箱式超大型浮体在不平底部海域中的水弹性响应

采用作者们(2007)提出的函数展开法描述箱式超大型浮体漂浮在不平底部海域中的水弹性响应问题.将速度势沿静水面位置展开,其系数是水平位置的函数.根据速度势满足拉普拉斯方程就可将这些系数简化到只有两个未知函数.海底条件和平板动力学方程或联合的自由面条件可以分别在Ⅰ区和Ⅱ区建立两个方程用于确定这两个未知函数.不同区域的解要在公共界面上进行匹配.在求解水弹性问题时,展开法必须要截断,从原理上来说,保留的项数越多,其解可以适用于更高阶的kh,其中k是波数,h是水深.作为一个例子,文中给出了只保留一项的结果,而这正好是人们所熟悉的浅水方程.

Mat-type VLFS on a Seaway over an Uneven Bottom

A function expansion method as in Liu et al (2007) is used to formulate the mat-type VLFS floating on the wave surface over uneven sea bottom.The velocity potential is expanded about the still water level with the coefficients being the functions of horizontal coordinates.The satisfaction of Laplace equation of the velocity potential reduces the coefficients to only two unknown functions.The seabed condition and the plate dynamic equation,or the combined free surface condition set up two equations separately in regions I and II to determine these two unknown coefficient functions in the associated regions.The solutions in different regions are matched at the common surface.When solving hydroelasiticy problems,the expansion should be truncated,the more terms are retained in the expansion,the solution can be used for higher kh,in principle,where k is the wave number and h is the water depth.As an example,only one term is kept and the equation used for shallow water case is recovered.