【摘要】 针对受俯仰激励作用的圆柱形贮箱中液体非线性晃动,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。计算发现,在一定的激励频率内面外主模态和次生模态发生同步Hopf分叉,并给出了发生分叉的频率区域。更多还原

【Abstract】 Under pitching excitation, the Lagrange equation for nonlinear sloshing of liquid in circle cylindrical tank by variational principle in the form of volume integration of pressure is developed. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematical and dynamic free surface boundary conditions are derived. At last, these equations are solved by the fourth order Runge-Kutta method. Through numerical simulation, synchronous Hopf bifurcation of the primary and the secondary nonplanar sloshing modes is observed, and the region of frequency is given.更多还原