基于有限元法求解含人工裂纹圆板水中振动频率

提出了一种简便计算镶嵌在无限大障板上的周界固定的含人工裂纹圆板在水中振动频率的计算方法。在假定流体不可压、圆板小振幅振动、水中模态挠度近似为真空模态挠度的条件下,利用瑞利积分得到了因流体压而引起的附加质量密度。进而应用瑞利方法得到了圆板水中振动频率与真空中振动频率、量纲-附加虚质量增量(Nondimensionalized added virtual mass incremental)之间的关系。在真空中模态的有限元法分析数据以及采用适当方法处理奇点积分的基础上,应用离散积分计算了量纲一附加虚质量增量的值。从真空中模态特征频率出发用迭代法直到水中频率收敛为止而得到水中裂纹圆板的特征频率。方法的有效性通过周界固定圆板的量纲-附加虚质量增量与参考文献结果对比的一致性来验证。

ON THE VIBRATION FREQUENCIES OF A CIRCULAR PLATE WITH AN ARTIFICIAL CRACK IN WATER BASED ON FINITE ELEMENT METHOD

A simple computational method for the vibration frequencies of a circular clamped baffled plate with an artificial crack in water is described. Under the conditions that water is incompressible, the plate vibrates in small amplitude and the modal deflection in water equals that in vacuo, the added mass density due to the water pressure is expressed using Rayleigh's integral. Then the relationship among the vibration frequency of the plate in water and that in vacuo and the nondimensionalized added virtual mass incremental(NAVMI) is obtain by utilizing Rayleigh method. Based upon the data of modal analysis for the plate in vacuo by finite element method(FEM) and properly dealing with the integral at singularity, the value of NAVMI is obtained by discretizing the integral. Moreover the vibration frequencies of the plate is computed using iterative method, which begins with the in vacuo eigenfrequency and continues until in-water eigenfrequency converges. The present approach is validated by comparison the NAVMI computed here with the results of M. K. Kwak .