水介质对多种边界条件方板振动频率及辐射效率的影响

EFFECT OF WATER ON TEH VIBRATION FREQUENCIES AND MODAL RADIATION EFFICIENCIES OF SQUARE PLATE WITH DIFFERENT BOUNDARY CONDITIONS

本文提出了一种简便计算置于无限大障板上的方板水中振动频率以及辐射效率的计算方法。在假定流体不可压、方板作小振幅振动、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方板水中振动频率与真空中振动频率、无量纲附加虚质量增量之间的关系。在真空中模态的有限元方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无量纲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方板的特征频率 ,进而计算了方板的模态辐射效率。方法的有效性通过方板的无量纲附加虚质量增量与文献 [11]结果对比的一致性来验证。

A method of computating the vibration frequencies and modal radiation efficiencies of clamped baffled square plate in water is described. The added mass density due to water pressure is expressed using Rayleigh's integral under the conditions that the water is incompressible, the plate vibrates in small amplitude and the modal deflection in water equal approximately that in vacuo. Then the relationship between the vibration frequency of the plate in water and that in vacuo and the effect of nondimensionalized added virtual mass incremental (NAVMI) are obtained 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 are computed using iterative method, which begins with the in vacuo eigenfrequency and continues until in water eigenfrequency converges. Then the modal radiation efficiencies of the plate are acquired. The present approach is validated by comparison the NAVMI computed here with the results of reference.