浮体运动时域解的奇异性讨论

The Singularity of Time-domain Solution for a floating Body

以推板造波的辐射问题为例，求出了线性时域解的解析表达式，并对线性时域解在造波板与自由面交线处的奇异特性进行了讨论，给出了奇异性的量阶。此奇异性结论对造波机的数值模拟有一定的指导意义。

By taking the radiation problem of a wave-making plate as an example,the analytic ex-pression of the solution for a linear time-domain problem is derived and the singularity of thevelocity potential at the intersecting line of the body surface and free surface is discussed.Itis shown that ,for the linear time-domain solutiori,the singularity of the instantaneous re-sponse part at the intersection is in zlnz and the singularity of the memory response part in-cludes the term z2lnz apart from zlnz. It is worthwhile to note that the singular terms zlnz inthe two parts can cancel each other,so the singular behavior at the intersection is just z2lnz(z is the distance between field points and intersection)。