SYNCHRONOUS HOPF BIFURCATION OF LIQUID NONLINEAR SLOSHING

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.