A rough nearly circular (and/or circular) plate submerged in some ice-covered ocean is undergoing a heaving motion. This radiation problem is reduced to a hypersingular integral equation over the surface of the rough plate. Perturbation method further simplifies the governing equation to get a system of hypersingular integral equations. The geometry of nearly circular plate has been conformally mapped onto a unit disc and the modified equations have been solved by a spectral method proved to be efficient for the case of a circular disc. Both rough disc and rough nearly circular plate have been considered for the numerical results. The effects of the flexural rigidity of ice cover and submergence depth of the plate on added mass and damping coefficient have been investigated along with the effect of roughness of the plate on these hydrodynamic coefficients.

中文翻译：

---

被冰覆盖的海洋中淹没的近圆形粗糙板的波浪辐射

淹没在一些冰覆盖的海洋中的粗糙的近圆形（和/或圆形）板块正在发生起伏运动。这个辐射问题被简化为粗糙板表面上的超奇异积分方程。微扰法进一步简化控制方程，得到超奇异积分方程组。近圆形板的几何形状已被共形地映射到单位圆盘上，并且已通过谱方法求解修改后的方程，该方法被证明对于圆盘的情况是有效的。数值结果考虑了粗糙的圆盘和粗糙的近圆形板。