On natural frequencies of liquid sloshing in 2-D tanks using Boundary Element Method

The paper investigates natural frequencies and mode shapes of liquid sloshing within two dimensional baffled tanks with arbitrary geometries. Without taking into account viscosity and compressibility, the fluid is considered to be potential. The vibration amplitude is presumed to be little and hence a linear free surface condition is used. The governing equations are solved using Boundary Element Method (BEM), where baffles are treated as two immersed adjacent layers. The resulted problem after discretization is transformed into a standard matrix eigenvalue issue, where only freedoms related to free surface are involved. The BEM approach is verified against analytical theories and existing numerical results. Natural frequencies of sloshing in tanks with a variety of shapes are studied. The effect of horizontal and vertical baffles is thoroughly investigated and empirical formulas are proposed to calculate natural frequencies of rectangular tanks with baffles.