At present, monopile-supported offshore wind turbines (MOWTs) are widely used in offshore wind farms. The influence of blade flexibility on the dynamic behaviors of MOWTs excited by waves and earthquakes was investigated in this study. Numerical analysis models were established for 5 MW and 10 MW MOWTs, incorporating flexible and rigid blade configurations. The modes and natural frequencies of the full system were compared between these two numerical models, and their dynamic responses were evaluated under wave-only and earthquake-only excitations. It was revealed that the influence of blade flexibility on the first- and second-order modes of the system can be neglected. The dynamic response of these MOWTs under wave excitation can be predicted by the rigid blade model, where the maximum relative difference is less than 5%. However, higher-order modes of the system are significantly affected by the blade flexibility. Under high-frequency excitations, these higher-order modes of the system are remarkably stimulated. Additionally, a large relative difference, exceeding 50%, is detected when the rigid blade model is used to predict the seismic response of the two MOWTs. Consequently, the blade flexibility should be adequately modeled when predicting the dynamic response of OWTs.

This study investigates the dynamic behavior of a jacket-supported offshore wind turbine (JOWT) by developing its substructure and controller tailored for the IEA 15 MW reference wind turbine. A fully coupled numerical model integrating the turbine, jacket, and pile is established to analyze the natural frequencies and dynamic responses of the system under wind–wave–current loading and seismic excitations. Validation studies confirm that the proposed 15 MW JOWT configuration complies with international standards regarding natural frequency constraints, bearing capacity requirements, and serviceability limit state criteria. Notably, the fixed-base assumption leads to overestimations of natural frequencies by 32.4% and 13.9% in the fore-aft third- and fourth-order modes, respectively, highlighting the necessity of soil–structure interaction (SSI) modeling. During both operational and extreme wind–wave conditions, structural responses are governed by first-mode vibrations, with the pile-head axial forces constituting the primary resistance against jacket overturning moments. In contrast, seismic excitations conversely trigger significantly higher-mode activation in the support structure, where SSI effects substantially influence response magnitudes. Comparative analysis demonstrates that neglecting SSI underestimates peak seismic responses under the BCR (Bonds Corner Record of 1979 Imperial Valley Earthquake) ground motion by 29% (nacelle acceleration), 21% (yaw-bearing bending moment), 42% (yaw-bearing shear force), and 17% (tower-base bending moment).

There is a significant interaction between wind and earthquakes for large-scaled wind turbines due to an aeroelastic effect. This study evaluates the accuracy of an uncoupled method extensively utilized to analyze the seismic response of wind turbines at the operational state. Initially, the oscillation of the blade for the National Renewable Energy Laboratory (NREL) 5 MW wind turbine excited by wind and wind-earthquake combination, respectively, is compared using the fully coupled method to verify the assumption in this uncoupled method. Subsequently, the influence of ground motions on the aerodynamic loadings of the rotor is discussed to evaluate the interaction between wind and earthquake loads. In addition, the accuracy of the uncoupled method is assessed by comparing the analysis results of the coupled and uncoupled methods, where different mean wind speed and equivalent aerodynamic damping ratio are considered. The results indicate that the oscillation velocity of blades and thrust on the rotor are significantly influenced by ground motions. Moreover, the amplitude of thrust variations caused by earthquakes increases monotonously with the oscillation velocity amplitude of blade-root. The errors between the two models are beyond the engineering margins for some earthquakes, such that it is difficult to optimize a consistent aerodynamic damping in the uncoupled model to accurately predict the seismic response of wind turbines.

An energy-based method for thermal stresses of various statically indeterminate structures is presented. Using the Lagrange multiplier method, internal forces of statically indeterminate structures are investigated. A new functional from unconditional generalized variational principles is presented. Based on the variational method, a general matrix solution for internal forces and thermal stresses of statically indeterminate structures is established. Several types of structures including the rivet, truss, and bilayer cantilever beam are considered. Compared with the traditional methods, the accuracy and universality of the present model are confirmed. This work provides a convenient and unified method to solve the thermal stresses of various statically indeterminate structures.