Nonlinear Vibration of Multi-Surface Liquid in a Lilguid Surface Tank

研究了矩形槽内多面液体运动特性。矩形罐体由隔板分成两部分，与罐体底部垂直，不到达底部。提出了一种近似解析方法来求得多表面液体运动的动力学特性。在晃动运动的响应分析中，考虑了液面振荡的非线性。应用伽辽金方法推导了控制液体表面振荡的非线性常微分方程。首先，将边界元法应用于具有线性化边界条件的拉普拉斯方程，得到其固有频率和相应的模态振型；然后通过求解非线性常微分方程，计算了俯仰激励下罐内液面位移的时程和频率响应。利用模型槽进行了实验。测量了液面位移在俯仰激励下的固有频率和时程。理论结果与实验结果吻合较好。阐明了隔板与罐底之间的距离对固有频率、相应振型和液面位移响应的影响。结果表明，高阶模的增长是可以观察到的，并且可以用非线性模耦合和内部共振来解释，非线性分析对于估计晃动特性是重要的。

The characteristics of multi-surface liquid motion in a rectangular tank are investigated. The rectangular tank is divided into two parts by the partition, which is perpendicular to the bottom of the tank and does not reach the bottom.An approximate analytical method is developed for obtaininng the dynamic behavior of mult-surface liquid motion. Nonlinearity of the liquid surface oscillation is considered in the response analysis of the sloshing motion. The nonlinear ordinary differential equations governing the liquid surface oscillation are derived by applying Galerkin's method.Firstly, the natural frequencies and corresponding mode shapes are obtained by applying boundary element method to the Laplace equation with linearized boundary conditions. Then the time histories and the frequency responses of the liquid surface displacement in the tank stubjected to pitching excitation are calculated by solving the nonlinear ordinary differential equations.An experiment was conducted by using a model tank. The natural frequencies and the time histories of the liquid surface displacement to the pitching excitation are measured. A fairly good agreement was found between the theoretical and experimental results.The effects of the distance between the partition and the tank bottom upon the natural frequencies, corresponding mode shapes and the liquid surface displacement responses are clarified. It is shown that the growth of the higher order mode is observed and can be explained by nonlinear mode coupling and internal resonance and that the nonlinear analysis is important for estimating the sloshing characteristics.