Analytical solution and simplified formula for earthquake induced hydrodynamic pressure on elliptical hollow cylinders in water

Analytical expressions for calculating the hydrodynamic pressure on an elliptical hollow cylinder caused by outer and inner water under earthquake are obtained. Based on the radiation theory, the analytical solutions of hydrodynamic pressure and hydrodynamic force on elliptical hollow cylinder are accurately derived by assigning reasonable boundary conditions and by solving the Mathieu's differential equation in elliptical coordinate system. Added mass expressions distributed over the height of the cylinder are used to represent the hydrodynamic interaction effects, which are extracted from the hydrodynamic force expressions. These added mass expressions are so complicated that lead to their value difficult to be calculated. Therefore, these added mass expressions are dealt with dimensionless method and are simplified by curve fitting method in this study. The simplified formulas are only relevant to three dimensionless parameters including width-depth ratio, ratio of long to short axis of the ellipse and relative distance above base. The calculation results show that the simplified formulas are in good agreement with the analytical solutions.