中文摘要：

研究带有环形弹性顶盖的刚性圆柱罐在充满液体时的流-固耦合振动特性。将液体域分割成一个圆柱形子域和一个圆环柱形子域，从而保证在2个子域内的液体速度势函数为c。类连续函数并具有连续的边界条件。利用分离变量法和叠加原理求得各子域内液体速度势的解析解，利用环形顶盖的干模态来展开环形顶盖的湿模态。对液体子域间的界面连接条件和自由表面波条件作级数展开：沿液体深度方向作Fourier展开，沿径向作Bessel展开。截断级数得到环形顶盖与液体耦合振动的特征方程。比较了数值结果与有限元法结果，显示出很好的一致性。

英文摘要：

The coupled vibration characteristics of liquid and the flexural annular cover in a cylindrical rigid tank were studied. The liquid domain was divided into two simple sub-domains so that the liquid velocity potential in each liquid sub-domain was of class C1 with continuous boundary conditions. Based on the superposition principle, the analytical solutions of the liquid velocity potential corresponding to each liquid sub-domain were obtained by separation of variables. The dry-modal functions were used to expand the wet modes to solve the differential equation of coupled vibration of the cover and the liquid. The eigen-frequency equation for the coupled vibration and the boundary conditions was expressed in terms of Fourier series in the liquid height direction and Bessel series in the radial direction. High stability and fast convergence of the proposed method were observed in the convergence study. Excellent agreements were achieved compared with results obtained by the proposed method with the finite element method.