带有边缘径向裂纹的固支圆板湿模态分析

Wet mode analysis of completely clamped circular plate with a side radial crack

基于Rayleigh-Ritz法,分析了置于无限大障板中、单面临水、带有边缘径向裂纹的固支圆板的固有频率和振型。引入角函数对裂纹的影响进行描述,采用薄板假设计算裂纹深度等于板半径的边缘径向裂纹圆板振动的最大动能和最大势能;在无旋、无粘、不可压和板微幅振动的假设条件下,采用速度势描述水体运动并获得了由位移基函数表达的附加动能,并通过Rayleigh-Ritz过程获得流固耦合振动系统的特征矩阵,进而求得湿模态对应的固有频率和振型。结果表明,固有频率降低率整体上随模态阶数的增大而减小,而干、湿模态振型的差别则整体上随模态阶数的增大而增大;水体对对称模态和反对称模态的影响有明显的区别。计算结果与ANSYS数值仿真的结果符合的较好。

In this paper,the free vibration of a completely clamped circular plate with a side crack and in contact with water on one side is investigated based on the Rayleigh-Ritz method.The plate is located at a hole of an infinite baffle and the crack whose depth is equal to the radius of the plate develops along the radial direction.First,the corner functions are introduced to describe the behavior of the cracks,and the Kirchhoff hypothesis is used during the calculation of the maximum strain energy and kinetic energy of the vibrating plate.Second,based on the hypothesis that the plate vibrates in small amplitude and the water is incompressible,inviscid and irrotational,the velocity potential is used to describe the motion of water and the added virtual mass increment expressed by the displacement trial functions is calculated by using Green function method.Then,the characteristics matrix of the vibration system is obtained through Rayleigh-Ritz technique,and the natural frequencies and the corresponding modes are calculated.It is found that the reduction rates of eigenfrequencies due to influence of water decrease with the increasing of mode order but not monotonically,while the differences between dry and wet mode shapes increase with the increasing of mode order on the whole,and the influences of water on the symmetric modes and antisymmetric modes are different.Finally,the results are compared with those gained by numerical simulation and good agreement has been shown.