, 2011, 679: 628-640
    [25] Wang P, Lu DQ.Analytic approximation to nonlinear hydroelastic waves traveling in a thin elastic plate floating on a fluid. Science China Physics, Mechanics and Astronomy, 2013, 56(11): 2170-2177
    [26] Bhatti MM, Lu DQ.Head-on collision between two hydroelastic solitary waves in shallow water. Qualitative Theory of Dynamical Systems, 2018, 17(1): 103-122
    [27] Su CH, Mirie RM.On head-on collisions between two solitary waves. Journal of Fluid Mechanics, 1980, 98(3): 509-525
    [28] Guyenne P, P$\check{a}$r$\check{a}$u EI. Finite-depth effects on solitary waves in a floating ice sheet. Journal of Fluids and Structures, 2014, 49: 242-262
    [29] Zhu Y, Dai SQ.On head-on collision between two gKdV solitary waves in a stratified fluid. Acta Mechanica Sinica, 1991, 7(4): 300-308
    [29] 附录A
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出版历程
  • 收稿日期:  2018-07-27
  • 刊出日期:  2018-11-18

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