Objectives  This paper studies the transient effects, different frequencies of spectral peaks and meaningful excitation amplitudes on liquid sloshing.

  Methods  A numerical model is established using the computational fluid dynamics (CFD) method, and the reliability of the numerical model is validated through comparison with the analytical solution of linear potential flow and experimental data.

  Results  The transient effects of random excitation have a significant influence on the fluctuation of the free water surface of liquid sloshing in the tank. By applying the buffer function, stable results can be obtained quickly. When the peak frequency of the excitation spectrum is close to the natural frequency of the tank, the energy of the wave-height response spectrum of the liquid sloshing in the tank is mainly concentrated at the natural frequency of the tank. When the peak frequency of the excitation spectrum is far from the natural frequency of the tank, the energy of the wave-height response spectrum is concentrated near the peak frequency. With the increase of the meaningful amplitude of the excitation spectrum, the amplitude deviation of the liquid sloshing response relative to the linear wave (the deviation degree is zero) increases, and the nonlinearity of the tank increases significantly.

  Conclusions  For the random excitation simulation, especially when the excitation frequency is far from the natural frequency, it is necessary to buffer the excitation duration. It is found that when the peak frequency of the excitation spectrum moves away from the first natural frequency to higher frequencies, the energy is dominant at the i-th order of the natural frequency when the peak frequency is close to it.