考虑液体晃荡的部分充液圆柱壳受迫振动分析

Forced vibration analysis of partially filled cylindrical shell considering liquid sloshing

充液圆柱壳结构广泛存在于在工程中,在外部激励作用下,圆柱壳会与流体产生耦合振动,且未充满的液面也会产生晃荡,这种耦合振动响应分析在工程中具有重要意义。提出了一种求解考虑内部液体小幅晃荡的弹性圆柱壳振动响应的半解析法。首先分别在壳体建立结构坐标系、在自由液面建立液体坐标系,各自用来描述结构及内部液体的运动。基于Flügge壳体理论建立了圆柱壳的运动控制方程。将液体视为无黏、不可压缩的理想流体,根据线性水波理论和液体自由表面运动边界条件,得出了内部液体的速度势函数。通过流固耦合界面的连续性条件,结合坐标变换推导得到流固耦合系统的运动控制方程。研究了壳体在径向点力激励下振动响应,并得出了对应的液面晃荡响应。和有限元法对比验证了方法的正确性,然后改变相关参数讨论了考虑内部液体晃荡的弹性圆柱壳振动响应特性。

Liquid filled cylindrical shell structure widely exists in engineering.Under external excitation,the shell can have vibration coupled with fluid,and under-filled liquid surface can also have sloshing.This coupled vibration response analysis is of important significance in engineering.Here,a semi-analytical method for solving vibration response of elastic cylindrical shell considering small amplitude sloshing of internal liquid was proposed.Firstly,a structural coordinate system on shell was established and a liquid coordinate system on free liquid surface was built to describe motions of structure and internal liquid,respectively.The governing equation of motion for cylindrical shell was established based on Flügge shell theory.Considering liquid as an inviscid and incompressible ideal fluid,the velocity potential function of internal liquid was obtained according to linear water wave theory and boundary conditions of liquid free surface motion.By using continuity conditions of fluid-structure interaction interface and combining coordinate transformation,the governing equation of motion for the fluid-structure interaction system was derived to study shell vibration response under force excitation at radial point,and obtain the corresponding liquid surface sloshing response.The correctness of the proposed method was verified by comparing the results obtained with the proposed method to those with finite element method.Vibration response characteristics of elastic cylindrical shell considering internal liquid sloshing were discussed by changing the relevant parameters.