Nonlinear liquid sloshing in square tanks subjected to horizontal random excitation

hing dynamics in a square tank are numerically investigated when the tank is subjected to horizontal, narrowband random ground excitation. The natural frequencies of the two predominant sloshing modes are identical and therefore 1:1 internal resonance may occur. Galerkin’s method is applied to derive the modal equations of motion for nonlinear sloshing including higher modes. The Monte Carlo simulation is used to calculate response statistics such as mean square values and probability density functions (PDFs). The two predominant modes exhibit complex phenomena including “autoparametric interaction” because they are nonlinearly coupled with each other. The mean square responses of these two modes and the liquid elevation are found to differ significantly from those of the corresponding linear model, depending on the characteristics of the random ground excitation such as bandwidth, center frequency and excitation direction. It is found that the direction of the excitation is a significant factor in predicting the mean square responses. The frequency response curves for the same system subjected to equivalent harmonic excitation are also calculated and compared with the mean square responses to further explain the phenomena. Changing the liquid level causes the peak of the mean square response to shift. Furthermore, the risk of the liquid overspill from the tank is discussed by showing the three-dimensional distribution charts of the mean square responses of liquid elevations.