A NONLINEAR SIMPLIFIED MODEL OF LIQUID STORAGE TANK AND PRIMARY RESONANCE ANALYSIS

Most simplified models for liquid storage tanks are the spring-mass models. These models are based on linear theory and are only applicable when frequencies of external excitations are sufficiently different from the convective natural frequencies of the storage tank systems. In this study, a nonlinear pendulum model is developed. The nonlinear equations of motion of model are derived using the Lagrange’s method. The first-order approximation solution of the nonlinear vibration is formulated using multiple-scale analysis, from which the stability conditions of system primary resonance are obtained. Numerical analysis of an extra-large liquefied natural gas (LNG) storage tank is carried out using this method. Results show that the primary resonance mode of the tank presents weakly nonlinear behaviour, and the nonlinear response is elevated as the level of the liquid decreases. A peak value of the primary resonance was observed when the level of liquid equals half of the storage tank height. This study shows the model is capable of capturing resonance responses of liquid storage tanks when external excitation frequencies are in the immediate neighbourhood of the convective natural frequencies of the tanks.