低重环境下俯仰运动圆柱贮箱中液体非线性晃动

在低重力环境下,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数,并将速度势函数在自由液面处作波高函数的级数展开,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;最后用四阶Runge-Kutta法求解非线性方程组。计算结果表明,随俯仰激励频率的逐渐变化,由于面外主模态和次生模态同时失稳,致使整个系统各阶模态和波高函数由稳态运动过渡为不稳定运动。

Low-gravity liquid nonlinear sloshing in a cylindrical tank under pitching excitation

In low gravity,the Lagrange equations of nonlinear liquid sloshing by variational principle in the form of volume integration of pressure are developed.Based on this,the analytical solution of nonlinear liquid sloshing in pitching tank can be investigated.Then the velocity potential function is expanded in series of wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions are derived.At last,these equations are solved by the fourth-order Runge-Kutta method.Through the example of a rigid,cylindrical tank,open tank without baffles,the liquid nonlinear sloshing problem is investigated.The result indicates that the mode of system and wave height function going from stable to unstable by the gradual change of the pitch excitation frequency,because of the primary non-planar sloshing mode and the secondary non-planar sloshing mode losing stable at the same time.