Primary and secondary resonance phenomenon for two-layer liquid sloshing in a rectangular container under horizontal excitation

Laboratory experiments were conducted to study primary and secondary resonant sloshing in a laterally excited rectangular container containing two-layer stratified liquids. The findings revealed that primary resonance of the free surface or the separation surface occurs when the forcing frequency closely matches the corresponding natural frequency. Some intriguing phenomena, such as the sudden wave amplitude increase and the downward shift in resonant peaks, can be observed due to the soft-spring effect. Secondary resonance arises when superharmonic or sub-harmonic frequencies associated with liquid sloshing closely align with the natural frequencies of the system. For the free surface, the secondary resonances of the first five modes occur at forcing frequencies closely related to a third of the first mode, half of the second mode, a third of the third mode, a quarter of the fourth mode, and a fifth of the fifth mode natural frequency of the free surface, respectively. Furthermore, secondary resonance can also manifest under other forcing conditions, such as when the harmonic at a fractional multiple is near the second mode natural frequency of the free surface. Regarding the separation surface, it is worth noting that secondary resonance occurs due to the dominant contribution of fractional harmonics of the forcing frequency. To the best of the authors' knowledge, this is the first systematic investigation of primary and secondary resonance behaviors in a two-layer liquid system.