| 滕斌,梁爽,勾莹.二阶挠曲重力波对直墙作用及其奇异解[J].,2020,60(5):530-536 |
| 二阶挠曲重力波对直墙作用及其奇异解 |
| The second order flexural gravity wave loads on vertical wall and singularity in solution |
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| DOI：10.7511/dllgxb202005009 |
| 中文关键词: 二阶 水弹性 挠曲重力波 特征函数展开法 奇异性 |
| 英文关键词: the second order hydroelasticity flexural gravity waves eigenfunction expansion method singularity |
| 基金项目:国家自然科学基金资助项目(51879039). |
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| 中文摘要: |
| 利用特征函数展开法，对有限水深下二阶挠曲重力波在直墙前的反射问题做了求解．计算了直墙上二阶挠曲重力波作用力随入射波浪频率的变化关系．数值结果显示在某一特殊频率下二阶挠曲重力波作用力会趋向无穷．进一步研究表明，在该频率下挠曲重力波的相速度与倍频下的相速度相等，使得挠曲重力波的二阶分量分母为零而出现奇异性．这一奇异解的出现，使得入射波浪存在不确定性，对非线性挠曲重力波与结构物作用问题的求解造成困难．这是一个非常有意义但尚未解决的问题，需进一步探索． |
| 英文摘要: |
| The problem of the second order flexural gravity wave reflection from a vertical wall in the finite water depth is investigated by the eigenfunction expansion method. The variation of the force of the second order flexural gravity wave on a vertical wall with the incident wave frequency is calculated. Numerical results show that the second order flexural gravity wave loads on a vertical wall will approach to infinity at a special frequency. Further studies show that at the special frequency the phase velocity of the flexural gravity waves is equal to that of the waves with the double frequency, and the second order component of the flexural gravity waves is singular with the denominator of it being zero. The existence of this singular solution will induce uncertainty of the incident waves, and limit the application of solutions for nonlinear flexural gravity wave loads on structures. This is a very meaningful but unresolved problem and deserves further exploration. |
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