An accurate and efficient numerical model is developed to calculate the earthquake-induced hydrodynamic pressure on uniform vertical cylinders with an arbitrary cross section surrounded by water. According to the boundary conditions and using the variables separation method, the three-dimensional Laplace equation governing the incompressible water is transformed into a two-dimensional (2D) Helmholtz equation. As a key element, a circular boundary surrounding the structures is introduced so that the computational domain is partitioned into unbounded and bounded domains. The unbounded domain is simulated by an exact artificial boundary condition, which is derived by using the separation variable method. The impedance matrix of the entire domain is obtained by the finite-element method. The hydrodynamic forces on rectangular and round-ended cylinders are calculated, which can be modeled as the product of an added mass of water and the acceleration of the cylinder. However, these complicated expressions of the hydrodynamic forces are not suitable for engineering application. Therefore, simplified formulas for the added mass of the round-ended and rectangular cylinders are obtained by the curve-fitting method. The results indicate that the precision of the present added mass formulas is enough for engineering applications.

The dynamic behaviors of wind turbines subjected to combined wind-earthquake loading were investigated. Numerical simulations were performed to examine the influence of wind speed and earthquake intensity on the dynamic behaviors of wind turbines after evaluating the influence of randomness of wind. Subsequently, the effect of start time and input angle of earthquakes on seismic responses of wind turbines was evaluated to explore the temporal and spatial combinations of wind and earthquake loads. It is noted that the wind increases and decreases the response amplitude of the wind turbine under weak and strong earthquake excitations, respectively. Consequently, the most unfavorable seismic load conditions are represented by the wind–earthquake combination in the former scenario and by only the earthquake case in the latter scenario. Because the start time of earthquakes can significantly affect the dynamic response of the wind turbine, sufficient wind samples must be generated to obtain the mean of the response amplitudes. Moreover, the input angle of earthquakes influences the seismic response of wind turbines, owing to the asymmetry of aerodynamic damping and blade stiffness. Consequently, the combination of wind and earthquake excitations in the space domain must be considered prudently.