Secondary resonance of liquid sloshing in square-base tanks undergoing the circular orbit motion

The transient wave sloshing in the square-base tank horizontally shaken in a circular orbit is numerically studied. The liquid sloshing is simulated by the boundary element method (BEM) based on the fully-nonlinear potential-flow theory. The tank is firstly excited at the first odd natural sloshing frequency. Resonant swirling waves are observed travelling along the tank sides, when the even sloshing mode is aroused. Then, the tank is excited at half of the first even natural frequency. Techniques of the FFT filter and wavelet analysis are applied to distinct the wave components from the wave elevation histories, through which the occurrence of the secondary resonance is identified. During the secondary resonance, three typical wave motion patterns are observed, i.e. swirling waves, standing waves and double-peak travelling waves. Effects of the excitation amplitude and the liquid depth on the secondary resonance are investigated. Further, the secondary resonance by oscillating the tank at the difference of the first even and first odd natural frequency is studied. The first odd sloshing mode is found to contribute to the dominance of the even mode wave component during the secondary resonance.