Effect of seismic frequency on resonant sloshing response: Influence of uneven bottom and Housner model modification

This study examines the sloshing behavior of rectangular water tanks under earthquake excitation using large-scale shaking table tests and OpenFOAM simulations, focusing on resonant effects. The results show that: (1) liquid sloshing exhibits strong frequency dependence, with more pronounced responses under low-frequency seismic excitations, and resonant sloshing occurs when the tank's natural frequency aligns with the dominant seismic excitation frequency, leading to significant wave amplitudes. (2) Resonant amplification is more pronounced at odd-order resonances, particularly at first-order resonance, while the third-order resonance is only 20.4% of that at first order. Higher-order and even-order resonances have negligible amplification effects. (3) The effect of an uneven tank bottom on sloshing behavior is also examined. Experimental results demonstrate that bottom-mounted barriers noticeably dampen the sloshing response, accelerating the decay of sloshing amplitudes from a near-linear to an exponential rate due to the additional vortices formed near the barriers. Furthermore, under resonant conditions, the introduction of the barrier causes the fluid's natural frequency to gradually shift away from the frequency of the applied earthquake, weakening the resonant effects. This ultimately results in the complete dissipation of resonance when the barrier height reaches 18 cm. (4) Hydrodynamic pressure in sloshing tanks is primarily dominated by impulsive motion under high-frequency seismic excitations but transitions to dominance by convective motion under low-frequency excitations, particularly at resonance. The Housner model accurately estimates impulsive-dominated pressures but shows obvious deviations under convective-dominated sloshing. A modified Housner model is proposed, using wave height to estimate the convective pressure, which improves the prediction of hydrodynamic pressures under low-frequency seismic excitations, especially under resonant conditions.