Abstract
Nonlinear responses of surface waves in square and rectangular tanks subjected to horizontal excitation along an oblique direction are investigated. When the direction of excitation is close to the diagonal line of the tank cross section, two sloshing modes (1,0) and (0,1) are directly excited and they also interact with each other due to nonlinear coupled terms. In the theoretical analysis, we derive modal equations of motion for the six sloshing modes with linear damping incorporated. Then, van der Pol's method is employed to determine the frequency response curves. Hopf bifurcations occur and amplitude modulated motions including chaotic vibrations appear depending on the excitation amplitude and frequency. The theoretical results were also observed in experiments.
