Liquid free surface sloshing in moving containers can occur in the form of one of three possible regimes: linear planar motion, weakly nonlinear non-planar motion, or strongly nonlinear motion characterized by hydrodynamic impacts. The interaction of the second or third regime with the dynamics of the supporting elastic structure has direct impact on the roll stability and safety of liquid tankers and automotive vehicles carrying gasoline tanks. The main objective of this research project is to develop analytical, numerical, and experimental tools to examine the stability and dynamic characteristic of these systems in order to improve their rollover stability. To accomplish this objective, analytical models are developed which are capable of describing liquid pressure impacts in moving partially filled tankers. The liquid pressure impact model is formulated based on representing the impact forces by a visco-elastic high power nonlinear damper. The resulting equations of motion are analyzed using nonlinear `non-smooth` generating solutions rather than trigonometric functions commonly used for weakly nonlinear systems. For weakly nonlinear regime, a unified approach combining the method of normal form and the theory of Lie groups is used to study the liquid-structure interaction in the presence of internal resonance. The validity of analytical results are verified by numerical simulation and experimental tests. The numerical simulations estimate the system response for both liquid sloshing regimes. The stability and characterization of the response are examined by numerically estimating the Lyapunov exponents and embedding dimensions. The experimental tests provide additional safety study regarding the favorable locations of baffles, to be inserted in liquid containers, which enhances the roll stability of liquid tankers. Another contribution of this research is to develop realistic models describing liquid sloshing impacts which can be used for vehicle dynamic simulation, and also that can be introduced in multibody dynamics codes.
