FINITE ELEMENT ANALYSIS OF LIQUID SLOSHING IN RIGID AND ELASTIC CONTAINERS WITH INTERNAL COMPONENTS AND FLOW INDUCED VIBRATION ABSTRACT Sloshing is a fascinating physical phenomenon characterized by the oscillation of the unrestrained free surface of the liquid in a partially filled container due to external excitation. The phenomenon is of great engineering importance associated with several engineering applications and is a potential source of disturbance in liquid storage containers in general. This is a challenging problem in the field of mechanics and is also mathematically quite difficult. The completely general problem involves the viscosity and compressibility of the liquid, complicated temporal and spatial motion of the liquid free surface, the elasticity of the container walls and the inertias of both. Often, a liquid tank contains submerged components that contribute greatly to the overall dynamical behavior of the system. The surface tension at the free surface may become important in situations where the gravity force is small. The general problem is difficult to treat analytically, or even numerically. In addition, the dynamic boundary condition at the fluid free surface is nonlinear and the position of the free surface varies with time in a manner not known a priori. The complexity increases many folds when the contained structure is flexible resulting in coupled interaction between the container and the contained fluid. In such a situation, neither the fluid domain nor the structural domain can be solved independently of the other due to the unknown interface forces. Such dynamic interaction between a partially filled flexible container and its contained fluid, due to oscillation of the unrestrained fluid free surface, is generally referred as “coupled slosh dynamics”, since the interaction that couples the dynamics of the liquid with that of the contained structure is primarily due to sloshing of the fluid. However, the solution of the completely general problem is not essential in many practical applications and many simplifying assumptions can be made. The effect of fluid viscosity on sloshing is usually very small except for the cases where the container is very small and/or rough.