摘要
Under low gravity,the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this,the analytical solution of nonlinear liquid sloshing in pitching tank could be investigated. Then the velocity potential function was expanded in series by wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions were derived. Finally,these nonlinear equations were investigated analytically by the multiple scales method. The result indicates that the system's amplitude-frequency response changes from ‘soft-spring’ to ‘hard-spring’ in the planar motion with the decreasing of the Bond number,while it changes from ‘hard-spring’ to ‘soft-spring’ in the rotary motion.
Under low gravity, the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this, the analytical solution of nonlinear liquid sloshing in pitching tank could be investigated. Then the velocity potential function was expanded in series by wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions were derived. Finally, these nonlinear equations were investigated analytically by the multiple scales method, The result indicates that the system＇s amplitude-frequency response changes from ‘soft- spring＇ to ‘hard-spring＇ in the planar motion with the decreasing of the Bond number, while it changes from ‘ hard-spring＇ to‘ soft-spring＇ in the rotary motion.
基金
the National Defense Foundation of China(Grant No.41320020301).
