Experimental and Numerical Study of the Sloshing Modes of Liquid Storage Tanks with the Virtual Mass Method

Accurate prediction of the vibration characteristics of the sloshing motion is essential for the analysis and design of liquid storage tanks subjected to base motion. The virtual mass method is a computationally efficient approach to determine the hydrodynamic forces generated by incompressible and inviscid fluids in accelerated containers since the virtual mass method involves meshing of the fluid boundaries rather than the entire fluid domain. Hydrodynamic actions of the sloshing liquid are taken into consideration by coupling a virtual fluid mass matrix to the structural points on the wetted regions of the tank wall. Analysis of the free surface displacements of the contained liquid can be carried out using the virtual mass method and this paper focuses on the application of the virtual mass method for the analysis of the vibration frequencies and mode shapes of the sloshing modes in rectangular and cylindrical liquid storage tanks. Firstly, the theoretical background for the analytical solution of the mode shapes and modal frequencies is presented for rectangular and cylindrical liquid tanks. This is followed by the description of the procedure used to apply the virtual mass method to obtain the sloshing modes and mode shapes of the contained liquid. The effects of various surface mesh topologies on the predicted vibration characteristics are compared with the analytical solutions as well as the results of an experimental study conducted on scaled rectangular and cylindrical containers mounted on a shake table.