谐波平衡法求解俯仰运动矩形贮箱中液体非线性晃动

针对俯仰运动贮箱中液体的晃动用变分原理建立了一类新的Lagrange函数，以此为基础可以解析方式来研究俯仰运动贮箱中液体的非线性晃动．首先将速度势函数Φ在自由液面处作波高函数叩的Taylor级数展开，从而导出自由液面运动学和动力学边界条件非线性方程组；然后用谐波平衡法(HBM)假设其解为各次主导谐波叠加的形式，并代入方程组中得到含有未知系数相应多个代数方程式；最后用Broyden法对代数方程组求解．以无挡板开口二维、刚性矩形贮箱为例，研究了液体的大幅晃动，就液体晃动的幅值而言，在一定激励频率范围内，理论计算值与试验结果吻合较好，同时液面波高出现明显的零点漂移现象．

Nonlinear sloshing of liqued in rectangular container under pitching excitation by harmonic balance method

A new kind of Lagrange function by variational principle of liquid sloshing in pitching tank is build. Based on this, the analytical solution of liquid nonlinear sloshing in pitching tank can be investigated. In the paper, the Taylor series about wave elevation function in the liquid free surface of velocity potential function is derived. After this, the nonlinear equations of free surface kinetic boundary condition and dynamic boundary condition is gained. Then, by supposing the solution in the form of the superposition of each dominated harmonic wave, the corresponding algebraic equations about unknown coefficients by Harmonic Balance Method (HBM) is derived. Last, the algebraic equations are solved by Broyden method. By the example of a two-dimensional, rigid, rectangular, open tank without baffles, the liquid large amplitude sloshing problem is investigated. As for the amplitude of liquid sloshing, comparison between theory and experiment show good agreement at certain frequency range. And at the same time, the phenomenon of zero shift at the liquid surface is found evidently.