Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency.

中文翻译：

---

3-D坦克中二阶晃荡共振的分析

基于势能理论和摄动技术，分析了三维水箱中与喘振和摇摆运动相结合的二次晃荡问题。当在两个水平方向上都施加激励时，如果任意两个激励分量的和频率或差频率等于自然频率之一，则可能发生二阶谐振。当激励频率之一和固有频​​率之一的和或差频率等于另一固有频率时，也会发生谐振。