Finite difference approximation to wave equation to simulate sloshing of ground supported tanks for earthquake loadings

Abstract

Sloshing is a liquid vibration physical phenomenon which causes when liquid storage tank is subjected to external loading. Major effects due to sloshing are higher impact pressure on tank walls and over spillage of liquid. Therefore, this study was aimed to investigate the sloshing pressure of ground supported rigid cylindrical tanks under earthquake loading. In this study, wave equation was used to convert the physical phenomenon to a mathematical model and nonlinear terms were approximated. Finite difference method was used to solve the mathematical model for the simulation of sloshing in frequency domain for 2D analysis. Input motions of earthquake loading were obtained from the average Fourier spectrum of seven earthquake records. Here, the liquid was assumed to be inviscid, incompressible and irrotational. Based on the results obtained using the generated finite difference code, the aspect ratio of the tank and frequency of ground motion affects the sloshing pressure.