A tank might be simultaneously excited by surge, heave, and pitch ground motions during earthquakes. A time-independent finite-difference method is used to intensively study the combined effects of surge, heave, and pitch motions on sloshing viscous fluid in a rigid, rectangular tank. A complete fully nonlinear free-surface condition is used in the analysis. The numerical results are validated by the existing reported results. The evolution of the velocity vectors are described and discussed in detail. The coupled surge and heave and combined surge, heave, and pitch motions would enhance the free-surface stability during the transition period, during which the free surface variation ceases and sloshing begins in the opposite direction. No clear eddies are generated during a surge motion as they are during a heave motion. While the tank is experiencing pitch motion, a clear clockwise eddy occurs during the transition period, when the slope of the surface is negative. However, the eddy is counterclockwise when the slope is positive. A comparison between the surface elevation with combined surge, heave, and pitch motion and that of the superposition of separated excitation is made. The coupling effects are significant, and simultaneous surge and pitch motions should be included during a real earthquake analysis. The dominance of the frequency of excitation, ${\omega }_x$ , on the frequency of the sloshing displacement is presented when ${\omega }_x$ is less than the first fundamental frequency of water in tank, ${\omega }_1$ . The first fundamental frequency dominates the frequency of the sloshing displacement throughout the sloshing when ${\omega }_x$ is greater than ${\omega }_1$ .

This study explores the damping effects of tuned liquid dampers (TLDs) on a monopile offshore wind turbine (OWT). The fluid–solid coupling of ANSYS was used to simulate the damping effect of a TLD on the structures. The environmental conditions refer to the IEC-61400-3 and the Design Load Case (DLC) 1.2 for the annual average environmental conditions and DLC 6.2 for the 50-year regression period, and the extreme environmental conditions were used in the study. The turbulent wind field simulation was performed by TurbSim, and the load of wind waves on structures was generated by FAST, which were all developed by the NREL (National Renewable Energy Laboratory). In addition to wind and waves, the seismic force was also considered. The cylindrical TLD was located above the rotor nacelle assembly (RNA). A TLD has different damping effects when acting under wind, wave, and earthquake loads, respectively. The effect of the TLD regarding motion reduction on the OWT under coupled wind, wave, and seismic loads was studied. This study also designed a simple experiment to verify the correctness of the numerical simulation results. Fatigue analysis shows that multi-layer TLDs can extend the fatigue life (37%) of an OWT. In addition, under extreme environmental load conditions, multi-layer TLDs have a better vibration damping performance than single-layer TLDs. The study demonstrates that multi-layer TLDs can be considered as a vibration reduction damper for OWTs.