Nonlinear dynamics of sloshing in tank based on Hamilton principle

Sloshing is a complex nonlinear dynamic phenomenon. It is difficult and challenging to model the coupling between the sloshing and the motion of the tank body. The sloshing has significant influence on the stability of the system. Hence, it is essential and necessary to study the dynamic characteristics of sloshing system. In this study, a wave height function and a potential function are used to describe sloshing phenomenon and the moving boundary conditions between the fluid and the structure. Nonlinear dynamics are established to model the coupled dynamic equations based on Hamilton principle with the assumption of ideal fluid. It is shown that the unity of fluid motion and rigid body motion can be realized by the application of Hamilton principle. The obtained equations are solved via Garlerkin's method to yield approximate numerical solutions. Finally, the theoretical analysis is verified by comparing the numerical solutions with the dynamic response of the FEM software.