带有任意边缘裂纹的自由圆板流固耦合动力特性  

Dynamic Analysis of Completely Free Circular Plate with an Arbitrary Side Crack and Fluid-structure Interaction

作　　者：佀晓辉[1] 卢文秀[1] 褚福磊[1] 

机构地区：[1]清华大学精密仪器与机械学系,北京100084

出　　处：《机械工程学报》2012年第9期50-55,共6页Journal of Mechanical Engineering

基　　金：国家杰出青年科学基金(50425516);国家自然科学基金(10702031)资助项目

摘　　要：提出一种基于Rayleigh-Ritz法,分析带有任意深度、任意角度边缘裂纹的自由圆板流固耦合动力特性的方法,其中,圆板被置于无限大障板中并与单面无限大水域相临。采用同时包含对称和反对称模态振型函数的位移基函数表达带有任意边缘裂纹圆板自由振动的位移;在水体无旋、无粘、不可压假设的基础上,根据Green函数法获得水体的附加质量密度,并基于Ritz过程获得裂纹圆板湿模态对应的固有频率和振型。在与ANSYS数值仿真结果进行对比并验证方法的有效性和精度后,分析水体对带有不同深度和不同角度边缘裂纹的自由圆板动力特性的影响。计算结果表明:水体引起的固有频率降低率整体上随模态阶数的增加而减小,而裂纹深度与角度对固有频率降低率的影响较小;裂纹的出现会增大干、湿振型的差别,某些高阶模态的干、湿振型差别较大。A computational method is proposed based on the Rayleigh-Ritz method for the dynamic characteristics of a baffled completely free circular plate with a side crack and in contact with an infinite water domain on one side,in which the crack could be with arbitrary angle and depth.The functions corresponding to symmetric and antisymmtric modes are included in the displacement trial functions to describe the vibration of the circular plate with an arbitrary side crack.Based on the hypothesis that the water is incompressible,inviscid and irrotational,the added mass density of water is calculated by utilizing Green function method,and the natural frequencies and mode shapes for the wet mode of the cracked circular plate are obtained through Ritz procedure.After the validity and the accuracy of the proposed method are proofed basing on the comparison with the results gained by ANSYS,the influences of water on the dynamic characteristics of the completely free circular plates with side cracks are investigated,in which the cracks with various depths and angles are considered.It is found that the reduction ratios of natural frequencies increase with increasing mode order on the whole due to the influence of water,and the influences of crack depth and angle on the reduction ratios are not evident.The appearance of the crack increases the differences between the dry and wet modes,and the differences are evident for some higher modes.

关 键 词：流固耦合 裂纹 自由圆板 动力特性 Rayleigh-Ritz 

分 类 号：O321[理学—一般力学与力学基础] TV312[理学—力学]